Daily Papers

The Empirical Interpolation Method (EIM) is a greedy procedure that constructs approximate representations of two-variable functions in separated form. In its classical presentation, the two variables play a non-symmetric role. In this work, we give an equivalent definition of the EIM approximation, in which the two variables play symmetric roles. Then, we give a proof for the existence of this approximation, and extend it up to the convergence of the EIM, and for any norm chosen to compute the error in the greedy step. Finally, we introduce a way to compute a separated representation in the case where the number of selected values is different for each variable. In the case of a physical field measured by sensors, this is useful to discard a broken sensor while keeping the information provided by the associated selected field.

Existing interpolation methods use pre-trained video diffusion priors to generate intermediate frames between sparsely sampled keyframes. In the absence of 3D geometric guidance, these methods struggle to produce plausible results for complex, articulated human motions and offer limited control over the synthesized dynamics. In this paper, we introduce PoseFuse3D Keyframe Interpolator (PoseFuse3D-KI), a novel framework that integrates 3D human guidance signals into the diffusion process for Controllable Human-centric Keyframe Interpolation (CHKI). To provide rich spatial and structural cues for interpolation, our PoseFuse3D, a 3D-informed control model, features a novel SMPL-X encoder that transforms 3D geometry and shape into the 2D latent conditioning space, alongside a fusion network that integrates these 3D cues with 2D pose embeddings. For evaluation, we build CHKI-Video, a new dataset annotated with both 2D poses and 3D SMPL-X parameters. We show that PoseFuse3D-KI consistently outperforms state-of-the-art baselines on CHKI-Video, achieving a 9% improvement in PSNR and a 38% reduction in LPIPS. Comprehensive ablations demonstrate that our PoseFuse3D model improves interpolation fidelity.

Image interpolation based on diffusion models is promising in creating fresh and interesting images. Advanced interpolation methods mainly focus on spherical linear interpolation, where images are encoded into the noise space and then interpolated for denoising to images. However, existing methods face challenges in effectively interpolating natural images (not generated by diffusion models), thereby restricting their practical applicability. Our experimental investigations reveal that these challenges stem from the invalidity of the encoding noise, which may no longer obey the expected noise distribution, e.g., a normal distribution. To address these challenges, we propose a novel approach to correct noise for image interpolation, NoiseDiffusion. Specifically, NoiseDiffusion approaches the invalid noise to the expected distribution by introducing subtle Gaussian noise and introduces a constraint to suppress noise with extreme values. In this context, promoting noise validity contributes to mitigating image artifacts, but the constraint and introduced exogenous noise typically lead to a reduction in signal-to-noise ratio, i.e., loss of original image information. Hence, NoiseDiffusion performs interpolation within the noisy image space and injects raw images into these noisy counterparts to address the challenge of information loss. Consequently, NoiseDiffusion enables us to interpolate natural images without causing artifacts or information loss, thus achieving the best interpolation results.

Temporal interpolation often plays a crucial role to learn meaningful representations in dynamic scenes. In this paper, we propose a novel method to train spatiotemporal neural radiance fields of dynamic scenes based on temporal interpolation of feature vectors. Two feature interpolation methods are suggested depending on underlying representations, neural networks or grids. In the neural representation, we extract features from space-time inputs via multiple neural network modules and interpolate them based on time frames. The proposed multi-level feature interpolation network effectively captures features of both short-term and long-term time ranges. In the grid representation, space-time features are learned via four-dimensional hash grids, which remarkably reduces training time. The grid representation shows more than 100 times faster training speed than the previous neural-net-based methods while maintaining the rendering quality. Concatenating static and dynamic features and adding a simple smoothness term further improve the performance of our proposed models. Despite the simplicity of the model architectures, our method achieved state-of-the-art performance both in rendering quality for the neural representation and in training speed for the grid representation.

The Reduced Basis Method can be exploited in an efficient way only if the so-called affine dependence assumption on the operator and right-hand side of the considered problem with respect to the parameters is satisfied. When it is not, the Empirical Interpolation Method is usually used to recover this assumption approximately. In both cases, the Reduced Basis Method requires to access and modify the assembly routines of the corresponding computational code, leading to an intrusive procedure. In this work, we derive variants of the EIM algorithm and explain how they can be used to turn the Reduced Basis Method into a nonintrusive procedure. We present examples of aeroacoustic problems solved by integral equations and show how our algorithms can benefit from the linear algebra tools available in the considered code.

We consider a family of linear systems A_mu alpha=C with system matrix A_mu depending on a parameter mu and for simplicity parameter-independent right-hand side C. These linear systems typically result from the finite-dimensional approximation of a parameter-dependent boundary-value problem. We derive a procedure based on the Empirical Interpolation Method to obtain a separated representation of the system matrix in the form A_muapproxsum_{m}beta_m(mu)A_{mu_m} for some selected values of the parameter. Such a separated representation is in particular useful in the Reduced Basis Method. The procedure is called nonintrusive since it only requires to access the matrices A_{mu_m}. As such, it offers a crucial advantage over existing approaches that instead derive separated representations requiring to enter the code at the level of assembly. Numerical examples illustrate the performance of our new procedure on a simple one-dimensional boundary-value problem and on three-dimensional acoustic scattering problems solved by a boundary element method.

Adapting a pre-trained foundation model on downstream tasks should ensure robustness against distribution shifts without the need to retrain the whole model. Although existing weight interpolation methods are simple yet effective, we argue their static nature limits downstream performance while achieving efficiency. In this work, we propose DaWin, a training-free dynamic weight interpolation method that leverages the entropy of individual models over each unlabeled test sample to assess model expertise, and compute per-sample interpolation coefficients dynamically. Unlike previous works that typically rely on additional training to learn such coefficients, our approach requires no training. Then, we propose a mixture modeling approach that greatly reduces inference overhead raised by dynamic interpolation. We validate DaWin on the large-scale visual recognition benchmarks, spanning 14 tasks across robust fine-tuning -- ImageNet and derived five distribution shift benchmarks -- and multi-task learning with eight classification tasks. Results demonstrate that DaWin achieves significant performance gain in considered settings, with minimal computational overhead. We further discuss DaWin's analytic behavior to explain its empirical success.

Video frame interpolation (VFI) is a challenging task that aims to generate intermediate frames between two consecutive frames in a video. Existing learning-based VFI methods have achieved great success, but they still suffer from limited generalization ability due to the limited motion distribution of training datasets. In this paper, we propose a novel optimization-based VFI method that can adapt to unseen motions at test time. Our method is based on a cycle-consistency adaptation strategy that leverages the motion characteristics among video frames. We also introduce a lightweight adapter that can be inserted into the motion estimation module of existing pre-trained VFI models to improve the efficiency of adaptation. Extensive experiments on various benchmarks demonstrate that our method can boost the performance of two-frame VFI models, outperforming the existing state-of-the-art methods, even those that use extra input.

The rapid and accurate direct multi-frame interpolation method for Digital Subtraction Angiography (DSA) images is crucial for reducing radiation and providing real-time assistance to physicians for precise diagnostics and treatment. DSA images contain complex vascular structures and various motions. Applying natural scene Video Frame Interpolation (VFI) methods results in motion artifacts, structural dissipation, and blurriness. Recently, MoSt-DSA has specifically addressed these issues for the first time and achieved SOTA results. However, MoSt-DSA's focus on real-time performance leads to insufficient suppression of high-frequency noise and incomplete filtering of low-frequency noise in the generated images. To address these issues within the same computational time scale, we propose GaraMoSt. Specifically, we optimize the network pipeline with a parallel design and propose a module named MG-MSFE. MG-MSFE extracts frame-relative motion and structural features at various granularities in a fully convolutional parallel manner and supports independent, flexible adjustment of context-aware granularity at different scales, thus enhancing computational efficiency and accuracy. Extensive experiments demonstrate that GaraMoSt achieves the SOTA performance in accuracy, robustness, visual effects, and noise suppression, comprehensively surpassing MoSt-DSA and other natural scene VFI methods. The code and models are available at https://github.com/ZyoungXu/GaraMoSt.

We derive a Fast Multipole Method (FMM) where a low-rank approximation of the kernel is obtained using the Empirical Interpolation Method (EIM). Contrary to classical interpolation-based FMM, where the interpolation points and basis are fixed beforehand, the EIM is a nonlinear approximation method which constructs interpolation points and basis which are adapted to the kernel under consideration. The basis functions are obtained using evaluations of the kernel itself. We restrict ourselves to translation-invariant kernels, for which a modified version of the EIM approximation can be used in a multilevel FMM context; we call the obtained algorithm Empirical Interpolation Fast Multipole Method (EIFMM). An important feature of the EIFMM is a built-in error estimation of the interpolation error made by the low-rank approximation of the far-field behavior of the kernel: the algorithm selects the optimal number of interpolation points required to ensure a given accuracy for the result, leading to important gains for inhomogeneous kernels.

Inter-frame modeling is pivotal in generating intermediate frames for video frame interpolation (VFI). Current approaches predominantly rely on convolution or attention-based models, which often either lack sufficient receptive fields or entail significant computational overheads. Recently, Selective State Space Models (S6) have emerged, tailored specifically for long sequence modeling, offering both linear complexity and data-dependent modeling capabilities. In this paper, we propose VFIMamba, a novel frame interpolation method for efficient and dynamic inter-frame modeling by harnessing the S6 model. Our approach introduces the Mixed-SSM Block (MSB), which initially rearranges tokens from adjacent frames in an interleaved fashion and subsequently applies multi-directional S6 modeling. This design facilitates the efficient transmission of information across frames while upholding linear complexity. Furthermore, we introduce a novel curriculum learning strategy that progressively cultivates proficiency in modeling inter-frame dynamics across varying motion magnitudes, fully unleashing the potential of the S6 model. Experimental findings showcase that our method attains state-of-the-art performance across diverse benchmarks, particularly excelling in high-resolution scenarios. In particular, on the X-TEST dataset, VFIMamba demonstrates a noteworthy improvement of 0.80 dB for 4K frames and 0.96 dB for 2K frames.

The reduced basis method is a model reduction technique yielding substantial savings of computational time when a solution to a parametrized equation has to be computed for many values of the parameter. Certification of the approximation is possible by means of an a posteriori error bound. Under appropriate assumptions, this error bound is computed with an algorithm of complexity independent of the size of the full problem. In practice, the evaluation of the error bound can become very sensitive to round-off errors. We propose herein an explanation of this fact. A first remedy has been proposed in [F. Casenave, Accurate a posteriori error evaluation in the reduced basis method. C. R. Math. Acad. Sci. Paris 350 (2012) 539--542.]. Herein, we improve this remedy by proposing a new approximation of the error bound using the Empirical Interpolation Method (EIM). This method achieves higher levels of accuracy and requires potentially less precomputations than the usual formula. A version of the EIM stabilized with respect to round-off errors is also derived. The method is illustrated on a simple one-dimensional diffusion problem and a three-dimensional acoustic scattering problem solved by a boundary element method.

Video generation has made remarkable progress in recent years, especially since the advent of the video diffusion models. Many video generation models can produce plausible synthetic videos, e.g., Stable Video Diffusion (SVD). However, most video models can only generate low frame rate videos due to the limited GPU memory as well as the difficulty of modeling a large set of frames. The training videos are always uniformly sampled at a specified interval for temporal compression. Previous methods promote the frame rate by either training a video interpolation model in pixel space as a postprocessing stage or training an interpolation model in latent space for a specific base video model. In this paper, we propose a training-free video interpolation method for generative video diffusion models, which is generalizable to different models in a plug-and-play manner. We investigate the non-linearity in the feature space of video diffusion models and transform a video model into a self-cascaded video diffusion model with incorporating the designed hidden state correction modules. The self-cascaded architecture and the correction module are proposed to retain the temporal consistency between key frames and the interpolated frames. Extensive evaluations are preformed on multiple popular video models to demonstrate the effectiveness of the propose method, especially that our training-free method is even comparable to trained interpolation models supported by huge compute resources and large-scale datasets.

The rapid progress of Transformers in artificial intelligence has come at the cost of increased resource consumption and greenhouse gas emissions due to growing model sizes. Prior work suggests using pretrained small models to improve training efficiency, but this approach may not be suitable for new model structures. On the other hand, training from scratch can be slow, and progressively stacking layers often fails to achieve significant acceleration. To address these challenges, we propose a novel method called Apollo, which prepares lessons for expanding operations by learning high-layer functionality during training of low layers. Our approach involves low-value-prioritized sampling (LVPS) to train different depths and weight sharing to facilitate efficient expansion. We also introduce an interpolation method for stable model depth extension. Experiments demonstrate that Apollo achieves state-of-the-art acceleration ratios, even rivaling methods using pretrained models, making it a universal and efficient solution for training deep models while reducing time, financial, and environmental costs.

We consider in this work quantities that can be obtained as limits of powers of parametrized matrices, for instance the inverse matrix or the logarithm of the determinant. Under the assumption of affine dependence in the parameters, we use the Empirical Interpolation Method (EIM) to derive an approximation for powers of these matrices, from which we derive a nonintrusive approximation for the aforementioned limits. We derive upper bounds of the error made by the obtained formula. Finally, numerical comparisons with classical intrusive and nonintrusive approximation techniques are provided: in the considered test-cases, our algorithm performs well compared to the nonintrusive ones.

We aim to address a significant but understudied problem in the anime industry, namely the inbetweening of cartoon line drawings. Inbetweening involves generating intermediate frames between two black-and-white line drawings and is a time-consuming and expensive process that can benefit from automation. However, existing frame interpolation methods that rely on matching and warping whole raster images are unsuitable for line inbetweening and often produce blurring artifacts that damage the intricate line structures. To preserve the precision and detail of the line drawings, we propose a new approach, AnimeInbet, which geometrizes raster line drawings into graphs of endpoints and reframes the inbetweening task as a graph fusion problem with vertex repositioning. Our method can effectively capture the sparsity and unique structure of line drawings while preserving the details during inbetweening. This is made possible via our novel modules, i.e., vertex geometric embedding, a vertex correspondence Transformer, an effective mechanism for vertex repositioning and a visibility predictor. To train our method, we introduce MixamoLine240, a new dataset of line drawings with ground truth vectorization and matching labels. Our experiments demonstrate that AnimeInbet synthesizes high-quality, clean, and complete intermediate line drawings, outperforming existing methods quantitatively and qualitatively, especially in cases with large motions. Data and code are available at https://github.com/lisiyao21/AnimeInbet.

Large Language Models (LLMs) have been well-researched in various long-context tasks. However, the scarcity of high-quality long-context summarization datasets has hindered further advancements in this area. To address this, we introduce CNNSum, a multi-scale long-context summarization benchmark based on Chinese novels, featuring human-driven annotations, which comprises four subsets totaling 695 samples, with lengths ranging from 16k to 128k. We evaluate numerous LLMs and conduct detailed case analyses. Furthermore, we conduct extensive fine-tuning experiments to explore and improve long-context summarization. In our study: (1) Advanced LLMs like GPT-4o may still generate subjective commentary, leading to vague summaries. (2) Currently, long-context summarization mainly relies on memory ability afforded by longer context lengths. The advantages of Large LLMs are hard to utilize, thus small LLMs are the most cost-effective. (3) Different prompt templates paired with various version models may cause large performance gaps. In further fine-tuning, these can be mitigated, and the Base version models perform better. (4) LLMs with RoPE-base scaled exhibit strong extrapolation potential; using short-context data can significantly improve long-context summarization performance. However, further applying other interpolation methods requires careful selection. (5) CNNSum provides more reliable and insightful evaluation results than other benchmarks. We release CNNSum to advance future research in this field. https://github.com/CxsGhost/CNNSum

This thesis presents and evaluates the Dilated Convolution with Learnable Spacings (DCLS) method. Through various supervised learning experiments in the fields of computer vision, audio, and speech processing, the DCLS method proves to outperform both standard and advanced convolution techniques. The research is organized into several steps, starting with an analysis of the literature and existing convolution techniques that preceded the development of the DCLS method. We were particularly interested in the methods that are closely related to our own and that remain essential to capture the nuances and uniqueness of our approach. The cornerstone of our study is the introduction and application of the DCLS method to convolutional neural networks (CNNs), as well as to hybrid architectures that rely on both convolutional and visual attention approaches. DCLS is shown to be particularly effective in tasks such as classification, semantic segmentation, and object detection. Initially using bilinear interpolation, the study also explores other interpolation methods, finding that Gaussian interpolation slightly improves performance. The DCLS method is further applied to spiking neural networks (SNNs) to enable synaptic delay learning within a neural network that could eventually be transferred to so-called neuromorphic chips. The results show that the DCLS method stands out as a new state-of-the-art technique in SNN audio classification for certain benchmark tasks in this field. These tasks involve datasets with a high temporal component. In addition, we show that DCLS can significantly improve the accuracy of artificial neural networks for the multi-label audio classification task. We conclude with a discussion of the chosen experimental setup, its limitations, the limitations of our method, and our results.

Video depth estimation has long been hindered by the scarcity of consistent and scalable ground truth data, leading to inconsistent and unreliable results. In this paper, we introduce Depth Any Video, a model that tackles the challenge through two key innovations. First, we develop a scalable synthetic data pipeline, capturing real-time video depth data from diverse synthetic environments, yielding 40,000 video clips of 5-second duration, each with precise depth annotations. Second, we leverage the powerful priors of generative video diffusion models to handle real-world videos effectively, integrating advanced techniques such as rotary position encoding and flow matching to further enhance flexibility and efficiency. Unlike previous models, which are limited to fixed-length video sequences, our approach introduces a novel mixed-duration training strategy that handles videos of varying lengths and performs robustly across different frame rates-even on single frames. At inference, we propose a depth interpolation method that enables our model to infer high-resolution video depth across sequences of up to 150 frames. Our model outperforms all previous generative depth models in terms of spatial accuracy and temporal consistency.

Recently, diffusion-based methods have achieved great improvements in the video inpainting task. However, these methods still face many challenges, such as maintaining temporal consistency and the time-consuming issue. This paper proposes an advanced video inpainting framework using optical Flow-guided Efficient Diffusion, called FloED. Specifically, FloED employs a dual-branch architecture, where a flow branch first restores corrupted flow and a multi-scale flow adapter provides motion guidance to the main inpainting branch. Additionally, a training-free latent interpolation method is proposed to accelerate the multi-step denoising process using flow warping. Further introducing a flow attention cache mechanism, FLoED efficiently reduces the computational cost brought by incorporating optical flow. Comprehensive experiments in both background restoration and object removal tasks demonstrate that FloED outperforms state-of-the-art methods from the perspective of both performance and efficiency.

In this paper, we introduce a novel unsupervised network to denoise microscopy videos featured by image sequences captured by a fixed location microscopy camera. Specifically, we propose a DeepTemporal Interpolation method, leveraging a temporal signal filter integrated into the bottom CNN layers, to restore microscopy videos corrupted by unknown noise types. Our unsupervised denoising architecture is distinguished by its ability to adapt to multiple noise conditions without the need for pre-existing noise distribution knowledge, addressing a significant challenge in real-world medical applications. Furthermore, we evaluate our denoising framework using both real microscopy recordings and simulated data, validating our outperforming video denoising performance across a broad spectrum of noise scenarios. Extensive experiments demonstrate that our unsupervised model consistently outperforms state-of-the-art supervised and unsupervised video denoising techniques, proving especially effective for microscopy videos.

Advancements in Large Language Models (LLMs) inspire various strategies for integrating video modalities. A key approach is Video-LLMs, which incorporate an optimizable interface linking sophisticated video encoders to LLMs. However, due to computation and data limitations, these Video-LLMs are typically pre-trained to process only short videos, limiting their broader application for understanding longer video content. Additionally, fine-tuning Video-LLMs to handle longer videos is cost-prohibitive. Consequently, it becomes essential to explore the interpolation of Video-LLMs under a completely training-free setting. In this paper, we first identify the primary challenges in interpolating Video-LLMs: (1) the video encoder and modality alignment projector are fixed, preventing the integration of additional frames into Video-LLMs, and (2) the LLM backbone is limited in its content length capabilities, which complicates the processing of an increased number of video tokens. To address these challenges, we propose a specific INTerPolation method for Video-LLMs (INTP-Video-LLMs). We introduce an alternative video token rearrangement technique that circumvents limitations imposed by the fixed video encoder and alignment projector. Furthermore, we introduce a training-free LLM context window extension method to enable Video-LLMs to understand a correspondingly increased number of visual tokens.

As the rapid progression of practical applications based on Large Language Models continues, the importance of extrapolating performance has grown exponentially in the research domain. In our study, we identified an anomalous behavior in Transformer models that had been previously overlooked, leading to a chaos around closest tokens which carried the most important information. We've coined this discovery the "headache of Transformers". To address this at its core, we introduced a novel self-attention structure named Collinear Constrained Attention (CoCA). This structure can be seamlessly integrated with existing extrapolation, interpolation methods, and other optimization strategies designed for traditional Transformer models. We have achieved excellent extrapolating performance even for 16 times to 24 times of sequence lengths during inference without any fine-tuning on our model. We have also enhanced CoCA's computational and spatial efficiency to ensure its practicality. We plan to open-source CoCA shortly. In the meantime, we've made our code available in the appendix for reappearing experiments.

Reconstructing dynamic assets from video data is central to many in computer vision and graphics tasks. Existing 4D reconstruction approaches are limited by category-specific models or slow optimization-based methods. Inspired by the recent Large Reconstruction Model (LRM), we present the Large Interpolation Model (LIM), a transformer-based feed-forward solution, guided by a novel causal consistency loss, for interpolating implicit 3D representations across time. Given implicit 3D representations at times t_0 and t_1, LIM produces a deformed shape at any continuous time tin[t_0,t_1], delivering high-quality interpolated frames in seconds. Furthermore, LIM allows explicit mesh tracking across time, producing a consistently uv-textured mesh sequence ready for integration into existing production pipelines. We also use LIM, in conjunction with a diffusion-based multiview generator, to produce dynamic 4D reconstructions from monocular videos. We evaluate LIM on various dynamic datasets, benchmarking against image-space interpolation methods (e.g., FiLM) and direct triplane linear interpolation, and demonstrate clear advantages. In summary, LIM is the first feed-forward model capable of high-speed tracked 4D asset reconstruction across diverse categories.

The research assesses soil salinity in the southwest coastal region of Bangladesh, collecting a total of 162 topsoil samples between March 1 and March 9, 2024, and processing them following the standard operating procedure for soil electrical conductivity (soil/water, 1:5). Electrical conductivity (EC) measurements obtained using a HI-6321 advanced conductivity benchtop meter were analyzed and visualized using bubble density mapping and the Empirical Bayesian Kriging interpolation method. The findings indicate that soil salinity in the study area ranges from 0.05 to 9.09 mS/cm, with the highest levels observed near Debhata and Koyra. A gradient of increasing soil salinity is clearly evident from the northern to southern regions. This dataset provides a critical resource for soil salinity-related research in the region, offering valuable insights to support decision-makers in understanding and mitigating the impacts of soil salinity in Bangladesh's coastal areas.

Existing video frame interpolation (VFI) methods blindly predict where each object is at a specific timestep t ("time indexing"), which struggles to predict precise object movements. Given two images of a baseball, there are infinitely many possible trajectories: accelerating or decelerating, straight or curved. This often results in blurry frames as the method averages out these possibilities. Instead of forcing the network to learn this complicated time-to-location mapping implicitly together with predicting the frames, we provide the network with an explicit hint on how far the object has traveled between start and end frames, a novel approach termed "distance indexing". This method offers a clearer learning goal for models, reducing the uncertainty tied to object speeds. We further observed that, even with this extra guidance, objects can still be blurry especially when they are equally far from both input frames (i.e., halfway in-between), due to the directional ambiguity in long-range motion. To solve this, we propose an iterative reference-based estimation strategy that breaks down a long-range prediction into several short-range steps. When integrating our plug-and-play strategies into state-of-the-art learning-based models, they exhibit markedly sharper outputs and superior perceptual quality in arbitrary time interpolations, using a uniform distance indexing map in the same format as time indexing. Additionally, distance indexing can be specified pixel-wise, which enables temporal manipulation of each object independently, offering a novel tool for video editing tasks like re-timing.

Artificial intelligence has become a crucial tool for medical image analysis. As an advanced cerebral angiography technique, Digital Subtraction Angiography (DSA) poses a challenge where the radiation dose to humans is proportional to the image count. By reducing images and using AI interpolation instead, the radiation can be cut significantly. However, DSA images present more complex motion and structural features than natural scenes, making interpolation more challenging. We propose MoSt-DSA, the first work that uses deep learning for DSA frame interpolation. Unlike natural scene Video Frame Interpolation (VFI) methods that extract unclear or coarse-grained features, we devise a general module that models motion and structural context interactions between frames in an efficient full convolution manner by adjusting optimal context range and transforming contexts into linear functions. Benefiting from this, MoSt-DSA is also the first method that directly achieves any number of interpolations at any time steps with just one forward pass during both training and testing. We conduct extensive comparisons with 7 representative VFI models for interpolating 1 to 3 frames, MoSt-DSA demonstrates robust results across 470 DSA image sequences (each typically 152 images), with average SSIM over 0.93, average PSNR over 38 (standard deviations of less than 0.030 and 3.6, respectively), comprehensively achieving state-of-the-art performance in accuracy, speed, visual effect, and memory usage. Our code is available at https://github.com/ZyoungXu/MoSt-DSA.

Data Augmentation (DA), \ie, synthesizing faithful and diverse samples to expand the original training set, is a prevalent and effective strategy to improve various visual recognition tasks. With the powerful image generation ability, diffusion-based DA has shown strong performance gains on different benchmarks. In this paper, we analyze today's diffusion-based DA methods, and argue that they cannot take account of both faithfulness and diversity, which are two critical keys for generating high-quality samples and boosting final classification performance. To this end, we propose a novel Diffusion-based Inversion Interpolation DA method: Diff-II. Specifically, Diff-II consists of three main steps: 1) Category concepts learning: Learning concept embeddings for each category. 2) Inversion interpolation: Calculating the inversion for each image, and conducting spherical interpolation for two randomly sampled inversions from the same category. 3) Two-stage denoising: Using different prompts to generate synthesized images in a coarse-to-fine manner. Extensive experiments on multiple image classification tasks (\eg, few-shot, long-tailed, and out-of-distribution classification) have demonstrated its effectiveness over state-of-the-art diffusion-based DA methods.

Knowledge distillation is one of the primary methods of transferring knowledge from large to small models. However, it requires massive task-specific data, which may not be plausible in many real-world applications. Data augmentation methods such as representation interpolation, token replacement, or augmentation with models are applied to tackle this problem. However, these data augmentation methods either potentially cause shifts in decision boundaries (representation interpolation), are not expressive enough (token replacement), or introduce too much computational overhead (augmentation with models). To this end, we propose AugPro (Augmentation with Projection), an effective and efficient data augmentation method for distillation. Our method builds on top of representation interpolation augmentation methods to maintain the diversity of expressions and converts the augmented data to tokens to avoid shifting decision boundaries. It uses simple operations that come with little computational overhead. The results on multiple GLUE tasks show that our methods can improve distillation performance by a large margin at a low time cost. Codes are available at https://github.com/google-research/google-research/tree/master/augpro.

Effectively training language models on long inputs poses many technical challenges. As a cost consideration, languages models are pretrained on a fixed sequence length before being adapted to longer sequences. We explore various methods for adapting models to longer inputs by training on segmented sequences and an interpolation-based method for extending absolute positional embeddings. We develop a training procedure to extend the input context size of pretrained models with no architectural changes and no additional memory costs than training on the original input lengths. By sub-sampling segments from long inputs while maintaining their original position the model is able to learn new positional interactions. Our method benefits both models trained with absolute positional embeddings, by extending their input contexts, as well as popular relative positional embedding methods showing a reduced perplexity on sequences longer than they were trained on. We demonstrate our method can extend input contexts by a factor of 4x while improving perplexity.

Deep model merging represents an emerging research direction that combines multiple fine-tuned models to harness their specialized capabilities across different tasks and domains. Current model merging techniques focus on merging all available models simultaneously, with weight interpolation-based methods being the predominant approaches. However, these conventional approaches are not well-suited for scenarios where models become available sequentially, and they often suffer from high memory requirements and potential interference between tasks. In this study, we propose a training-free projection-based continual merging method that processes models sequentially through orthogonal projections of weight matrices and adaptive scaling mechanisms. Our method operates by projecting new parameter updates onto subspaces orthogonal to existing merged parameter updates while using an adaptive scaling mechanism to maintain stable parameter distances, enabling efficient sequential integration of task-specific knowledge. Our approach maintains constant memory complexity to the number of models, minimizes interference between tasks through orthogonal projections, and retains the performance of previously merged models through adaptive task vector scaling. Extensive experiments on CLIP-ViT models demonstrate that our method achieves a 5-8% average accuracy improvement while maintaining robust performance in different task orderings.

Diffusion-based manifold learning methods have proven useful in representation learning and dimensionality reduction of modern high dimensional, high throughput, noisy datasets. Such datasets are especially present in fields like biology and physics. While it is thought that these methods preserve underlying manifold structure of data by learning a proxy for geodesic distances, no specific theoretical links have been established. Here, we establish such a link via results in Riemannian geometry explicitly connecting heat diffusion to manifold distances. In this process, we also formulate a more general heat kernel based manifold embedding method that we call heat geodesic embeddings. This novel perspective makes clearer the choices available in manifold learning and denoising. Results show that our method outperforms existing state of the art in preserving ground truth manifold distances, and preserving cluster structure in toy datasets. We also showcase our method on single cell RNA-sequencing datasets with both continuum and cluster structure, where our method enables interpolation of withheld timepoints of data. Finally, we show that parameters of our more general method can be configured to give results similar to PHATE (a state-of-the-art diffusion based manifold learning method) as well as SNE (an attraction/repulsion neighborhood based method that forms the basis of t-SNE).

Existing research has shown that large language models (LLMs) exhibit remarkable performance in language understanding and generation. However, when LLMs are continuously fine-tuned on complex and diverse domain-specific downstream tasks, the inference performance on historical tasks decreases dramatically, which is known as a catastrophic forgetting problem. A trade-off needs to be kept between learning plasticity and memory stability. Plenty of existing works have explored strategies like memory replay, regularization and parameter isolation, but little is known about the geometric connection of various adjacent minima in the continual LLMs fine-tuning scenarios. In this work, we investigate the geometric connections of different minima through the lens of mode connectivity, which means different minima can be connected by a low-loss valley. Through extensive experiments, we uncover the mode connectivity phenomenon in the LLMs continual learning scenario and find that it can strike a balance between plasticity and stability. Building upon these findings, we propose a simple yet effective method called Interpolation-based LoRA (I-LoRA), which constructs a dual-memory experience replay framework based on LoRA parameter interpolations. Extensive experiments and analysis on eight domain-specific CL benchmarks demonstrate that I-LoRA consistently show significant improvement over the previous state-of-the-art approaches with up to 11% performance gains, providing a strong baseline and insights for future research on the large language model continual learning problem. Our code is available at https://github.com/which47/LLMCL.

Adversarial robustness has become a central goal in deep learning, both in the theory and the practice. However, successful methods to improve the adversarial robustness (such as adversarial training) greatly hurt generalization performance on the unperturbed data. This could have a major impact on how the adversarial robustness affects real world systems (i.e. many may opt to forego robustness if it can improve accuracy on the unperturbed data). We propose Interpolated Adversarial Training, which employs recently proposed interpolation based training methods in the framework of adversarial training. On CIFAR-10, adversarial training increases the standard test error (when there is no adversary) from 4.43% to 12.32%, whereas with our Interpolated adversarial training we retain the adversarial robustness while achieving a standard test error of only 6.45%. With our technique, the relative increase in the standard error for the robust model is reduced from 178.1% to just 45.5%. Moreover, we provide mathematical analysis of Interpolated Adversarial Training to confirm its efficiencies and demonstrate its advantages in terms of robustness and generalization.

The remarkable performance of the pre-trained language model (LM) using self-supervised learning has led to a major paradigm shift in the study of natural language processing. In line with these changes, leveraging the performance of speech recognition systems with massive deep learning-based LMs is a major topic of speech recognition research. Among the various methods of applying LMs to speech recognition systems, in this paper, we focus on a cross-modal knowledge distillation method that transfers knowledge between two types of deep neural networks with different modalities. We propose an acoustic model structure with multiple auxiliary output layers for cross-modal distillation and demonstrate that the proposed method effectively compensates for the shortcomings of the existing label-interpolation-based distillation method. In addition, we extend the proposed method to a hierarchical distillation method using LMs trained in different units (senones, monophones, and subwords) and reveal the effectiveness of the hierarchical distillation method through an ablation study.

Large Language Models (LLMs) demand significant computational resources, making it essential to enhance their capabilities without retraining from scratch. A key challenge in this domain is catastrophic forgetting (CF), which hampers performance during Continuous Pre-training (CPT) and Continuous Supervised Fine-Tuning (CSFT). We propose Control LLM, a novel approach that leverages parallel pre-trained and expanded transformer blocks, aligning their hidden-states through interpolation strategies This method effectively preserves performance on existing tasks while seamlessly integrating new knowledge. Extensive experiments demonstrate the effectiveness of Control LLM in both CPT and CSFT. On Llama3.1-8B-Instruct, it achieves significant improvements in mathematical reasoning (+14.4% on Math-Hard) and coding performance (+10% on MBPP-PLUS). On Llama3.1-8B, it enhances multilingual capabilities (+10.6% on C-Eval, +6.8% on CMMLU, and +30.2% on CMMLU-0shot-CoT). It surpasses existing methods and achieves SOTA among open-source models tuned from the same base model, using substantially less data and compute. Crucially, these gains are realized while preserving strong original capabilities, with minimal degradation (<4.3% on MMLU) compared to >35% in open-source Math and Coding models. This approach has been successfully deployed in LinkedIn's GenAI-powered job seeker and Ads unit products. To support further research, we release the training and evaluation code (https://github.com/linkedin/ControlLLM) along with models trained on public datasets ( https://huggingface.co/ControlLLM) to the community.

We present a new way to merge any two point distribution approaches using distance fields. Our new process allows us to produce digital stippling that fills areas with stipple dots without visual artifacts as well as includes clear linear features without fussiness. Our merging thus benefits from past work that can optimize for either goal individually, yet typically by sacrificing the other. The new possibility of combining any two distributions using different distance field functions and their parameters also allows us to produce a vast range of stippling styles, which we demonstrate as well.

Recent progress in large-scale text-to-video (T2V) and image-to-video (I2V) diffusion models has greatly enhanced video generation, especially in terms of keyframe interpolation. However, current image-to-video diffusion models, while powerful in generating videos from a single conditioning frame, need adaptation for two-frame (start & end) conditioned generation, which is essential for effective bounded interpolation. Unfortunately, existing approaches that fuse temporally forward and backward paths in parallel often suffer from off-manifold issues, leading to artifacts or requiring multiple iterative re-noising steps. In this work, we introduce a novel, bidirectional sampling strategy to address these off-manifold issues without requiring extensive re-noising or fine-tuning. Our method employs sequential sampling along both forward and backward paths, conditioned on the start and end frames, respectively, ensuring more coherent and on-manifold generation of intermediate frames. Additionally, we incorporate advanced guidance techniques, CFG++ and DDS, to further enhance the interpolation process. By integrating these, our method achieves state-of-the-art performance, efficiently generating high-quality, smooth videos between keyframes. On a single 3090 GPU, our method can interpolate 25 frames at 1024 x 576 resolution in just 195 seconds, establishing it as a leading solution for keyframe interpolation.

Conditional diffusion models can create unseen images in various settings, aiding image interpolation. Interpolation in latent spaces is well-studied, but interpolation with specific conditions like text or poses is less understood. Simple approaches, such as linear interpolation in the space of conditions, often result in images that lack consistency, smoothness, and fidelity. To that end, we introduce a novel training-free technique named Attention Interpolation via Diffusion (AID). Our key contributions include 1) proposing an inner/outer interpolated attention layer; 2) fusing the interpolated attention with self-attention to boost fidelity; and 3) applying beta distribution to selection to increase smoothness. We also present a variant, Prompt-guided Attention Interpolation via Diffusion (PAID), that considers interpolation as a condition-dependent generative process. This method enables the creation of new images with greater consistency, smoothness, and efficiency, and offers control over the exact path of interpolation. Our approach demonstrates effectiveness for conceptual and spatial interpolation. Code and demo are available at https://github.com/QY-H00/attention-interpolation-diffusion.

We introduce ToonCrafter, a novel approach that transcends traditional correspondence-based cartoon video interpolation, paving the way for generative interpolation. Traditional methods, that implicitly assume linear motion and the absence of complicated phenomena like dis-occlusion, often struggle with the exaggerated non-linear and large motions with occlusion commonly found in cartoons, resulting in implausible or even failed interpolation results. To overcome these limitations, we explore the potential of adapting live-action video priors to better suit cartoon interpolation within a generative framework. ToonCrafter effectively addresses the challenges faced when applying live-action video motion priors to generative cartoon interpolation. First, we design a toon rectification learning strategy that seamlessly adapts live-action video priors to the cartoon domain, resolving the domain gap and content leakage issues. Next, we introduce a dual-reference-based 3D decoder to compensate for lost details due to the highly compressed latent prior spaces, ensuring the preservation of fine details in interpolation results. Finally, we design a flexible sketch encoder that empowers users with interactive control over the interpolation results. Experimental results demonstrate that our proposed method not only produces visually convincing and more natural dynamics, but also effectively handles dis-occlusion. The comparative evaluation demonstrates the notable superiority of our approach over existing competitors.

We present a frame interpolation algorithm that synthesizes multiple intermediate frames from two input images with large in-between motion. Recent methods use multiple networks to estimate optical flow or depth and a separate network dedicated to frame synthesis. This is often complex and requires scarce optical flow or depth ground-truth. In this work, we present a single unified network, distinguished by a multi-scale feature extractor that shares weights at all scales, and is trainable from frames alone. To synthesize crisp and pleasing frames, we propose to optimize our network with the Gram matrix loss that measures the correlation difference between feature maps. Our approach outperforms state-of-the-art methods on the Xiph large motion benchmark. We also achieve higher scores on Vimeo-90K, Middlebury and UCF101, when comparing to methods that use perceptual losses. We study the effect of weight sharing and of training with datasets of increasing motion range. Finally, we demonstrate our model's effectiveness in synthesizing high quality and temporally coherent videos on a challenging near-duplicate photos dataset. Codes and pre-trained models are available at https://film-net.github.io.

Backward compatibility of model predictions is a desired property when updating a machine learning driven application. It allows to seamlessly improve the underlying model without introducing regression bugs. In classification tasks these bugs occur in the form of negative flips. This means an instance that was correctly classified by the old model is now classified incorrectly by the updated model. This has direct negative impact on the user experience of such systems e.g. a frequently used voice assistant query is suddenly misclassified. A common reason to update the model is when new training data becomes available and needs to be incorporated. Simply retraining the model with the updated data introduces the unwanted negative flips. We study the problem of regression during data updates and propose Backward Compatible Weight Interpolation (BCWI). This method interpolates between the weights of the old and new model and we show in extensive experiments that it reduces negative flips without sacrificing the improved accuracy of the new model. BCWI is straight forward to implement and does not increase inference cost. We also explore the use of importance weighting during interpolation and averaging the weights of multiple new models in order to further reduce negative flips.

Dilated Convolution with Learnable Spacings (DCLS) is a recently proposed variation of the dilated convolution in which the spacings between the non-zero elements in the kernel, or equivalently their positions, are learnable. Non-integer positions are handled via interpolation. Thanks to this trick, positions have well-defined gradients. The original DCLS used bilinear interpolation, and thus only considered the four nearest pixels. Yet here we show that longer range interpolations, and in particular a Gaussian interpolation, allow improving performance on ImageNet1k classification on two state-of-the-art convolutional architectures (ConvNeXt and Conv\-Former), without increasing the number of parameters. The method code is based on PyTorch and is available at https://github.com/K-H-Ismail/Dilated-Convolution-with-Learnable-Spacings-PyTorch

Vision-language models (VLMs) have demonstrated impressive zero-shot transfer capabilities in image-level visual perception tasks. However, they fall short in 3D instance-level segmentation tasks that require accurate localization and recognition of individual objects. To bridge this gap, we introduce a novel 3D Gaussian Splatting based hard visual prompting approach that leverages camera interpolation to generate diverse viewpoints around target objects without any 2D-3D optimization or fine-tuning. Our method simulates realistic 3D perspectives, effectively augmenting existing hard visual prompts by enforcing geometric consistency across viewpoints. This training-free strategy seamlessly integrates with prior hard visual prompts, enriching object-descriptive features and enabling VLMs to achieve more robust and accurate 3D instance segmentation in diverse 3D scenes.

Video frame interpolation (VFI) aims to synthesize intermediate frames in between existing frames to enhance visual smoothness and quality. Beyond the conventional methods based on the reconstruction loss, recent works employ the high quality generative models for perceptual quality. However, they require complex training and large computational cost for modeling on the pixel space. In this paper, we introduce disentangled Motion Modeling (MoMo), a diffusion-based approach for VFI that enhances visual quality by focusing on intermediate motion modeling. We propose disentangled two-stage training process, initially training a frame synthesis model to generate frames from input pairs and their optical flows. Subsequently, we propose a motion diffusion model, equipped with our novel diffusion U-Net architecture designed for optical flow, to produce bi-directional flows between frames. This method, by leveraging the simpler low-frequency representation of motions, achieves superior perceptual quality with reduced computational demands compared to generative modeling methods on the pixel space. Our method surpasses state-of-the-art methods in perceptual metrics across various benchmarks, demonstrating its efficacy and efficiency in VFI. Our code is available at: https://github.com/JHLew/MoMo

Recent work in Video Frame Interpolation (VFI) tries to formulate VFI as a diffusion-based conditional image generation problem, synthesizing the intermediate frame given a random noise and neighboring frames. Due to the relatively high resolution of videos, Latent Diffusion Models (LDMs) are employed as the conditional generation model, where the autoencoder compresses images into latent representations for diffusion and then reconstructs images from these latent representations. Such a formulation poses a crucial challenge: VFI expects that the output is deterministically equal to the ground truth intermediate frame, but LDMs randomly generate a diverse set of different images when the model runs multiple times. The reason for the diverse generation is that the cumulative variance (variance accumulated at each step of generation) of generated latent representations in LDMs is large. This makes the sampling trajectory random, resulting in diverse rather than deterministic generations. To address this problem, we propose our unique solution: Frame Interpolation with Consecutive Brownian Bridge Diffusion. Specifically, we propose consecutive Brownian Bridge diffusion that takes a deterministic initial value as input, resulting in a much smaller cumulative variance of generated latent representations. Our experiments suggest that our method can improve together with the improvement of the autoencoder and achieve state-of-the-art performance in VFI, leaving strong potential for further enhancement.

We present a method for generating video sequences with coherent motion between a pair of input key frames. We adapt a pretrained large-scale image-to-video diffusion model (originally trained to generate videos moving forward in time from a single input image) for key frame interpolation, i.e., to produce a video in between two input frames. We accomplish this adaptation through a lightweight fine-tuning technique that produces a version of the model that instead predicts videos moving backwards in time from a single input image. This model (along with the original forward-moving model) is subsequently used in a dual-directional diffusion sampling process that combines the overlapping model estimates starting from each of the two keyframes. Our experiments show that our method outperforms both existing diffusion-based methods and traditional frame interpolation techniques.

Preventing the performance decay of Transformers on inputs longer than those used for training has been an important challenge in extending the context length of these models. Though the Transformer architecture has fundamentally no limits on the input sequence lengths it can process, the choice of position encoding used during training can limit the performance of these models on longer inputs. We propose a novel functional relative position encoding with progressive interpolation, FIRE, to improve Transformer generalization to longer contexts. We theoretically prove that this can represent some of the popular relative position encodings, such as T5's RPE, Alibi, and Kerple. We next empirically show that FIRE models have better generalization to longer contexts on both zero-shot language modeling and long text benchmarks.

In this work, we propose a new diffusion-based method for video frame interpolation (VFI), in the context of traditional hand-made animation. We introduce three main contributions: The first is that we explicitly handle the interpolation time in our model, which we also re-estimate during the training process, to cope with the particularly large variations observed in the animation domain, compared to natural videos; The second is that we adapt and generalize a diffusion scheme called ResShift recently proposed in the super-resolution community to VFI, which allows us to perform a very low number of diffusion steps (in the order of 10) to produce our estimates; The third is that we leverage the stochastic nature of the diffusion process to provide a pixel-wise estimate of the uncertainty on the interpolated frame, which could be useful to anticipate where the model may be wrong. We provide extensive comparisons with respect to state-of-the-art models and show that our model outperforms these models on animation videos. Our code is available at https://github.com/VicFonch/Multi-Input-Resshift-Diffusion-VFI.

Video Frame Interpolation aims to recover realistic missing frames between observed frames, generating a high-frame-rate video from a low-frame-rate video. However, without additional guidance, the large motion between frames makes this problem ill-posed. Event-based Video Frame Interpolation (EVFI) addresses this challenge by using sparse, high-temporal-resolution event measurements as motion guidance. This guidance allows EVFI methods to significantly outperform frame-only methods. However, to date, EVFI methods have relied on a limited set of paired event-frame training data, severely limiting their performance and generalization capabilities. In this work, we overcome the limited data challenge by adapting pre-trained video diffusion models trained on internet-scale datasets to EVFI. We experimentally validate our approach on real-world EVFI datasets, including a new one that we introduce. Our method outperforms existing methods and generalizes across cameras far better than existing approaches.

Recent progress in neural forecasting accelerated improvements in the performance of large-scale forecasting systems. Yet, long-horizon forecasting remains a very difficult task. Two common challenges afflicting the task are the volatility of the predictions and their computational complexity. We introduce N-HiTS, a model which addresses both challenges by incorporating novel hierarchical interpolation and multi-rate data sampling techniques. These techniques enable the proposed method to assemble its predictions sequentially, emphasizing components with different frequencies and scales while decomposing the input signal and synthesizing the forecast. We prove that the hierarchical interpolation technique can efficiently approximate arbitrarily long horizons in the presence of smoothness. Additionally, we conduct extensive large-scale dataset experiments from the long-horizon forecasting literature, demonstrating the advantages of our method over the state-of-the-art methods, where N-HiTS provides an average accuracy improvement of almost 20% over the latest Transformer architectures while reducing the computation time by an order of magnitude (50 times). Our code is available at bit.ly/3VA5DoT

We present Envision3D, a novel method for efficiently generating high-quality 3D content from a single image. Recent methods that extract 3D content from multi-view images generated by diffusion models show great potential. However, it is still challenging for diffusion models to generate dense multi-view consistent images, which is crucial for the quality of 3D content extraction. To address this issue, we propose a novel cascade diffusion framework, which decomposes the challenging dense views generation task into two tractable stages, namely anchor views generation and anchor views interpolation. In the first stage, we train the image diffusion model to generate global consistent anchor views conditioning on image-normal pairs. Subsequently, leveraging our video diffusion model fine-tuned on consecutive multi-view images, we conduct interpolation on the previous anchor views to generate extra dense views. This framework yields dense, multi-view consistent images, providing comprehensive 3D information. To further enhance the overall generation quality, we introduce a coarse-to-fine sampling strategy for the reconstruction algorithm to robustly extract textured meshes from the generated dense images. Extensive experiments demonstrate that our method is capable of generating high-quality 3D content in terms of texture and geometry, surpassing previous image-to-3D baseline methods.

Current audio-driven facial animation methods achieve impressive results for short videos but suffer from error accumulation and identity drift when extended to longer durations. Existing methods attempt to mitigate this through external spatial control, increasing long-term consistency but compromising the naturalness of motion. We propose KeyFace, a novel two-stage diffusion-based framework, to address these issues. In the first stage, keyframes are generated at a low frame rate, conditioned on audio input and an identity frame, to capture essential facial expressions and movements over extended periods of time. In the second stage, an interpolation model fills in the gaps between keyframes, ensuring smooth transitions and temporal coherence. To further enhance realism, we incorporate continuous emotion representations and handle a wide range of non-speech vocalizations (NSVs), such as laughter and sighs. We also introduce two new evaluation metrics for assessing lip synchronization and NSV generation. Experimental results show that KeyFace outperforms state-of-the-art methods in generating natural, coherent facial animations over extended durations, successfully encompassing NSVs and continuous emotions.

In astrophysical and cosmological analyses, the increasing quality and volume of astronomical data demand efficient and precise computational tools. This work introduces a novel adaptive algorithm for automatic knots (AutoKnots) allocation in spline interpolation, designed to meet user-defined precision requirements. Unlike traditional methods that rely on manually configured knot distributions with numerous parameters, the proposed technique automatically determines the optimal number and placement of knots based on interpolation error criteria. This simplifies configuration, often requiring only a single parameter. The algorithm progressively improves the interpolation by adaptively sampling the function-to-be-approximated, f(x), in regions where the interpolation error exceeds the desired threshold. All function evaluations contribute directly to the final approximation, ensuring efficiency. While each resampling step involves recomputing the interpolation table, this process is highly optimized and usually computationally negligible compared to the cost of evaluating f(x). We show the algorithm's efficacy through a series of precision tests on different functions. However, the study underscores the necessity for caution when dealing with certain function types, notably those featuring plateaus. To address this challenge, a heuristic enhancement is incorporated, improving accuracy in flat regions. This algorithm has been extensively used and tested over the years. NumCosmo includes a comprehensive set of unit tests that rigorously evaluate the algorithm both directly and indirectly, underscoring its robustness and reliability. As a practical application, we compute the surface mass density Sigma(R) and the average surface mass density Sigma(<R) for Navarro-Frenk-White and Hernquist halo density profiles, which provide analytical benchmarks. (abridged)

Geographical, physical, or economic constraints often result in missing traces within seismic data, making the reconstruction of complete seismic data a crucial step in seismic data processing. Traditional methods for seismic data reconstruction require the selection of multiple empirical parameters and struggle to handle large-scale continuous missing data. With the development of deep learning, various neural networks have demonstrated powerful reconstruction capabilities. However, these convolutional neural networks represent a point-to-point reconstruction approach that may not cover the entire distribution of the dataset. Consequently, when dealing with seismic data featuring complex missing patterns, such networks may experience varying degrees of performance degradation. In response to this challenge, we propose a novel diffusion model reconstruction framework tailored for 3D seismic data. To constrain the results generated by the diffusion model, we introduce conditional supervision constraints into the diffusion model, constraining the generated data of the diffusion model based on the input data to be reconstructed. We introduce a 3D neural network architecture into the diffusion model, successfully extending the 2D diffusion model to 3D space. Additionally, we refine the model's generation process by incorporating missing data into the generation process, resulting in reconstructions with higher consistency. Through ablation studies determining optimal parameter values, our method exhibits superior reconstruction accuracy when applied to both field datasets and synthetic datasets, effectively addressing a wide range of complex missing patterns. Our implementation is available at https://github.com/WAL-l/SeisFusion.

Generative frame interpolation, empowered by large-scale pre-trained video generation models, has demonstrated remarkable advantages in complex scenes. However, existing methods heavily rely on the generative model to independently infer the correspondences between input frames, an ability that is inadequately developed during pre-training. In this work, we propose a novel framework, termed Motion-aware Generative frame interpolation (MoG), to significantly enhance the model's motion awareness by integrating explicit motion guidance. Specifically we investigate two key questions: what can serve as an effective motion guidance, and how we can seamlessly embed this guidance into the generative model. For the first question, we reveal that the intermediate flow from flow-based interpolation models could efficiently provide task-oriented motion guidance. Regarding the second, we first obtain guidance-based representations of intermediate frames by warping input frames' representations using guidance, and then integrate them into the model at both latent and feature levels. To demonstrate the versatility of our method, we train MoG on both real-world and animation datasets. Comprehensive evaluations show that our MoG significantly outperforms the existing methods in both domains, achieving superior video quality and improved fidelity.

We present LongQLoRA, an efficient and effective method to extend context length of large language models with less training resources. LongQLoRA combines the advantages of Position Interpolation, QLoRA and Shift Short Attention of LongLoRA. With a single 32GB V100 GPU, LongQLoRA can extend the context length of LLaMA2 7B and 13B from 4096 to 8192 and even to 12k within 1000 finetuning steps. LongQLoRA achieves competitive perplexity performance on PG19 and Proof-pile datasets, our model outperforms LongLoRA and is very close to MPT-7B-8K within the evaluation context length of 8192. We collect and build 39k long instruction data to extend context length of Vicuna-13B from 4096 to 8192 and achieve good performance both in long and short context generation task. We also do some ablation experiments to study the effect of LoRA rank, finetuning steps and attention patterns in inference.The model weights, training data and code are avaliable at https://github.com/yangjianxin1/LongQLoRA.

We present VIDIM, a generative model for video interpolation, which creates short videos given a start and end frame. In order to achieve high fidelity and generate motions unseen in the input data, VIDIM uses cascaded diffusion models to first generate the target video at low resolution, and then generate the high-resolution video conditioned on the low-resolution generated video. We compare VIDIM to previous state-of-the-art methods on video interpolation, and demonstrate how such works fail in most settings where the underlying motion is complex, nonlinear, or ambiguous while VIDIM can easily handle such cases. We additionally demonstrate how classifier-free guidance on the start and end frame and conditioning the super-resolution model on the original high-resolution frames without additional parameters unlocks high-fidelity results. VIDIM is fast to sample from as it jointly denoises all the frames to be generated, requires less than a billion parameters per diffusion model to produce compelling results, and still enjoys scalability and improved quality at larger parameter counts.

Continual Learning (CL) investigates how to train Deep Networks on a stream of tasks without incurring forgetting. CL settings proposed in literature assume that every incoming example is paired with ground-truth annotations. However, this clashes with many real-world applications: gathering labeled data, which is in itself tedious and expensive, becomes infeasible when data flow as a stream. This work explores Continual Semi-Supervised Learning (CSSL): here, only a small fraction of labeled input examples are shown to the learner. We assess how current CL methods (e.g.: EWC, LwF, iCaRL, ER, GDumb, DER) perform in this novel and challenging scenario, where overfitting entangles forgetting. Subsequently, we design a novel CSSL method that exploits metric learning and consistency regularization to leverage unlabeled examples while learning. We show that our proposal exhibits higher resilience to diminishing supervision and, even more surprisingly, relying only on 25% supervision suffices to outperform SOTA methods trained under full supervision.

Transition videos play a crucial role in media production, enhancing the flow and coherence of visual narratives. Traditional methods like morphing often lack artistic appeal and require specialized skills, limiting their effectiveness. Recent advances in diffusion model-based video generation offer new possibilities for creating transitions but face challenges such as poor inter-frame relationship modeling and abrupt content changes. We propose a novel training-free Transition Video Generation (TVG) approach using video-level diffusion models that addresses these limitations without additional training. Our method leverages Gaussian Process Regression (GPR) to model latent representations, ensuring smooth and dynamic transitions between frames. Additionally, we introduce interpolation-based conditional controls and a Frequency-aware Bidirectional Fusion (FBiF) architecture to enhance temporal control and transition reliability. Evaluations of benchmark datasets and custom image pairs demonstrate the effectiveness of our approach in generating high-quality smooth transition videos. The code are provided in https://sobeymil.github.io/tvg.com.

We propose to study and promote the robustness of a model as per its performance through the interpolation of training data distributions. Specifically, (1) we augment the data by finding the worst-case Wasserstein barycenter on the geodesic connecting subpopulation distributions of different categories. (2) We regularize the model for smoother performance on the continuous geodesic path connecting subpopulation distributions. (3) Additionally, we provide a theoretical guarantee of robustness improvement and investigate how the geodesic location and the sample size contribute, respectively. Experimental validations of the proposed strategy on four datasets, including CIFAR-100 and ImageNet, establish the efficacy of our method, e.g., our method improves the baselines' certifiable robustness on CIFAR10 up to 7.7%, with 16.8% on empirical robustness on CIFAR-100. Our work provides a new perspective of model robustness through the lens of Wasserstein geodesic-based interpolation with a practical off-the-shelf strategy that can be combined with existing robust training methods.

Real-time video frame interpolation (VFI) is very useful in video processing, media players, and display devices. We propose RIFE, a Real-time Intermediate Flow Estimation algorithm for VFI. To realize a high-quality flow-based VFI method, RIFE uses a neural network named IFNet that can estimate the intermediate flows end-to-end with much faster speed. A privileged distillation scheme is designed for stable IFNet training and improve the overall performance. RIFE does not rely on pre-trained optical flow models and can support arbitrary-timestep frame interpolation with the temporal encoding input. Experiments demonstrate that RIFE achieves state-of-the-art performance on several public benchmarks. Compared with the popular SuperSlomo and DAIN methods, RIFE is 4--27 times faster and produces better results. Furthermore, RIFE can be extended to wider applications thanks to temporal encoding. The code is available at https://github.com/megvii-research/ECCV2022-RIFE.

A retrieval model should not only interpolate the training data but also extrapolate well to the queries that are different from the training data. While neural retrieval models have demonstrated impressive performance on ad-hoc search benchmarks, we still know little about how they perform in terms of interpolation and extrapolation. In this paper, we demonstrate the importance of separately evaluating the two capabilities of neural retrieval models. Firstly, we examine existing ad-hoc search benchmarks from the two perspectives. We investigate the distribution of training and test data and find a considerable overlap in query entities, query intent, and relevance labels. This finding implies that the evaluation on these test sets is biased toward interpolation and cannot accurately reflect the extrapolation capacity. Secondly, we propose a novel evaluation protocol to separately evaluate the interpolation and extrapolation performance on existing benchmark datasets. It resamples the training and test data based on query similarity and utilizes the resampled dataset for training and evaluation. Finally, we leverage the proposed evaluation protocol to comprehensively revisit a number of widely-adopted neural retrieval models. Results show models perform differently when moving from interpolation to extrapolation. For example, representation-based retrieval models perform almost as well as interaction-based retrieval models in terms of interpolation but not extrapolation. Therefore, it is necessary to separately evaluate both interpolation and extrapolation performance and the proposed resampling method serves as a simple yet effective evaluation tool for future IR studies.

Human-centric video frame interpolation has great potential for improving people's entertainment experiences and finding commercial applications in the sports analysis industry, e.g., synthesizing slow-motion videos. Although there are multiple benchmark datasets available in the community, none of them is dedicated for human-centric scenarios. To bridge this gap, we introduce SportsSloMo, a benchmark consisting of more than 130K video clips and 1M video frames of high-resolution (geq720p) slow-motion sports videos crawled from YouTube. We re-train several state-of-the-art methods on our benchmark, and the results show a decrease in their accuracy compared to other datasets. It highlights the difficulty of our benchmark and suggests that it poses significant challenges even for the best-performing methods, as human bodies are highly deformable and occlusions are frequent in sports videos. To improve the accuracy, we introduce two loss terms considering the human-aware priors, where we add auxiliary supervision to panoptic segmentation and human keypoints detection, respectively. The loss terms are model agnostic and can be easily plugged into any video frame interpolation approaches. Experimental results validate the effectiveness of our proposed loss terms, leading to consistent performance improvement over 5 existing models, which establish strong baseline models on our benchmark. The dataset and code can be found at: https://neu-vi.github.io/SportsSlomo/.

Transformer-based Large Language Models (LLMs) struggle to process inputs exceeding their training context window, with performance degrading due to positional out-of-distribution (O.O.D.) that disrupt attention computations. Existing solutions, fine-tuning and training-free methods, are limited by computational inefficiency, attention logit outliers or loss of local positional information. To address this, we propose Greedy Attention Logit Interpolation (GALI), a training-free length extrapolation method that maximizes the utilization of pretrained positional intervals while avoiding attention logit outliers through attention logit interpolation. The result demonstrates that GALI consistently outperforms state-of-the-art training-free methods. Our findings reveal that LLMs interpret positional intervals unevenly within their training context window, suggesting that extrapolating within a smaller positional interval range yields superior results-even for short-context tasks. GALI represents a significant step toward resolving the positional O.O.D. challenge, enabling more reliable long-text understanding in LLMs. Our implementation of GALI, along with the experiments from our paper, is open-sourced at https://github.com/AcademyCityL/GALI.

We prove new convergence rates for a generalized version of stochastic Nesterov acceleration under interpolation conditions. Unlike previous analyses, our approach accelerates any stochastic gradient method which makes sufficient progress in expectation. The proof, which proceeds using the estimating sequences framework, applies to both convex and strongly convex functions and is easily specialized to accelerated SGD under the strong growth condition. In this special case, our analysis reduces the dependence on the strong growth constant from rho to rho as compared to prior work. This improvement is comparable to a square-root of the condition number in the worst case and address criticism that guarantees for stochastic acceleration could be worse than those for SGD.

Text analysis of social media for sentiment, topic analysis, and other analysis depends initially on the selection of keywords and phrases that will be used to create the research corpora. However, keywords that researchers choose may occur infrequently, leading to errors that arise from using small samples. In this paper, we use the capacity for memorization, interpolation, and extrapolation of Transformer Language Models such as the GPT series to learn the linguistic behaviors of a subgroup within larger corpora of Yelp reviews. We then use prompt-based queries to generate synthetic text that can be analyzed to produce insights into specific opinions held by the populations that the models were trained on. Once learned, more specific sentiment queries can be made of the model with high levels of accuracy when compared to traditional keyword searches. We show that even in cases where a specific keyphrase is limited or not present at all in the training corpora, the GPT is able to accurately generate large volumes of text that have the correct sentiment.

We present Position Interpolation (PI) that extends the context window sizes of RoPE-based pretrained LLMs such as LLaMA models to up to 32768 with minimal fine-tuning (within 1000 steps), while demonstrating strong empirical results on various tasks that require long context, including passkey retrieval, language modeling, and long document summarization from LLaMA 7B to 65B. Meanwhile, the extended model by Position Interpolation preserve quality relatively well on tasks within its original context window. To achieve this goal, Position Interpolation linearly down-scales the input position indices to match the original context window size, rather than extrapolating beyond the trained context length which may lead to catastrophically high attention scores that completely ruin the self-attention mechanism. Our theoretical study shows that the upper bound of interpolation is at least sim 600 times smaller than that of extrapolation, further demonstrating its stability. Models extended via Position Interpolation retain its original architecture and can reuse most pre-existing optimization and infrastructure.

We propose a simple but effective training-free approach tailored to diffusion-based image-to-image translation. Our approach revises the original noise prediction network of a pretrained diffusion model by introducing a noise correction term. We formulate the noise correction term as the difference between two noise predictions; one is computed from the denoising network with a progressive interpolation of the source and target prompt embeddings, while the other is the noise prediction with the source prompt embedding. The final noise prediction network is given by a linear combination of the standard denoising term and the noise correction term, where the former is designed to reconstruct must-be-preserved regions while the latter aims to effectively edit regions of interest relevant to the target prompt. Our approach can be easily incorporated into existing image-to-image translation methods based on diffusion models. Extensive experiments verify that the proposed technique achieves outstanding performance with low latency and consistently improves existing frameworks when combined with them.

In molecular dynamics (MD) simulations, rare events, such as protein folding, are typically studied by means of enhanced sampling techniques, most of which rely on the definition of a collective variable (CV) along which the acceleration occurs. Obtaining an expressive CV is crucial, but often hindered by the lack of information about the particular event, e.g., the transition from unfolded to folded conformation. We propose a simulation-free data augmentation strategy using physics-inspired metrics to generate geodesic interpolations resembling protein folding transitions, thereby improving sampling efficiency without true transition state samples. Leveraging interpolation progress parameters, we introduce a regression-based learning scheme for CV models, which outperforms classifier-based methods when transition state data is limited and noisy

Few-shot learning aims to transfer the knowledge acquired from training on a diverse set of tasks to unseen tasks from the same task distribution with a limited amount of labeled data. The underlying requirement for effective few-shot generalization is to learn a good representation of the task manifold. This becomes more difficult when only a limited number of tasks are available for training. In such a few-task few-shot setting, it is beneficial to explicitly preserve the local neighborhoods from the task manifold and exploit this to generate artificial tasks for training. To this end, we introduce the notion of interval bounds from the provably robust training literature to few-shot learning. The interval bounds are used to characterize neighborhoods around the training tasks. These neighborhoods can then be preserved by minimizing the distance between a task and its respective bounds. We then use a novel strategy to artificially form new tasks for training by interpolating between the available tasks and their respective interval bounds. We apply our framework to both model-agnostic meta-learning as well as prototype-based metric-learning paradigms. The efficacy of our proposed approach is evident from the improved performance on several datasets from diverse domains compared to current methods.

Video Frame Interpolation (VFI) aims to predict the intermediate frame I_n (we use n to denote time in videos to avoid notation overload with the timestep t in diffusion models) based on two consecutive neighboring frames I_0 and I_1. Recent approaches apply diffusion models (both image-based and video-based) in this task and achieve strong performance. However, image-based diffusion models are unable to extract temporal information and are relatively inefficient compared to non-diffusion methods. Video-based diffusion models can extract temporal information, but they are too large in terms of training scale, model size, and inference time. To mitigate the above issues, we propose Temporal-Aware Latent Brownian Bridge Diffusion for Video Frame Interpolation (TLB-VFI), an efficient video-based diffusion model. By extracting rich temporal information from video inputs through our proposed 3D-wavelet gating and temporal-aware autoencoder, our method achieves 20% improvement in FID on the most challenging datasets over recent SOTA of image-based diffusion models. Meanwhile, due to the existence of rich temporal information, our method achieves strong performance while having 3times fewer parameters. Such a parameter reduction results in 2.3x speed up. By incorporating optical flow guidance, our method requires 9000x less training data and achieves over 20x fewer parameters than video-based diffusion models. Codes and results are available at our project page: https://zonglinl.github.io/tlbvfi_page.

Recently, the state space model Mamba has demonstrated efficient long-sequence modeling capabilities, particularly for addressing long-sequence visual tasks in 3D medical imaging. However, existing generative self-supervised learning methods have not yet fully unleashed Mamba's potential for handling long-range dependencies because they overlook the inherent causal properties of state space sequences in masked modeling. To address this challenge, we propose a general-purpose pre-training framework called MambaMIM, a masked image modeling method based on a novel TOKen-Interpolation strategy (TOKI) for the selective structure state space sequence, which learns causal relationships of state space within the masked sequence. Further, MambaMIM introduces a bottom-up 3D hybrid masking strategy to maintain a masking consistency across different architectures and can be used on any single or hybrid Mamba architecture to enhance its multi-scale and long-range representation capability. We pre-train MambaMIM on a large-scale dataset of 6.8K CT scans and evaluate its performance across eight public medical segmentation benchmarks. Extensive downstream experiments reveal the feasibility and advancement of using Mamba for medical image pre-training. In particular, when we apply the MambaMIM to a customized architecture that hybridizes MedNeXt and Vision Mamba, we consistently obtain the state-of-the-art segmentation performance. The code is available at: https://github.com/FengheTan9/MambaMIM.

Video frame interpolation (VFI) in scenarios with large motion remains challenging due to motion ambiguity between frames. While event cameras can capture high temporal resolution motion information, existing event-based VFI methods struggle with limited training data and complex motion patterns. In this paper, we introduce Event-Guided Video Diffusion Model (EGVD), a novel framework that leverages the powerful priors of pre-trained stable video diffusion models alongside the precise temporal information from event cameras. Our approach features a Multi-modal Motion Condition Generator (MMCG) that effectively integrates RGB frames and event signals to guide the diffusion process, producing physically realistic intermediate frames. We employ a selective fine-tuning strategy that preserves spatial modeling capabilities while efficiently incorporating event-guided temporal information. We incorporate input-output normalization techniques inspired by recent advances in diffusion modeling to enhance training stability across varying noise levels. To improve generalization, we construct a comprehensive dataset combining both real and simulated event data across diverse scenarios. Extensive experiments on both real and simulated datasets demonstrate that EGVD significantly outperforms existing methods in handling large motion and challenging lighting conditions, achieving substantial improvements in perceptual quality metrics (27.4% better LPIPS on Prophesee and 24.1% on BSRGB) while maintaining competitive fidelity measures. Code and datasets available at: https://github.com/OpenImagingLab/EGVD.

Irregularly sampled time series data arise naturally in many application domains including biology, ecology, climate science, astronomy, and health. Such data represent fundamental challenges to many classical models from machine learning and statistics due to the presence of non-uniform intervals between observations. However, there has been significant progress within the machine learning community over the last decade on developing specialized models and architectures for learning from irregularly sampled univariate and multivariate time series data. In this survey, we first describe several axes along which approaches to learning from irregularly sampled time series differ including what data representations they are based on, what modeling primitives they leverage to deal with the fundamental problem of irregular sampling, and what inference tasks they are designed to perform. We then survey the recent literature organized primarily along the axis of modeling primitives. We describe approaches based on temporal discretization, interpolation, recurrence, attention and structural invariance. We discuss similarities and differences between approaches and highlight primary strengths and weaknesses.

With the development of video generation models has advanced significantly in recent years, we adopt large-scale image-to-video diffusion models for video frame interpolation. We present a conditional encoder designed to adapt an image-to-video model for large-motion frame interpolation. To enhance performance, we integrate a dual-branch feature extractor and propose a cross-frame attention mechanism that effectively captures both spatial and temporal information, enabling accurate interpolations of intermediate frames. Our approach demonstrates superior performance on the Fr\'echet Video Distance (FVD) metric when evaluated against other state-of-the-art approaches, particularly in handling large motion scenarios, highlighting advancements in generative-based methodologies.

Effectively extracting inter-frame motion and appearance information is important for video frame interpolation (VFI). Previous works either extract both types of information in a mixed way or elaborate separate modules for each type of information, which lead to representation ambiguity and low efficiency. In this paper, we propose a novel module to explicitly extract motion and appearance information via a unifying operation. Specifically, we rethink the information process in inter-frame attention and reuse its attention map for both appearance feature enhancement and motion information extraction. Furthermore, for efficient VFI, our proposed module could be seamlessly integrated into a hybrid CNN and Transformer architecture. This hybrid pipeline can alleviate the computational complexity of inter-frame attention as well as preserve detailed low-level structure information. Experimental results demonstrate that, for both fixed- and arbitrary-timestep interpolation, our method achieves state-of-the-art performance on various datasets. Meanwhile, our approach enjoys a lighter computation overhead over models with close performance. The source code and models are available at https://github.com/MCG-NJU/EMA-VFI.

We present TANGO, a framework for generating co-speech body-gesture videos. Given a few-minute, single-speaker reference video and target speech audio, TANGO produces high-fidelity videos with synchronized body gestures. TANGO builds on Gesture Video Reenactment (GVR), which splits and retrieves video clips using a directed graph structure - representing video frames as nodes and valid transitions as edges. We address two key limitations of GVR: audio-motion misalignment and visual artifacts in GAN-generated transition frames. In particular, (i) we propose retrieving gestures using latent feature distance to improve cross-modal alignment. To ensure the latent features could effectively model the relationship between speech audio and gesture motion, we implement a hierarchical joint embedding space (AuMoCLIP); (ii) we introduce the diffusion-based model to generate high-quality transition frames. Our diffusion model, Appearance Consistent Interpolation (ACInterp), is built upon AnimateAnyone and includes a reference motion module and homography background flow to preserve appearance consistency between generated and reference videos. By integrating these components into the graph-based retrieval framework, TANGO reliably produces realistic, audio-synchronized videos and outperforms all existing generative and retrieval methods. Our codes and pretrained models are available: https://pantomatrix.github.io/TANGO/

Embedding models play a pivot role in modern NLP applications such as IR and RAG. While the context limit of LLMs has been pushed beyond 1 million tokens, embedding models are still confined to a narrow context window not exceeding 8k tokens, refrained from application scenarios requiring long inputs such as legal contracts. This paper explores context window extension of existing embedding models, pushing the limit to 32k without requiring additional training. First, we examine the performance of current embedding models for long context retrieval on our newly constructed LongEmbed benchmark. LongEmbed comprises two synthetic tasks and four carefully chosen real-world tasks, featuring documents of varying length and dispersed target information. Benchmarking results underscore huge room for improvement in these models. Based on this, comprehensive experiments show that training-free context window extension strategies like position interpolation can effectively extend the context window of existing embedding models by several folds, regardless of their original context being 512 or beyond 4k. Furthermore, for models employing absolute position encoding (APE), we show the possibility of further fine-tuning to harvest notable performance gains while strictly preserving original behavior for short inputs. For models using rotary position embedding (RoPE), significant enhancements are observed when employing RoPE-specific methods, such as NTK and SelfExtend, indicating RoPE's superiority over APE for context window extension. To facilitate future research, we release E5-Base-4k and E5-RoPE-Base, along with the LongEmbed benchmark.

Rapid growth of high-dimensional datasets in fields such as single-cell RNA sequencing and spatial genomics has led to unprecedented opportunities for scientific discovery, but it also presents unique computational and statistical challenges. Traditional methods struggle with geometry-aware data generation, interpolation along meaningful trajectories, and transporting populations via feasible paths. To address these issues, we introduce Geometry-Aware Generative Autoencoder (GAGA), a novel framework that combines extensible manifold learning with generative modeling. GAGA constructs a neural network embedding space that respects the intrinsic geometries discovered by manifold learning and learns a novel warped Riemannian metric on the data space. This warped metric is derived from both the points on the data manifold and negative samples off the manifold, allowing it to characterize a meaningful geometry across the entire latent space. Using this metric, GAGA can uniformly sample points on the manifold, generate points along geodesics, and interpolate between populations across the learned manifold using geodesic-guided flows. GAGA shows competitive performance in simulated and real-world datasets, including a 30% improvement over the state-of-the-art methods in single-cell population-level trajectory inference.

We introduce a novel approach to counter adversarial attacks, namely, image resampling. Image resampling transforms a discrete image into a new one, simulating the process of scene recapturing or rerendering as specified by a geometrical transformation. The underlying rationale behind our idea is that image resampling can alleviate the influence of adversarial perturbations while preserving essential semantic information, thereby conferring an inherent advantage in defending against adversarial attacks. To validate this concept, we present a comprehensive study on leveraging image resampling to defend against adversarial attacks. We have developed basic resampling methods that employ interpolation strategies and coordinate shifting magnitudes. Our analysis reveals that these basic methods can partially mitigate adversarial attacks. However, they come with apparent limitations: the accuracy of clean images noticeably decreases, while the improvement in accuracy on adversarial examples is not substantial. We propose implicit representation-driven image resampling (IRAD) to overcome these limitations. First, we construct an implicit continuous representation that enables us to represent any input image within a continuous coordinate space. Second, we introduce SampleNet, which automatically generates pixel-wise shifts for resampling in response to different inputs. Furthermore, we can extend our approach to the state-of-the-art diffusion-based method, accelerating it with fewer time steps while preserving its defense capability. Extensive experiments demonstrate that our method significantly enhances the adversarial robustness of diverse deep models against various attacks while maintaining high accuracy on clean images.

We present FreeMorph, the first tuning-free method for image morphing that accommodates inputs with different semantics or layouts. Unlike existing methods that rely on finetuning pre-trained diffusion models and are limited by time constraints and semantic/layout discrepancies, FreeMorph delivers high-fidelity image morphing without requiring per-instance training. Despite their efficiency and potential, tuning-free methods face challenges in maintaining high-quality results due to the non-linear nature of the multi-step denoising process and biases inherited from the pre-trained diffusion model. In this paper, we introduce FreeMorph to address these challenges by integrating two key innovations. 1) We first propose a guidance-aware spherical interpolation design that incorporates explicit guidance from the input images by modifying the self-attention modules, thereby addressing identity loss and ensuring directional transitions throughout the generated sequence. 2) We further introduce a step-oriented variation trend that blends self-attention modules derived from each input image to achieve controlled and consistent transitions that respect both inputs. Our extensive evaluations demonstrate that FreeMorph outperforms existing methods, being 10x ~ 50x faster and establishing a new state-of-the-art for image morphing.

Health conditions among patients in intensive care units (ICUs) are monitored via electronic health records (EHRs), composed of numerical time series and lengthy clinical note sequences, both taken at irregular time intervals. Dealing with such irregularity in every modality, and integrating irregularity into multimodal representations to improve medical predictions, is a challenging problem. Our method first addresses irregularity in each single modality by (1) modeling irregular time series by dynamically incorporating hand-crafted imputation embeddings into learned interpolation embeddings via a gating mechanism, and (2) casting a series of clinical note representations as multivariate irregular time series and tackling irregularity via a time attention mechanism. We further integrate irregularity in multimodal fusion with an interleaved attention mechanism across temporal steps. To the best of our knowledge, this is the first work to thoroughly model irregularity in multimodalities for improving medical predictions. Our proposed methods for two medical prediction tasks consistently outperforms state-of-the-art (SOTA) baselines in each single modality and multimodal fusion scenarios. Specifically, we observe relative improvements of 6.5\%, 3.6\%, and 4.3\% in F1 for time series, clinical notes, and multimodal fusion, respectively. These results demonstrate the effectiveness of our methods and the importance of considering irregularity in multimodal EHRs.

Data mixing augmentation have proved to be effective in improving the generalization ability of deep neural networks. While early methods mix samples by hand-crafted policies (e.g., linear interpolation), recent methods utilize saliency information to match the mixed samples and labels via complex offline optimization. However, there arises a trade-off between precise mixing policies and optimization complexity. To address this challenge, we propose a novel automatic mixup (AutoMix) framework, where the mixup policy is parameterized and serves the ultimate classification goal directly. Specifically, AutoMix reformulates the mixup classification into two sub-tasks (i.e., mixed sample generation and mixup classification) with corresponding sub-networks and solves them in a bi-level optimization framework. For the generation, a learnable lightweight mixup generator, Mix Block, is designed to generate mixed samples by modeling patch-wise relationships under the direct supervision of the corresponding mixed labels. To prevent the degradation and instability of bi-level optimization, we further introduce a momentum pipeline to train AutoMix in an end-to-end manner. Extensive experiments on nine image benchmarks prove the superiority of AutoMix compared with state-of-the-art in various classification scenarios and downstream tasks.

This paper introduces Uniform Orthogonal Reinitialization Adaptation (UORA), a novel parameter-efficient fine-tuning (PEFT) approach for Large Language Models (LLMs). UORA achieves state-of-the-art performance and parameter efficiency by leveraging a low-rank approximation method to reduce the number of trainable parameters. Unlike existing methods such as LoRA and VeRA, UORA employs an interpolation-based reparametrization mechanism that selectively reinitializes rows and columns in frozen projection matrices, guided by the vector magnitude heuristic. This results in substantially fewer trainable parameters compared to LoRA and outperforms VeRA in computation and storage efficiency. Comprehensive experiments across various benchmarks demonstrate UORA's superiority in achieving competitive fine-tuning performance with negligible computational overhead. We demonstrate its performance on GLUE and E2E benchmarks and its effectiveness in instruction-tuning large language models and image classification models. Our contributions establish a new paradigm for scalable and resource-efficient fine-tuning of LLMs.

We present latentSplat, a method to predict semantic Gaussians in a 3D latent space that can be splatted and decoded by a light-weight generative 2D architecture. Existing methods for generalizable 3D reconstruction either do not scale to large scenes and resolutions, or are limited to interpolation of close input views. latentSplat combines the strengths of regression-based and generative approaches while being trained purely on readily available real video data. The core of our method are variational 3D Gaussians, a representation that efficiently encodes varying uncertainty within a latent space consisting of 3D feature Gaussians. From these Gaussians, specific instances can be sampled and rendered via efficient splatting and a fast, generative decoder. We show that latentSplat outperforms previous works in reconstruction quality and generalization, while being fast and scalable to high-resolution data.

Text embeddings are vital for tasks such as text retrieval and semantic textual similarity (STS). Recently, the advent of pretrained language models, along with unified benchmarks like the Massive Text Embedding Benchmark (MTEB), has facilitated the development of versatile general-purpose text embedding models. Advanced embedding models are typically developed using large-scale multi-task data and joint training across multiple tasks. However, our experimental analysis reveals two significant drawbacks of joint training: 1) Task Conflict: Gradients from different tasks interfere with each other, leading to negative transfer. 2) Data Imbalance: Disproportionate data distribution introduces biases that negatively impact performance across tasks. To overcome these challenges, we explore model merging-a technique that combines independently trained models to mitigate gradient conflicts and balance data distribution. We introduce a novel method, Self Positioning, which efficiently searches for optimal model combinations within the interpolation space of task vectors using stochastic gradient descent. Our experiments demonstrate that Self Positioning significantly enhances multi-task performance on the MTEB dataset, achieving an absolute improvement of 0.7 points. It outperforms traditional resampling methods while reducing computational costs. This work offers a robust approach to building generalized text embedding models with superior performance across diverse embedding-related tasks.

Training diffusion models for audiovisual sequences allows for a range of generation tasks by learning conditional distributions of various input-output combinations of the two modalities. Nevertheless, this strategy often requires training a separate model for each task which is expensive. Here, we propose a novel training approach to effectively learn arbitrary conditional distributions in the audiovisual space.Our key contribution lies in how we parameterize the diffusion timestep in the forward diffusion process. Instead of the standard fixed diffusion timestep, we propose applying variable diffusion timesteps across the temporal dimension and across modalities of the inputs. This formulation offers flexibility to introduce variable noise levels for various portions of the input, hence the term mixture of noise levels. We propose a transformer-based audiovisual latent diffusion model and show that it can be trained in a task-agnostic fashion using our approach to enable a variety of audiovisual generation tasks at inference time. Experiments demonstrate the versatility of our method in tackling cross-modal and multimodal interpolation tasks in the audiovisual space. Notably, our proposed approach surpasses baselines in generating temporally and perceptually consistent samples conditioned on the input. Project page: avdit2024.github.io

Motion trajectories offer reliable references for physics-based motion learning but suffer from sparsity, particularly in regions that lack sufficient data coverage. To address this challenge, we introduce a self-supervised, structured representation and generation method that extracts spatial-temporal relationships in periodic or quasi-periodic motions. The motion dynamics in a continuously parameterized latent space enable our method to enhance the interpolation and generalization capabilities of motion learning algorithms. The motion learning controller, informed by the motion parameterization, operates online tracking of a wide range of motions, including targets unseen during training. With a fallback mechanism, the controller dynamically adapts its tracking strategy and automatically resorts to safe action execution when a potentially risky target is proposed. By leveraging the identified spatial-temporal structure, our work opens new possibilities for future advancements in general motion representation and learning algorithms.

3D indoor scenes are widely used in computer graphics, with applications ranging from interior design to gaming to virtual and augmented reality. They also contain rich information, including room layout, as well as furniture type, geometry, and placement. High-quality 3D indoor scenes are highly demanded while it requires expertise and is time-consuming to design high-quality 3D indoor scenes manually. Existing research only addresses partial problems: some works learn to generate room layout, and other works focus on generating detailed structure and geometry of individual furniture objects. However, these partial steps are related and should be addressed together for optimal synthesis. We propose SCENEHGN, a hierarchical graph network for 3D indoor scenes that takes into account the full hierarchy from the room level to the object level, then finally to the object part level. Therefore for the first time, our method is able to directly generate plausible 3D room content, including furniture objects with fine-grained geometry, and their layout. To address the challenge, we introduce functional regions as intermediate proxies between the room and object levels to make learning more manageable. To ensure plausibility, our graph-based representation incorporates both vertical edges connecting child nodes with parent nodes from different levels, and horizontal edges encoding relationships between nodes at the same level. Extensive experiments demonstrate that our method produces superior generation results, even when comparing results of partial steps with alternative methods that can only achieve these. We also demonstrate that our method is effective for various applications such as part-level room editing, room interpolation, and room generation by arbitrary room boundaries.

We propose a GAN-based image compression method working at extremely low bitrates below 0.1bpp. Most existing learned image compression methods suffer from blur at extremely low bitrates. Although GAN can help to reconstruct sharp images, there are two drawbacks. First, GAN makes training unstable. Second, the reconstructions often contain unpleasing noise or artifacts. To address both of the drawbacks, our method adopts two-stage training and network interpolation. The two-stage training is effective to stabilize the training. Moreover, the network interpolation utilizes the models in both stages and reduces undesirable noise and artifacts, while maintaining important edges. Hence, we can control the trade-off between perceptual quality and fidelity without re-training models. The experimental results show that our model can reconstruct high quality images. Furthermore, our user study confirms that our reconstructions are preferable to state-of-the-art GAN-based image compression model. The code will be available.

Recently, several models based on deep neural networks have achieved great success in terms of both reconstruction accuracy and computational performance for single image super-resolution. In these methods, the low resolution (LR) input image is upscaled to the high resolution (HR) space using a single filter, commonly bicubic interpolation, before reconstruction. This means that the super-resolution (SR) operation is performed in HR space. We demonstrate that this is sub-optimal and adds computational complexity. In this paper, we present the first convolutional neural network (CNN) capable of real-time SR of 1080p videos on a single K2 GPU. To achieve this, we propose a novel CNN architecture where the feature maps are extracted in the LR space. In addition, we introduce an efficient sub-pixel convolution layer which learns an array of upscaling filters to upscale the final LR feature maps into the HR output. By doing so, we effectively replace the handcrafted bicubic filter in the SR pipeline with more complex upscaling filters specifically trained for each feature map, whilst also reducing the computational complexity of the overall SR operation. We evaluate the proposed approach using images and videos from publicly available datasets and show that it performs significantly better (+0.15dB on Images and +0.39dB on Videos) and is an order of magnitude faster than previous CNN-based methods.

Implicit neural representation has paved the way for new approaches to dynamic scene reconstruction and rendering. Nonetheless, cutting-edge dynamic neural rendering methods rely heavily on these implicit representations, which frequently struggle to capture the intricate details of objects in the scene. Furthermore, implicit methods have difficulty achieving real-time rendering in general dynamic scenes, limiting their use in a variety of tasks. To address the issues, we propose a deformable 3D Gaussians Splatting method that reconstructs scenes using 3D Gaussians and learns them in canonical space with a deformation field to model monocular dynamic scenes. We also introduce an annealing smoothing training mechanism with no extra overhead, which can mitigate the impact of inaccurate poses on the smoothness of time interpolation tasks in real-world datasets. Through a differential Gaussian rasterizer, the deformable 3D Gaussians not only achieve higher rendering quality but also real-time rendering speed. Experiments show that our method outperforms existing methods significantly in terms of both rendering quality and speed, making it well-suited for tasks such as novel-view synthesis, time interpolation, and real-time rendering.

Speech bandwidth expansion is crucial for expanding the frequency range of low-bandwidth speech signals, thereby improving audio quality, clarity and perceptibility in digital applications. Its applications span telephony, compression, text-to-speech synthesis, and speech recognition. This paper presents a novel approach using a high-fidelity generative adversarial network, unlike cascaded systems, our system is trained end-to-end on paired narrowband and wideband speech signals. Our method integrates various bandwidth upsampling ratios into a single unified model specifically designed for speech bandwidth expansion applications. Our approach exhibits robust performance across various bandwidth expansion factors, including those not encountered during training, demonstrating zero-shot capability. To the best of our knowledge, this is the first work to showcase this capability. The experimental results demonstrate that our method outperforms previous end-to-end approaches, as well as interpolation and traditional techniques, showcasing its effectiveness in practical speech enhancement applications.

This paper describes a machine learning method to automate reading of cockpit gauges, using a CNN to invert affine transformations and deduce aircraft states from instrument images. Validated with synthetic images of a turn-and-bank indicator, this research introduces methods such as generating datasets from a single image, the 'Clean Training Principle' for optimal noise-free training, and CNN interpolation for continuous value predictions from categorical data. It also offers insights into hyperparameter optimization and ML system software engineering.

We propose VidStyleODE, a spatiotemporally continuous disentangled Video representation based upon StyleGAN and Neural-ODEs. Effective traversal of the latent space learned by Generative Adversarial Networks (GANs) has been the basis for recent breakthroughs in image editing. However, the applicability of such advancements to the video domain has been hindered by the difficulty of representing and controlling videos in the latent space of GANs. In particular, videos are composed of content (i.e., appearance) and complex motion components that require a special mechanism to disentangle and control. To achieve this, VidStyleODE encodes the video content in a pre-trained StyleGAN W_+ space and benefits from a latent ODE component to summarize the spatiotemporal dynamics of the input video. Our novel continuous video generation process then combines the two to generate high-quality and temporally consistent videos with varying frame rates. We show that our proposed method enables a variety of applications on real videos: text-guided appearance manipulation, motion manipulation, image animation, and video interpolation and extrapolation. Project website: https://cyberiada.github.io/VidStyleODE

We propose an alternative generator architecture for generative adversarial networks, borrowing from style transfer literature. The new architecture leads to an automatically learned, unsupervised separation of high-level attributes (e.g., pose and identity when trained on human faces) and stochastic variation in the generated images (e.g., freckles, hair), and it enables intuitive, scale-specific control of the synthesis. The new generator improves the state-of-the-art in terms of traditional distribution quality metrics, leads to demonstrably better interpolation properties, and also better disentangles the latent factors of variation. To quantify interpolation quality and disentanglement, we propose two new, automated methods that are applicable to any generator architecture. Finally, we introduce a new, highly varied and high-quality dataset of human faces.

Current image-to-image translations do not control the output domain beyond the classes used during training, nor do they interpolate between different domains well, leading to implausible results. This limitation largely arises because labels do not consider the semantic distance. To mitigate such problems, we propose a style-aware discriminator that acts as a critic as well as a style encoder to provide conditions. The style-aware discriminator learns a controllable style space using prototype-based self-supervised learning and simultaneously guides the generator. Experiments on multiple datasets verify that the proposed model outperforms current state-of-the-art image-to-image translation methods. In contrast with current methods, the proposed approach supports various applications, including style interpolation, content transplantation, and local image translation.

Mixup, a simple data augmentation method that randomly mixes two data points via linear interpolation, has been extensively applied in various deep learning applications to gain better generalization. However, the theoretical underpinnings of its efficacy are not yet fully understood. In this paper, we aim to seek a fundamental understanding of the benefits of Mixup. We first show that Mixup using different linear interpolation parameters for features and labels can still achieve similar performance to the standard Mixup. This indicates that the intuitive linearity explanation in Zhang et al., (2018) may not fully explain the success of Mixup. Then we perform a theoretical study of Mixup from the feature learning perspective. We consider a feature-noise data model and show that Mixup training can effectively learn the rare features (appearing in a small fraction of data) from its mixture with the common features (appearing in a large fraction of data). In contrast, standard training can only learn the common features but fails to learn the rare features, thus suffering from bad generalization performance. Moreover, our theoretical analysis also shows that the benefits of Mixup for feature learning are mostly gained in the early training phase, based on which we propose to apply early stopping in Mixup. Experimental results verify our theoretical findings and demonstrate the effectiveness of the early-stopped Mixup training.

Managing long sequences has become an important and necessary feature for large language models (LLMs). However, it is still an open question of how to comprehensively and systematically evaluate the long-sequence capability of LLMs. One of the reasons is that conventional and widely-used benchmarks mainly consist of short sequences. In this paper, we propose M4LE, a Multi-ability, Multi-range, Multi-task, Multi-domain benchmark for Long-context Evaluation. M4LE is based on a diverse NLP task pool comprising 36 NLP datasets, 11 task types and 12 domains. To alleviate the scarcity of tasks with naturally long sequences and incorporate multiple-ability assessment, we propose an automatic approach (but with negligible human annotations) to convert short-sequence tasks into a unified long-sequence scenario where LLMs have to identify single or multiple relevant spans in long contexts based on explicit or semantic hints. Specifically, the scenario includes five different types of abilities: (1) explicit single-span; (2) semantic single-span; (3) explicit multiple-span; (4) semantic multiple-span; and (5) global context understanding. The resulting samples in M4LE are evenly distributed from 1k to 8k input length. We conducted a systematic evaluation on 11 well-established LLMs, especially those optimized for long-sequence inputs. Our results reveal that: 1) Current LLMs struggle to understand long context, particularly when tasks require multiple-span attention. 2) Semantic retrieval task is more difficult for competent LLMs. 3) Models fine-tuned on longer text with position interpolation have comparable performance to those using Neural Tangent Kernel (NTK) aware scaling methods without fine-tuning. We make our benchmark publicly available to encourage future research in this challenging area.

We introduce a diffusion-based framework that performs aligned novel view image and geometry generation via a warping-and-inpainting methodology. Unlike prior methods that require dense posed images or pose-embedded generative models limited to in-domain views, our method leverages off-the-shelf geometry predictors to predict partial geometries viewed from reference images, and formulates novel-view synthesis as an inpainting task for both image and geometry. To ensure accurate alignment between generated images and geometry, we propose cross-modal attention distillation, where attention maps from the image diffusion branch are injected into a parallel geometry diffusion branch during both training and inference. This multi-task approach achieves synergistic effects, facilitating geometrically robust image synthesis as well as well-defined geometry prediction. We further introduce proximity-based mesh conditioning to integrate depth and normal cues, interpolating between point cloud and filtering erroneously predicted geometry from influencing the generation process. Empirically, our method achieves high-fidelity extrapolative view synthesis on both image and geometry across a range of unseen scenes, delivers competitive reconstruction quality under interpolation settings, and produces geometrically aligned colored point clouds for comprehensive 3D completion. Project page is available at https://cvlab-kaist.github.io/MoAI.

A jump cut offers an abrupt, sometimes unwanted change in the viewing experience. We present a novel framework for smoothing these jump cuts, in the context of talking head videos. We leverage the appearance of the subject from the other source frames in the video, fusing it with a mid-level representation driven by DensePose keypoints and face landmarks. To achieve motion, we interpolate the keypoints and landmarks between the end frames around the cut. We then use an image translation network from the keypoints and source frames, to synthesize pixels. Because keypoints can contain errors, we propose a cross-modal attention scheme to select and pick the most appropriate source amongst multiple options for each key point. By leveraging this mid-level representation, our method can achieve stronger results than a strong video interpolation baseline. We demonstrate our method on various jump cuts in the talking head videos, such as cutting filler words, pauses, and even random cuts. Our experiments show that we can achieve seamless transitions, even in the challenging cases where the talking head rotates or moves drastically in the jump cut.

Protein backbone generation plays a central role in de novo protein design and is significant for many biological and medical applications. Although diffusion and flow-based generative models provide potential solutions to this challenging task, they often generate proteins with undesired designability and suffer computational inefficiency. In this study, we propose a novel rectified quaternion flow (ReQFlow) matching method for fast and high-quality protein backbone generation. In particular, our method generates a local translation and a 3D rotation from random noise for each residue in a protein chain, which represents each 3D rotation as a unit quaternion and constructs its flow by spherical linear interpolation (SLERP) in an exponential format. We train the model by quaternion flow (QFlow) matching with guaranteed numerical stability and rectify the QFlow model to accelerate its inference and improve the designability of generated protein backbones, leading to the proposed ReQFlow model. Experiments show that ReQFlow achieves state-of-the-art performance in protein backbone generation while requiring much fewer sampling steps and significantly less inference time (e.g., being 37x faster than RFDiffusion and 62x faster than Genie2 when generating a backbone of length 300), demonstrating its effectiveness and efficiency. The code is available at https://github.com/AngxiaoYue/ReQFlow.

Increasing numbers of patients with disabilities or elderly people with mobility issues often suffer from a pressure ulcer. The affected areas need regular checks, but they have a difficulty in accessing a hospital. Some remote diagnosis systems are being used for them, but there are limitations in checking a patient's status regularly. In this paper, we present a remote medical assistant that can help pressure ulcer management with image processing techniques. The proposed system includes a mobile application with a deep learning model for wound segmentation and analysis. As there are not enough data to train the deep learning model, we make use of a pretrained model from a relevant domain and data augmentation that is appropriate for this task. First of all, an image preprocessing method using bilinear interpolation is used to resize images and normalize the images. Second, for data augmentation, we use rotation, reflection, and a watershed algorithm. Third, we use a pretrained deep learning model generated from skin wound images similar to pressure ulcer images. Finally, we added an attention module that can provide hints on the pressure ulcer image features. The resulting model provides an accuracy of 99.0%, an intersection over union (IoU) of 99.99%, and a dice similarity coefficient (DSC) of 93.4% for pressure ulcer segmentation, which is better than existing results.

In this paper, we address the challenge of performing open-vocabulary video instance segmentation (OV-VIS) in real-time. We analyze the computational bottlenecks of state-of-the-art foundation models that performs OV-VIS, and propose a new method, TROY-VIS, that significantly improves processing speed while maintaining high accuracy. We introduce three key techniques: (1) Decoupled Attention Feature Enhancer to speed up information interaction between different modalities and scales; (2) Flash Embedding Memory for obtaining fast text embeddings of object categories; and, (3) Kernel Interpolation for exploiting the temporal continuity in videos. Our experiments demonstrate that TROY-VIS achieves the best trade-off between accuracy and speed on two large-scale OV-VIS benchmarks, BURST and LV-VIS, running 20x faster than GLEE-Lite (25 FPS v.s. 1.25 FPS) with comparable or even better accuracy. These results demonstrate TROY-VIS's potential for real-time applications in dynamic environments such as mobile robotics and augmented reality. Code and model will be released at https://github.com/google-research/troyvis.

This paper addresses the challenge of train-short-test-long (TSTL) scenarios in Large Language Models (LLMs) equipped with Rotary Position Embedding (RoPE), where models pre-trained on shorter sequences face difficulty with out-of-distribution (OOD) token positions in longer sequences. We introduce Resonance RoPE, a novel approach designed to narrow the generalization gap in TSTL scenarios by refining the interpolation of RoPE features for OOD positions, significantly improving the model performance without additional online computational costs. Furthermore, we present PosGen, a new synthetic benchmark specifically designed for fine-grained behavior analysis in TSTL scenarios, aiming to isolate the constantly increasing difficulty of token generation on long contexts from the challenges of recognizing new token positions. Our experiments on synthetic tasks show that after applying Resonance RoPE, Transformers recognize OOD position better and more robustly. Our extensive LLM experiments also show superior performance after applying Resonance RoPE to the current state-of-the-art RoPE scaling method, YaRN, on both upstream language modeling tasks and a variety of downstream long-text applications.

Recent advances in attention-free sequence models rely on convolutions as alternatives to the attention operator at the core of Transformers. In particular, long convolution sequence models have achieved state-of-the-art performance in many domains, but incur a significant cost during auto-regressive inference workloads -- naively requiring a full pass (or caching of activations) over the input sequence for each generated token -- similarly to attention-based models. In this paper, we seek to enable mathcal O(1) compute and memory cost per token in any pre-trained long convolution architecture to reduce memory footprint and increase throughput during generation. Concretely, our methods consist in extracting low-dimensional linear state-space models from each convolution layer, building upon rational interpolation and model-order reduction techniques. We further introduce architectural improvements to convolution-based layers such as Hyena: by weight-tying the filters across channels into heads, we achieve higher pre-training quality and reduce the number of filters to be distilled. The resulting model achieves 10x higher throughput than Transformers and 1.5x higher than Hyena at 1.3B parameters, without any loss in quality after distillation.

Transformer has taken the field of natural language processing (NLP) by storm since its birth. Further, Large language models (LLMs) built upon it have captured worldwide attention due to its superior abilities. Nevertheless, all Transformer-based models including these powerful LLMs suffer from a preset length limit and can hardly generalize from short training sequences to longer inference ones, namely, they can not perform length extrapolation. Hence, a plethora of methods have been proposed to enhance length extrapolation of Transformer, in which the positional encoding (PE) is recognized as the major factor. In this survey, we present these advances towards length extrapolation in a unified notation from the perspective of PE. Specifically, we first introduce extrapolatable PEs, including absolute and relative PEs. Then, we dive into extrapolation methods based on them, covering position interpolation and randomized position methods. Finally, several challenges and future directions in this area are highlighted. Through this survey, We aim to enable the reader to gain a deep understanding of existing methods and provide stimuli for future research.

Mixup is an efficient data augmentation approach that improves the generalization of neural networks by smoothing the decision boundary with mixed data. Recently, dynamic mixup methods have improved previous static policies effectively (e.g., linear interpolation) by maximizing target-related salient regions in mixed samples, but excessive additional time costs are not acceptable. These additional computational overheads mainly come from optimizing the mixed samples according to the mixed labels. However, we found that the extra optimizing step may be redundant because label-mismatched mixed samples are informative hard mixed samples for deep models to localize discriminative features. In this paper, we thus are not trying to propose a more complicated dynamic mixup policy but rather an efficient mixup objective function with a decoupled regularizer named Decoupled Mixup (DM). The primary effect is that DM can adaptively utilize those hard mixed samples to mine discriminative features without losing the original smoothness of mixup. As a result, DM enables static mixup methods to achieve comparable or even exceed the performance of dynamic methods without any extra computation. This also leads to an interesting objective design problem for mixup training that we need to focus on both smoothing the decision boundaries and identifying discriminative features. Extensive experiments on supervised and semi-supervised learning benchmarks across seven datasets validate the effectiveness of DM as a plug-and-play module. Source code and models are available at https://github.com/Westlake-AI/openmixup

Understanding the glassy nature of neural networks is pivotal both for theoretical and computational advances in Machine Learning and Theoretical Artificial Intelligence. Keeping the focus on dense associative Hebbian neural networks, the purpose of this paper is two-fold: at first we develop rigorous mathematical approaches to address properly a statistical mechanical picture of the phenomenon of {\em replica symmetry breaking} (RSB) in these networks, then -- deepening results stemmed via these routes -- we aim to inspect the {\em glassiness} that they hide. In particular, regarding the methodology, we provide two techniques: the former is an adaptation of the transport PDE to the case, while the latter is an extension of Guerra's interpolation breakthrough. Beyond coherence among the results, either in replica symmetric and in the one-step replica symmetry breaking level of description, we prove the Gardner's picture and we identify the maximal storage capacity by a ground-state analysis in the Baldi-Venkatesh high-storage regime. In the second part of the paper we investigate the glassy structure of these networks: in contrast with the replica symmetric scenario (RS), RSB actually stabilizes the spin-glass phase. We report huge differences w.r.t. the standard pairwise Hopfield limit: in particular, it is known that it is possible to express the free energy of the Hopfield neural network as a linear combination of the free energies of an hard spin glass (i.e. the Sherrington-Kirkpatrick model) and a soft spin glass (the Gaussian or "spherical" model). This is no longer true when interactions are more than pairwise (whatever the level of description, RS or RSB): for dense networks solely the free energy of the hard spin glass survives, proving a huge diversity in the underlying glassiness of associative neural networks.

We identity a by-far-unrecognized problem of Adam-style optimizers which results from unnecessary coupling between momentum and adaptivity. The coupling leads to instability and divergence when the momentum and adaptivity parameters are mismatched. In this work, we propose a method, Laprop, which decouples momentum and adaptivity in the Adam-style methods. We show that the decoupling leads to greater flexibility in the hyperparameters and allows for a straightforward interpolation between the signed gradient methods and the adaptive gradient methods. We experimentally show that Laprop has consistently improved speed and stability over Adam on a variety of tasks. We also bound the regret of Laprop on a convex problem and show that our bound differs from that of Adam by a key factor, which demonstrates its advantage.

Human health can be critically affected by cardiovascular diseases, such as hypertension, arrhythmias, and stroke. Heart rate and blood pressure are important biometric information for the monitoring of cardiovascular system and early diagnosis of cardiovascular diseases. Existing methods for estimating the heart rate are based on electrocardiography and photoplethyomography, which require contacting the sensor to the skin surface. Moreover, catheter and cuff-based methods for measuring blood pressure cause inconvenience and have limited applicability. Therefore, in this thesis, we propose a vision-based method for estimating the heart rate and blood pressure. This thesis proposes a 2-stage deep learning framework consisting of a dual remote photoplethysmography network (DRP-Net) and bounded blood pressure network (BBP-Net). In the first stage, DRP-Net infers remote photoplethysmography (rPPG) signals for the acral and facial regions, and these phase-shifted rPPG signals are utilized to estimate the heart rate. In the second stage, BBP-Net integrates temporal features and analyzes phase discrepancy between the acral and facial rPPG signals to estimate SBP and DBP values. To improve the accuracy of estimating the heart rate, we employed a data augmentation method based on a frame interpolation model. Moreover, we designed BBP-Net to infer blood pressure within a predefined range by incorporating a scaled sigmoid function. Our method resulted in estimating the heart rate with the mean absolute error (MAE) of 1.78 BPM, reducing the MAE by 34.31 % compared to the recent method, on the MMSE-HR dataset. The MAE for estimating the systolic blood pressure (SBP) and diastolic blood pressure (DBP) were 10.19 mmHg and 7.09 mmHg. On the V4V dataset, the MAE for the heart rate, SBP, and DBP were 3.83 BPM, 13.64 mmHg, and 9.4 mmHg, respectively.

Kernel methods are widely used in machine learning, especially for classification problems. However, the theoretical analysis of kernel classification is still limited. This paper investigates the statistical performances of kernel classifiers. With some mild assumptions on the conditional probability eta(x)=P(Y=1mid X=x), we derive an upper bound on the classification excess risk of a kernel classifier using recent advances in the theory of kernel regression. We also obtain a minimax lower bound for Sobolev spaces, which shows the optimality of the proposed classifier. Our theoretical results can be extended to the generalization error of overparameterized neural network classifiers. To make our theoretical results more applicable in realistic settings, we also propose a simple method to estimate the interpolation smoothness of 2eta(x)-1 and apply the method to real datasets.

Reconstructing 3D shapes from planar cross-sections is a challenge inspired by downstream applications like medical imaging and geographic informatics. The input is an in/out indicator function fully defined on a sparse collection of planes in space, and the output is an interpolation of the indicator function to the entire volume. Previous works addressing this sparse and ill-posed problem either produce low quality results, or rely on additional priors such as target topology, appearance information, or input normal directions. In this paper, we present OReX, a method for 3D shape reconstruction from slices alone, featuring a Neural Field as the interpolation prior. A modest neural network is trained on the input planes to return an inside/outside estimate for a given 3D coordinate, yielding a powerful prior that induces smoothness and self-similarities. The main challenge for this approach is high-frequency details, as the neural prior is overly smoothing. To alleviate this, we offer an iterative estimation architecture and a hierarchical input sampling scheme that encourage coarse-to-fine training, allowing the training process to focus on high frequencies at later stages. In addition, we identify and analyze a ripple-like effect stemming from the mesh extraction step. We mitigate it by regularizing the spatial gradients of the indicator function around input in/out boundaries during network training, tackling the problem at the root. Through extensive qualitative and quantitative experimentation, we demonstrate our method is robust, accurate, and scales well with the size of the input. We report state-of-the-art results compared to previous approaches and recent potential solutions, and demonstrate the benefit of our individual contributions through analysis and ablation studies.

We introduce Z-SASLM, a Zero-Shot Style-Aligned SLI (Spherical Linear Interpolation) Blending Latent Manipulation pipeline that overcomes the limitations of current multi-style blending methods. Conventional approaches rely on linear blending, assuming a flat latent space leading to suboptimal results when integrating multiple reference styles. In contrast, our framework leverages the non-linear geometry of the latent space by using SLI Blending to combine weighted style representations. By interpolating along the geodesic on the hypersphere, Z-SASLM preserves the intrinsic structure of the latent space, ensuring high-fidelity and coherent blending of diverse styles - all without the need for fine-tuning. We further propose a new metric, Weighted Multi-Style DINO ViT-B/8, designed to quantitatively evaluate the consistency of the blended styles. While our primary focus is on the theoretical and practical advantages of SLI Blending for style manipulation, we also demonstrate its effectiveness in a multi-modal content fusion setting through comprehensive experimental studies. Experimental results show that Z-SASLM achieves enhanced and robust style alignment. The implementation code can be found at: https://github.com/alessioborgi/Z-SASLM.

Continuous space-time video super-resolution (C-STVSR) aims to simultaneously enhance video resolution and frame rate at an arbitrary scale. Recently, implicit neural representation (INR) has been applied to video restoration, representing videos as implicit fields that can be decoded at an arbitrary scale. However, the highly ill-posed nature of C-STVSR limits the effectiveness of current INR-based methods: they assume linear motion between frames and use interpolation or feature warping to generate features at arbitrary spatiotemporal positions with two consecutive frames. This restrains C-STVSR from capturing rapid and nonlinear motion and long-term dependencies (involving more than two frames) in complex dynamic scenes. In this paper, we propose a novel C-STVSR framework, called HR-INR, which captures both holistic dependencies and regional motions based on INR. It is assisted by an event camera, a novel sensor renowned for its high temporal resolution and low latency. To fully utilize the rich temporal information from events, we design a feature extraction consisting of (1) a regional event feature extractor - taking events as inputs via the proposed event temporal pyramid representation to capture the regional nonlinear motion and (2) a holistic event-frame feature extractor for long-term dependence and continuity motion. We then propose a novel INR-based decoder with spatiotemporal embeddings to capture long-term dependencies with a larger temporal perception field. We validate the effectiveness and generalization of our method on four datasets (both simulated and real data), showing the superiority of our method.

Irregular sampling intervals and missing values in real-world time series data present challenges for conventional methods that assume consistent intervals and complete data. Neural Ordinary Differential Equations (Neural ODEs) offer an alternative approach, utilizing neural networks combined with ODE solvers to learn continuous latent representations through parameterized vector fields. Neural Stochastic Differential Equations (Neural SDEs) extend Neural ODEs by incorporating a diffusion term, although this addition is not trivial, particularly when addressing irregular intervals and missing values. Consequently, careful design of drift and diffusion functions is crucial for maintaining stability and enhancing performance, while incautious choices can result in adverse properties such as the absence of strong solutions, stochastic destabilization, or unstable Euler discretizations, significantly affecting Neural SDEs' performance. In this study, we propose three stable classes of Neural SDEs: Langevin-type SDE, Linear Noise SDE, and Geometric SDE. Then, we rigorously demonstrate their robustness in maintaining excellent performance under distribution shift, while effectively preventing overfitting. To assess the effectiveness of our approach, we conduct extensive experiments on four benchmark datasets for interpolation, forecasting, and classification tasks, and analyze the robustness of our methods with 30 public datasets under different missing rates. Our results demonstrate the efficacy of the proposed method in handling real-world irregular time series data.

One little-explored frontier of image generation and editing is the task of interpolating between two input images, a feature missing from all currently deployed image generation pipelines. We argue that such a feature can expand the creative applications of such models, and propose a method for zero-shot interpolation using latent diffusion models. We apply interpolation in the latent space at a sequence of decreasing noise levels, then perform denoising conditioned on interpolated text embeddings derived from textual inversion and (optionally) subject poses. For greater consistency, or to specify additional criteria, we can generate several candidates and use CLIP to select the highest quality image. We obtain convincing interpolations across diverse subject poses, image styles, and image content, and show that standard quantitative metrics such as FID are insufficient to measure the quality of an interpolation. Code and data are available at https://clintonjwang.github.io/interpolation.

The increased demand for 3D data in AR/VR, robotics and gaming applications, gave rise to powerful generative pipelines capable of synthesizing high-quality 3D objects. Most of these models rely on the Score Distillation Sampling (SDS) algorithm to optimize a 3D representation such that the rendered image maintains a high likelihood as evaluated by a pre-trained diffusion model. However, finding a correct mode in the high-dimensional distribution produced by the diffusion model is challenging and often leads to issues such as over-saturation, over-smoothing, and Janus-like artifacts. In this paper, we propose a novel learning paradigm for 3D synthesis that utilizes pre-trained diffusion models. Instead of focusing on mode-seeking, our method directly models the distribution discrepancy between multi-view renderings and diffusion priors in an adversarial manner, which unlocks the generation of high-fidelity and photorealistic 3D content, conditioned on a single image and prompt. Moreover, by harnessing the latent space of GANs and expressive diffusion model priors, our method facilitates a wide variety of 3D applications including single-view reconstruction, high diversity generation and continuous 3D interpolation in the open domain. The experiments demonstrate the superiority of our pipeline compared to previous works in terms of generation quality and diversity.

Multi-resolution hash encoding has recently been proposed to reduce the computational cost of neural renderings, such as NeRF. This method requires accurate camera poses for the neural renderings of given scenes. However, contrary to previous methods jointly optimizing camera poses and 3D scenes, the naive gradient-based camera pose refinement method using multi-resolution hash encoding severely deteriorates performance. We propose a joint optimization algorithm to calibrate the camera pose and learn a geometric representation using efficient multi-resolution hash encoding. Showing that the oscillating gradient flows of hash encoding interfere with the registration of camera poses, our method addresses the issue by utilizing smooth interpolation weighting to stabilize the gradient oscillation for the ray samplings across hash grids. Moreover, the curriculum training procedure helps to learn the level-wise hash encoding, further increasing the pose refinement. Experiments on the novel-view synthesis datasets validate that our learning frameworks achieve state-of-the-art performance and rapid convergence of neural rendering, even when initial camera poses are unknown.

In the pursuit to understand the intricacies of human brain's visual processing, reconstructing dynamic visual experiences from brain activities emerges as a challenging yet fascinating endeavor. While recent advancements have achieved success in reconstructing static images from non-invasive brain recordings, the domain of translating continuous brain activities into video format remains underexplored. In this work, we introduce NeuroCine, a novel dual-phase framework to targeting the inherent challenges of decoding fMRI data, such as noises, spatial redundancy and temporal lags. This framework proposes spatial masking and temporal interpolation-based augmentation for contrastive learning fMRI representations and a diffusion model enhanced by dependent prior noise for video generation. Tested on a publicly available fMRI dataset, our method shows promising results, outperforming the previous state-of-the-art models by a notable margin of {20.97%}, {31.00%} and {12.30%} respectively on decoding the brain activities of three subjects in the fMRI dataset, as measured by SSIM. Additionally, our attention analysis suggests that the model aligns with existing brain structures and functions, indicating its biological plausibility and interpretability.

Normalizing flow models have been used successfully for generative image super-resolution (SR) by approximating complex distribution of natural images to simple tractable distribution in latent space through Invertible Neural Networks (INN). These models can generate multiple realistic SR images from one low-resolution (LR) input using randomly sampled points in the latent space, simulating the ill-posed nature of image upscaling where multiple high-resolution (HR) images correspond to the same LR. Lately, the invertible process in INN has also been used successfully by bidirectional image rescaling models like IRN and HCFlow for joint optimization of downscaling and inverse upscaling, resulting in significant improvements in upscaled image quality. While they are optimized for image downscaling too, the ill-posed nature of image downscaling, where one HR image could be downsized to multiple LR images depending on different interpolation kernels and resampling methods, is not considered. A new downscaling latent variable, in addition to the original one representing uncertainties in image upscaling, is introduced to model variations in the image downscaling process. This dual latent variable enhancement is applicable to different image rescaling models and it is shown in extensive experiments that it can improve image upscaling accuracy consistently without sacrificing image quality in downscaled LR images. It is also shown to be effective in enhancing other INN-based models for image restoration applications like image hiding.

Text-to-motion generation holds potential for film, gaming, and robotics, yet current methods often prioritize short motion generation, making it challenging to produce long motion sequences effectively: (1) Current methods struggle to handle long motion sequences as a single input due to prohibitively high computational cost; (2) Breaking down the generation of long motion sequences into shorter segments can result in inconsistent transitions and requires interpolation or inpainting, which lacks entire sequence modeling. To solve these challenges, we propose InfiniMotion, a method that generates continuous motion sequences of arbitrary length within an autoregressive framework. We highlight its groundbreaking capability by generating a continuous 1-hour human motion with around 80,000 frames. Specifically, we introduce the Motion Memory Transformer with Bidirectional Mamba Memory, enhancing the transformer's memory to process long motion sequences effectively without overwhelming computational resources. Notably our method achieves over 30% improvement in FID and 6 times longer demonstration compared to previous state-of-the-art methods, showcasing significant advancements in long motion generation. See project webpage: https://steve-zeyu-zhang.github.io/InfiniMotion/

We present a method for computing free-energy differences using thermodynamic integration with a neural network potential that interpolates between two target Hamiltonians. The interpolation is defined at the sample distribution level, and the neural network potential is optimized to match the corresponding equilibrium potential at every intermediate time-step. Once the interpolating potentials and samples are well-aligned, the free-energy difference can be estimated using (neural) thermodynamic integration. To target molecular systems, we simultaneously couple Lennard-Jones and electrostatic interactions and model the rigid-body rotation of molecules. We report accurate results for several benchmark systems: a Lennard-Jones particle in a Lennard-Jones fluid, as well as the insertion of both water and methane solutes in a water solvent at atomistic resolution using a simple three-body neural-network potential.

This paper proposes a method for the automatic creation of variables (in the case of regression) that complement the information contained in the initial input vector. The method works as a pre-processing step in which the continuous values of the variable to be regressed are discretized into a set of intervals which are then used to define value thresholds. Then classifiers are trained to predict whether the value to be regressed is less than or equal to each of these thresholds. The different outputs of the classifiers are then concatenated in the form of an additional vector of variables that enriches the initial vector of the regression problem. The implemented system can thus be considered as a generic pre-processing tool. We tested the proposed enrichment method with 5 types of regressors and evaluated it in 33 regression datasets. Our experimental results confirm the interest of the approach.

Colloquially speaking, image generation models based upon diffusion processes are frequently said to exhibit "hallucinations," samples that could never occur in the training data. But where do such hallucinations come from? In this paper, we study a particular failure mode in diffusion models, which we term mode interpolation. Specifically, we find that diffusion models smoothly "interpolate" between nearby data modes in the training set, to generate samples that are completely outside the support of the original training distribution; this phenomenon leads diffusion models to generate artifacts that never existed in real data (i.e., hallucinations). We systematically study the reasons for, and the manifestation of this phenomenon. Through experiments on 1D and 2D Gaussians, we show how a discontinuous loss landscape in the diffusion model's decoder leads to a region where any smooth approximation will cause such hallucinations. Through experiments on artificial datasets with various shapes, we show how hallucination leads to the generation of combinations of shapes that never existed. Finally, we show that diffusion models in fact know when they go out of support and hallucinate. This is captured by the high variance in the trajectory of the generated sample towards the final few backward sampling process. Using a simple metric to capture this variance, we can remove over 95% of hallucinations at generation time while retaining 96% of in-support samples. We conclude our exploration by showing the implications of such hallucination (and its removal) on the collapse (and stabilization) of recursive training on synthetic data with experiments on MNIST and 2D Gaussians dataset. We release our code at https://github.com/locuslab/diffusion-model-hallucination.

We study the robust interpolation problem of arbitrary data distributions supported on a bounded space and propose a two-fold law of robustness. Robust interpolation refers to the problem of interpolating n noisy training data points in R^d by a Lipschitz function. Although this problem has been well understood when the samples are drawn from an isoperimetry distribution, much remains unknown concerning its performance under generic or even the worst-case distributions. We prove a Lipschitzness lower bound Omega(n/p) of the interpolating neural network with p parameters on arbitrary data distributions. With this result, we validate the law of robustness conjecture in prior work by Bubeck, Li, and Nagaraj on two-layer neural networks with polynomial weights. We then extend our result to arbitrary interpolating approximators and prove a Lipschitzness lower bound Omega(n^{1/d}) for robust interpolation. Our results demonstrate a two-fold law of robustness: i) we show the potential benefit of overparametrization for smooth data interpolation when n=poly(d), and ii) we disprove the potential existence of an O(1)-Lipschitz robust interpolating function when n=exp(omega(d)).

A class of generative models that unifies flow-based and diffusion-based methods is introduced. These models extend the framework proposed in Albergo & Vanden-Eijnden (2023), enabling the use of a broad class of continuous-time stochastic processes called `stochastic interpolants' to bridge any two arbitrary probability density functions exactly in finite time. These interpolants are built by combining data from the two prescribed densities with an additional latent variable that shapes the bridge in a flexible way. The time-dependent probability density function of the stochastic interpolant is shown to satisfy a first-order transport equation as well as a family of forward and backward Fokker-Planck equations with tunable diffusion coefficient. Upon consideration of the time evolution of an individual sample, this viewpoint immediately leads to both deterministic and stochastic generative models based on probability flow equations or stochastic differential equations with an adjustable level of noise. The drift coefficients entering these models are time-dependent velocity fields characterized as the unique minimizers of simple quadratic objective functions, one of which is a new objective for the score of the interpolant density. We show that minimization of these quadratic objectives leads to control of the likelihood for generative models built upon stochastic dynamics, while likelihood control for deterministic dynamics is more stringent. We also discuss connections with other methods such as score-based diffusion models, stochastic localization processes, probabilistic denoising techniques, and rectifying flows. In addition, we demonstrate that stochastic interpolants recover the Schr\"odinger bridge between the two target densities when explicitly optimizing over the interpolant. Finally, algorithmic aspects are discussed and the approach is illustrated on numerical examples.

Given an input painting, we reconstruct a time-lapse video of how it may have been painted. We formulate this as an autoregressive image generation problem, in which an initially blank "canvas" is iteratively updated. The model learns from real artists by training on many painting videos. Our approach incorporates text and region understanding to define a set of painting "instructions" and updates the canvas with a novel diffusion-based renderer. The method extrapolates beyond the limited, acrylic style paintings on which it has been trained, showing plausible results for a wide range of artistic styles and genres.

Automatic analysis of the enormous sets of images is a critical task in life sciences. This faces many challenges such as: algorithms are highly parameterized, significant human input is intertwined, and lacking a standard meta-visualization approach. This paper proposes an alternative iterative approach for optimizing input parameters, saving time by minimizing the user involvement, and allowing for understanding the workflow of algorithms and discovering new ones. The main focus is on developing an interactive visualization technique that enables users to analyze the relationships between sampled input parameters and corresponding output. This technique is implemented as a prototype called Veni Vidi Vici, or "I came, I saw, I conquered." This strategy is inspired by the mathematical formulas of numbering computable functions and is developed atop ImageJ, a scientific image processing program. A case study is presented to investigate the proposed framework. Finally, the paper explores some potential future issues in the application of the proposed approach in parameter space analysis in visualization.

Computers calculate transcendental functions by approximating them through the composition of a few limited-precision instructions. For example, an exponential can be calculated with a Taylor series. These approximation methods were developed over the centuries by mathematicians, who emphasized the attainability of arbitrary precision. Computers, however, operate on few limited precision types, such as the popular float32. In this study, we show that when aiming for limited precision, existing approximation methods can be outperformed by programs automatically discovered from scratch by a simple evolutionary algorithm. In particular, over real numbers, our method can approximate the exponential function reaching orders of magnitude more precision for a given number of operations when compared to previous approaches. More practically, over float32 numbers and constrained to less than 1 ULP of error, the same method attains a speedup over baselines by generating code that triggers better XLA/LLVM compilation paths. In other words, in both cases, evolution searched a vast space of possible programs, without knowledge of mathematics, to discover previously unknown optimized approximations to high precision, for the first time. We also give evidence that these results extend beyond the exponential. The ubiquity of transcendental functions suggests that our method has the potential to reduce the cost of scientific computing applications.

We propose Framer for interactive frame interpolation, which targets producing smoothly transitioning frames between two images as per user creativity. Concretely, besides taking the start and end frames as inputs, our approach supports customizing the transition process by tailoring the trajectory of some selected keypoints. Such a design enjoys two clear benefits. First, incorporating human interaction mitigates the issue arising from numerous possibilities of transforming one image to another, and in turn enables finer control of local motions. Second, as the most basic form of interaction, keypoints help establish the correspondence across frames, enhancing the model to handle challenging cases (e.g., objects on the start and end frames are of different shapes and styles). It is noteworthy that our system also offers an "autopilot" mode, where we introduce a module to estimate the keypoints and refine the trajectory automatically, to simplify the usage in practice. Extensive experimental results demonstrate the appealing performance of Framer on various applications, such as image morphing, time-lapse video generation, cartoon interpolation, etc. The code, the model, and the interface will be released to facilitate further research.

We propose an algorithm for inexpensive gradient-based hyperparameter optimization that combines the implicit function theorem (IFT) with efficient inverse Hessian approximations. We present results about the relationship between the IFT and differentiating through optimization, motivating our algorithm. We use the proposed approach to train modern network architectures with millions of weights and millions of hyper-parameters. For example, we learn a data-augmentation network - where every weight is a hyperparameter tuned for validation performance - outputting augmented training examples. Jointly tuning weights and hyperparameters with our approach is only a few times more costly in memory and compute than standard training.

The aim of this article is to introduce a new methodology for constructing morphings between shapes that have identical topology. This morphing is obtained by deforming a reference shape, through the resolution of a sequence of linear elasticity equations, onto the target shape. In particular, our approach does not assume any knowledge of a boundary parametrization. Furthermore, we demonstrate how constraints can be imposed on specific points, lines and surfaces in the reference domain to ensure alignment with their counterparts in the target domain after morphing. Additionally, we show how the proposed methodology can be integrated in an offline and online paradigm, which is useful in reduced-order modeling scenarii involving variable shapes. This framework facilitates the efficient computation of the morphings in various geometric configurations, thus improving the versatility and applicability of the approach. The methodology is illustrated on the regression problem of the drag and lift coefficients of airfoils of non-parameterized variable shapes.

We develop a fast, tractable technique called Net-Trim for simplifying a trained neural network. The method is a convex post-processing module, which prunes (sparsifies) a trained network layer by layer, while preserving the internal responses. We present a comprehensive analysis of Net-Trim from both the algorithmic and sample complexity standpoints, centered on a fast, scalable convex optimization program. Our analysis includes consistency results between the initial and retrained models before and after Net-Trim application and guarantees on the number of training samples needed to discover a network that can be expressed using a certain number of nonzero terms. Specifically, if there is a set of weights that uses at most s terms that can re-create the layer outputs from the layer inputs, we can find these weights from O(slog N/s) samples, where N is the input size. These theoretical results are similar to those for sparse regression using the Lasso, and our analysis uses some of the same recently-developed tools (namely recent results on the concentration of measure and convex analysis). Finally, we propose an algorithmic framework based on the alternating direction method of multipliers (ADMM), which allows a fast and simple implementation of Net-Trim for network pruning and compression.

New geometric methods for fast evaluation of derivatives of polynomial and rational B\'{e}zier curves are proposed. They apply an algorithm for evaluating polynomial or rational B\'{e}zier curves, which was recently given by the authors. Numerical tests show that the new approach is more efficient than the methods which use the famous de Casteljau algorithm. The algorithms work well even for high-order derivatives of rational B\'{e}zier curves of high degrees.

We present Scalable Interpolant Transformers (SiT), a family of generative models built on the backbone of Diffusion Transformers (DiT). The interpolant framework, which allows for connecting two distributions in a more flexible way than standard diffusion models, makes possible a modular study of various design choices impacting generative models built on dynamical transport: using discrete vs. continuous time learning, deciding the objective for the model to learn, choosing the interpolant connecting the distributions, and deploying a deterministic or stochastic sampler. By carefully introducing the above ingredients, SiT surpasses DiT uniformly across model sizes on the conditional ImageNet 256x256 benchmark using the exact same backbone, number of parameters, and GFLOPs. By exploring various diffusion coefficients, which can be tuned separately from learning, SiT achieves an FID-50K score of 2.06.

Hoffmann et al. (2022) propose three methods for estimating a compute-optimal scaling law. We attempt to replicate their third estimation procedure, which involves fitting a parametric loss function to a reconstruction of data from their plots. We find that the reported estimates are inconsistent with their first two estimation methods, fail at fitting the extracted data, and report implausibly narrow confidence intervals--intervals this narrow would require over 600,000 experiments, while they likely only ran fewer than 500. In contrast, our rederivation of the scaling law using the third approach yields results that are compatible with the findings from the first two estimation procedures described by Hoffmann et al.

Practitioners frequently aim to infer an unobserved population trajectory using sample snapshots at multiple time points. For instance, in single-cell sequencing, scientists would like to learn how gene expression evolves over time. But sequencing any cell destroys that cell. So we cannot access any cell's full trajectory, but we can access snapshot samples from many cells. Stochastic differential equations are commonly used to analyze systems with full individual-trajectory access; since here we have only sample snapshots, these methods are inapplicable. The deep learning community has recently explored using Schr\"odinger bridges (SBs) and their extensions to estimate these dynamics. However, these methods either (1) interpolate between just two time points or (2) require a single fixed reference dynamic within the SB, which is often just set to be Brownian motion. But learning piecewise from adjacent time points can fail to capture long-term dependencies. And practitioners are typically able to specify a model class for the reference dynamic but not the exact values of the parameters within it. So we propose a new method that (1) learns the unobserved trajectories from sample snapshots across multiple time points and (2) requires specification only of a class of reference dynamics, not a single fixed one. In particular, we suggest an iterative projection method inspired by Schr\"odinger bridges; we alternate between learning a piecewise SB on the unobserved trajectories and using the learned SB to refine our best guess for the dynamics within the reference class. We demonstrate the advantages of our method via a well-known simulated parametric model from ecology, simulated and real data from systems biology, and real motion-capture data.

Denoising Diffusion Probabilistic Models (DDPMs) exhibit remarkable capabilities in image generation, with studies suggesting that they can generalize by composing latent factors learned from the training data. In this work, we go further and study DDPMs trained on strictly separate subsets of the data distribution with large gaps on the support of the latent factors. We show that such a model can effectively generate images in the unexplored, intermediate regions of the distribution. For instance, when trained on clearly smiling and non-smiling faces, we demonstrate a sampling procedure which can generate slightly smiling faces without reference images (zero-shot interpolation). We replicate these findings for other attributes as well as other datasets. Our code is available at https://github.com/jdeschena/ddpm-zero-shot-interpolation.

A Transformer-based deep direct sampling method is proposed for electrical impedance tomography, a well-known severely ill-posed nonlinear boundary value inverse problem. A real-time reconstruction is achieved by evaluating the learned inverse operator between carefully designed data and the reconstructed images. An effort is made to give a specific example to a fundamental question: whether and how one can benefit from the theoretical structure of a mathematical problem to develop task-oriented and structure-conforming deep neural networks? Specifically, inspired by direct sampling methods for inverse problems, the 1D boundary data in different frequencies are preprocessed by a partial differential equation-based feature map to yield 2D harmonic extensions as different input channels. Then, by introducing learnable non-local kernels, the direct sampling is recast to a modified attention mechanism. The new method achieves superior accuracy over its predecessors and contemporary operator learners and shows robustness to noises in benchmarks. This research shall strengthen the insights that, despite being invented for natural language processing tasks, the attention mechanism offers great flexibility to be modified in conformity with the a priori mathematical knowledge, which ultimately leads to the design of more physics-compatible neural architectures.

Solving the inverse problem is the key step in evaluating the capacity of a physical model to describe real phenomena. In medical image computing, it aligns with the classical theme of image-based model personalization. Traditionally, a solution to the problem is obtained by performing either sampling or variational inference based methods. Both approaches aim to identify a set of free physical model parameters that results in a simulation best matching an empirical observation. When applied to brain tumor modeling, one of the instances of image-based model personalization in medical image computing, the overarching drawback of the methods is the time complexity for finding such a set. In a clinical setting with limited time between imaging and diagnosis or even intervention, this time complexity may prove critical. As the history of quantitative science is the history of compression, we align in this paper with the historical tendency and propose a method compressing complex traditional strategies for solving an inverse problem into a simple database query task. We evaluated different ways of performing the database query task assessing the trade-off between accuracy and execution time. On the exemplary task of brain tumor growth modeling, we prove that the proposed method achieves one order speed-up compared to existing approaches for solving the inverse problem. The resulting compute time offers critical means for relying on more complex and, hence, realistic models, for integrating image preprocessing and inverse modeling even deeper, or for implementing the current model into a clinical workflow.

Generative models inspired by dynamical transport of measure -- such as flows and diffusions -- construct a continuous-time map between two probability densities. Conventionally, one of these is the target density, only accessible through samples, while the other is taken as a simple base density that is data-agnostic. In this work, using the framework of stochastic interpolants, we formalize how to couple the base and the target densities. This enables us to incorporate information about class labels or continuous embeddings to construct dynamical transport maps that serve as conditional generative models. We show that these transport maps can be learned by solving a simple square loss regression problem analogous to the standard independent setting. We demonstrate the usefulness of constructing dependent couplings in practice through experiments in super-resolution and in-painting.

Previous literature offers limited clues on how to learn a periodic function using modern neural networks. We start with a study of the extrapolation properties of neural networks; we prove and demonstrate experimentally that the standard activations functions, such as ReLU, tanh, sigmoid, along with their variants, all fail to learn to extrapolate simple periodic functions. We hypothesize that this is due to their lack of a "periodic" inductive bias. As a fix of this problem, we propose a new activation, namely, x + sin^2(x), which achieves the desired periodic inductive bias to learn a periodic function while maintaining a favorable optimization property of the ReLU-based activations. Experimentally, we apply the proposed method to temperature and financial data prediction.

We present an online post-hoc calibration method, called Online Platt Scaling (OPS), which combines the Platt scaling technique with online logistic regression. We demonstrate that OPS smoothly adapts between i.i.d. and non-i.i.d. settings with distribution drift. Further, in scenarios where the best Platt scaling model is itself miscalibrated, we enhance OPS by incorporating a recently developed technique called calibeating to make it more robust. Theoretically, our resulting OPS+calibeating method is guaranteed to be calibrated for adversarial outcome sequences. Empirically, it is effective on a range of synthetic and real-world datasets, with and without distribution drifts, achieving superior performance without hyperparameter tuning. Finally, we extend all OPS ideas to the beta scaling method.

Which functions can be used as activations in deep neural networks? This article explores families of functions based on orthonormal bases, including the Hermite polynomial basis and the Fourier trigonometric basis, as well as a basis resulting from the tropicalization of a polynomial basis. Our study shows that, through simple variance-preserving initialization and without additional clamping mechanisms, these activations can successfully be used to train deep models, such as GPT-2 for next-token prediction on OpenWebText and ConvNeXt for image classification on ImageNet. Our work addresses the issue of exploding and vanishing activations and gradients, particularly prevalent with polynomial activations, and opens the door for improving the efficiency of large-scale learning tasks. Furthermore, our approach provides insight into the structure of neural networks, revealing that networks with polynomial activations can be interpreted as multivariate polynomial mappings. Finally, using Hermite interpolation, we show that our activations can closely approximate classical ones in pre-trained models by matching both the function and its derivative, making them especially useful for fine-tuning tasks. These activations are available in the torchortho library, which can be accessed via: https://github.com/K-H-Ismail/torchortho.

This work investigates the use of smooth neural networks for modeling dynamic variations of implicit surfaces under the level set equation (LSE). For this, it extends the representation of neural implicit surfaces to the space-time R^3times R, which opens up mechanisms for continuous geometric transformations. Examples include evolving an initial surface towards general vector fields, smoothing and sharpening using the mean curvature equation, and interpolations of initial conditions. The network training considers two constraints. A data term is responsible for fitting the initial condition to the corresponding time instant, usually R^3 times {0}. Then, a LSE term forces the network to approximate the underlying geometric evolution given by the LSE, without any supervision. The network can also be initialized based on previously trained initial conditions, resulting in faster convergence compared to the standard approach.

Generative methods for image and video editing use generative models as priors to perform edits despite incomplete information, such as changing the composition of 3D objects shown in a single image. Recent methods have shown promising composition editing results in the image setting, but in the video setting, editing methods have focused on editing object's appearance and motion, or camera motion, and as a result, methods to edit object composition in videos are still missing. We propose \name as a method for editing 3D object compositions in videos of static scenes with camera motion. Our approach allows editing the 3D position of a 3D object across all frames of a video in a temporally consistent manner. This is achieved by lifting intermediate features of a generative model to a 3D reconstruction that is shared between all frames, editing the reconstruction, and projecting the features on the edited reconstruction back to each frame. To the best of our knowledge, this is the first generative approach to edit object compositions in videos. Our approach is simple and training-free, while outperforming state-of-the-art image editing baselines.

For improving image composition and aesthetic quality, most existing methods modulate the captured images by striking out redundant content near the image borders. However, such image cropping methods are limited in the range of image views. Some methods have been suggested to extrapolate the images and predict cropping boxes from the extrapolated image. Nonetheless, the synthesized extrapolated regions may be included in the cropped image, making the image composition result not real and potentially with degraded image quality. In this paper, we circumvent this issue by presenting a joint framework for both unbounded recommendation of camera view and image composition (i.e., UNIC). In this way, the cropped image is a sub-image of the image acquired by the predicted camera view, and thus can be guaranteed to be real and consistent in image quality. Specifically, our framework takes the current camera preview frame as input and provides a recommendation for view adjustment, which contains operations unlimited by the image borders, such as zooming in or out and camera movement. To improve the prediction accuracy of view adjustment prediction, we further extend the field of view by feature extrapolation. After one or several times of view adjustments, our method converges and results in both a camera view and a bounding box showing the image composition recommendation. Extensive experiments are conducted on the datasets constructed upon existing image cropping datasets, showing the effectiveness of our UNIC in unbounded recommendation of camera view and image composition. The source code, dataset, and pretrained models is available at https://github.com/liuxiaoyu1104/UNIC.

In physics and engineering literature, the distribution of the excursion-above-zero time distribution (exceedance distribution) for a stationary Gaussian process has been approximated by a stationary switching process with independently distributed switching times. The approach matched the covariance of the clipped Gaussian process with the one for the stationary switching process and the distribution of the latter was used as the so-called independent interval approximation (IIA). The approach successfully assessed the persistency exponent for many physically important processes but left an unanswered question when such an approach leads to a mathematically meaningful and proper exceedance distribution. Here we address this question by proposing an alternative matching of the expected values of the clipped Slepian process and the corresponding switched process initiated at the origin. The method has allowed resolving the mathematical correctness of the matching method for a large subclass of the Gaussian processes with monotonic covariance, for which we provide a sufficient condition for the validity of the IIA. Within this class, the IIA produces a valid distribution for the excursion time and is represented in an explicit stochastic form that connects directly to the covariance of the underlying Gaussian process. We compare the excursion level distributions as well as the corresponding persistency exponents obtained through the IIA method with numerically computed exact distributions, and the simulated distribution for several important Gaussian models. We also argue that for stationary Gaussian processes with a non-monotonic covariance, the IIA fails and should not be used.

We consider the problem of approximating a function from L^2 by an element of a given m-dimensional space V_m, associated with some feature map varphi, using evaluations of the function at random points x_1,dots,x_n. After recalling some results on optimal weighted least-squares using independent and identically distributed points, we consider weighted least-squares using projection determinantal point processes (DPP) or volume sampling. These distributions introduce dependence between the points that promotes diversity in the selected features varphi(x_i). We first provide a generalized version of volume-rescaled sampling yielding quasi-optimality results in expectation with a number of samples n = O(mlog(m)), that means that the expected L^2 error is bounded by a constant times the best approximation error in L^2. Also, further assuming that the function is in some normed vector space H continuously embedded in L^2, we further prove that the approximation is almost surely bounded by the best approximation error measured in the H-norm. This includes the cases of functions from L^infty or reproducing kernel Hilbert spaces. Finally, we present an alternative strategy consisting in using independent repetitions of projection DPP (or volume sampling), yielding similar error bounds as with i.i.d. or volume sampling, but in practice with a much lower number of samples. Numerical experiments illustrate the performance of the different strategies.

Large models training is plagued by the intense compute cost and limited hardware memory. A practical solution is low-precision representation but is troubled by loss in numerical accuracy and unstable training rendering the model less useful. We argue that low-precision floating points can perform well provided the error is properly compensated at the critical locations in the training process. We propose Collage which utilizes multi-component float representation in low-precision to accurately perform operations with numerical errors accounted. To understand the impact of imprecision to training, we propose a simple and novel metric which tracks the lost information during training as well as differentiates various precision strategies. Our method works with commonly used low-precision such as half-precision (16-bit floating points) and can be naturally extended to work with even lower precision such as 8-bit. Experimental results show that pre-training using Collage removes the requirement of using 32-bit floating-point copies of the model and attains similar/better training performance compared to (16, 32)-bit mixed-precision strategy, with up to 3.7times speedup and sim 15% to 23% less memory usage in practice.

Earth system models suffer from various structural and parametric errors in their representation of nonlinear, multi-scale processes, leading to uncertainties in their long-term projections. The effects of many of these errors (particularly those due to fast physics) can be quantified in short-term simulations, e.g., as differences between the predicted and observed states (analysis increments). With the increase in the availability of high-quality observations and simulations, learning nudging from these increments to correct model errors has become an active research area. However, most studies focus on using neural networks, which while powerful, are hard to interpret, are data-hungry, and poorly generalize out-of-distribution. Here, we show the capabilities of Model Error Discovery with Interpretability and Data Assimilation (MEDIDA), a general, data-efficient framework that uses sparsity-promoting equation-discovery techniques to learn model errors from analysis increments. Using two-layer quasi-geostrophic turbulence as the test case, MEDIDA is shown to successfully discover various linear and nonlinear structural/parametric errors when full observations are available. Discovery from spatially sparse observations is found to require highly accurate interpolation schemes. While NNs have shown success as interpolators in recent studies, here, they are found inadequate due to their inability to accurately represent small scales, a phenomenon known as spectral bias. We show that a general remedy, adding a random Fourier feature layer to the NN, resolves this issue enabling MEDIDA to successfully discover model errors from sparse observations. These promising results suggest that with further development, MEDIDA could be scaled up to models of the Earth system and real observations.

Diffusion models excel at capturing the natural design spaces of images, molecules, DNA, RNA, and protein sequences. However, rather than merely generating designs that are natural, we often aim to optimize downstream reward functions while preserving the naturalness of these design spaces. Existing methods for achieving this goal often require ``differentiable'' proxy models (e.g., classifier guidance or DPS) or involve computationally expensive fine-tuning of diffusion models (e.g., classifier-free guidance, RL-based fine-tuning). In our work, we propose a new method to address these challenges. Our algorithm is an iterative sampling method that integrates soft value functions, which looks ahead to how intermediate noisy states lead to high rewards in the future, into the standard inference procedure of pre-trained diffusion models. Notably, our approach avoids fine-tuning generative models and eliminates the need to construct differentiable models. This enables us to (1) directly utilize non-differentiable features/reward feedback, commonly used in many scientific domains, and (2) apply our method to recent discrete diffusion models in a principled way. Finally, we demonstrate the effectiveness of our algorithm across several domains, including image generation, molecule generation, and DNA/RNA sequence generation. The code is available at https://github.com/masa-ue/SVDD{https://github.com/masa-ue/SVDD}.

In this work, we present a variety of novel information-theoretic generalization bounds for learning algorithms, from the supersample setting of Steinke & Zakynthinou (2020)-the setting of the "conditional mutual information" framework. Our development exploits projecting the loss pair (obtained from a training instance and a testing instance) down to a single number and correlating loss values with a Rademacher sequence (and its shifted variants). The presented bounds include square-root bounds, fast-rate bounds, including those based on variance and sharpness, and bounds for interpolating algorithms etc. We show theoretically or empirically that these bounds are tighter than all information-theoretic bounds known to date on the same supersample setting.

We develop a framework for non-asymptotic analysis of deterministic samplers used for diffusion generative modeling. Several recent works have analyzed stochastic samplers using tools like Girsanov's theorem and a chain rule variant of the interpolation argument. Unfortunately, these techniques give vacuous bounds when applied to deterministic samplers. We give a new operational interpretation for deterministic sampling by showing that one step along the probability flow ODE can be expressed as two steps: 1) a restoration step that runs gradient ascent on the conditional log-likelihood at some infinitesimally previous time, and 2) a degradation step that runs the forward process using noise pointing back towards the current iterate. This perspective allows us to extend denoising diffusion implicit models to general, non-linear forward processes. We then develop the first polynomial convergence bounds for these samplers under mild conditions on the data distribution.

We develop a method to generate predictive regions that cover a multivariate response variable with a user-specified probability. Our work is composed of two components. First, we use a deep generative model to learn a representation of the response that has a unimodal distribution. Existing multiple-output quantile regression approaches are effective in such cases, so we apply them on the learned representation, and then transform the solution to the original space of the response. This process results in a flexible and informative region that can have an arbitrary shape, a property that existing methods lack. Second, we propose an extension of conformal prediction to the multivariate response setting that modifies any method to return sets with a pre-specified coverage level. The desired coverage is theoretically guaranteed in the finite-sample case for any distribution. Experiments conducted on both real and synthetic data show that our method constructs regions that are significantly smaller compared to existing techniques.

Diffusion models have achieved remarkable image generation quality surpassing previous generative models. However, a notable limitation of diffusion models, in comparison to GANs, is their difficulty in smoothly interpolating between two image samples, due to their highly unstructured latent space. Such a smooth interpolation is intriguing as it naturally serves as a solution for the image morphing task with many applications. In this work, we present DiffMorpher, the first approach enabling smooth and natural image interpolation using diffusion models. Our key idea is to capture the semantics of the two images by fitting two LoRAs to them respectively, and interpolate between both the LoRA parameters and the latent noises to ensure a smooth semantic transition, where correspondence automatically emerges without the need for annotation. In addition, we propose an attention interpolation and injection technique and a new sampling schedule to further enhance the smoothness between consecutive images. Extensive experiments demonstrate that DiffMorpher achieves starkly better image morphing effects than previous methods across a variety of object categories, bridging a critical functional gap that distinguished diffusion models from GANs.

In this work, we focus on a fractional differential equation in Riesz form discretized by a polynomial B-spline collocation method. For an arbitrary polynomial degree p, we show that the resulting coefficient matrices possess a Toeplitz-like structure. We investigate their spectral properties via their symbol and we prove that, like for second order differential problems, also in this case the given matrices are ill-conditioned both in the low and high frequencies for large p. More precisely, in the fractional scenario the symbol has a single zero at 0 of order α, with α the fractional derivative order that ranges from 1 to 2, and it presents an exponential decay to zero at π for increasing p that becomes faster as α approaches 1. This translates in a mitigated conditioning in the low frequencies and in a deterioration in the high frequencies when compared to second order problems. Furthermore, the derivation of the symbol reveals another similarity of our problem with a classical diffusion problem. Since the entries of the coefficient matrices are defined as evaluations of fractional derivatives of the B-spline basis at the collocation points, we are able to express the central entries of the coefficient matrix as inner products of two fractional derivatives of cardinal B-splines. Finally, we perform a numerical study of the approximation behavior of polynomial B-spline collocation. This study suggests that, in line with non-fractional diffusion problems, the approximation order for smooth solutions in the fractional case is p+2-α for even p, and p+1-α for odd p.

We propose Gaussian Frosting, a novel mesh-based representation for high-quality rendering and editing of complex 3D effects in real-time. Our approach builds on the recent 3D Gaussian Splatting framework, which optimizes a set of 3D Gaussians to approximate a radiance field from images. We propose first extracting a base mesh from Gaussians during optimization, then building and refining an adaptive layer of Gaussians with a variable thickness around the mesh to better capture the fine details and volumetric effects near the surface, such as hair or grass. We call this layer Gaussian Frosting, as it resembles a coating of frosting on a cake. The fuzzier the material, the thicker the frosting. We also introduce a parameterization of the Gaussians to enforce them to stay inside the frosting layer and automatically adjust their parameters when deforming, rescaling, editing or animating the mesh. Our representation allows for efficient rendering using Gaussian splatting, as well as editing and animation by modifying the base mesh. We demonstrate the effectiveness of our method on various synthetic and real scenes, and show that it outperforms existing surface-based approaches. We will release our code and a web-based viewer as additional contributions. Our project page is the following: https://anttwo.github.io/frosting/

The interdiffusion coefficients are estimated either following the Wagner's method expressed with respect to the composition (mol or atomic fraction) normalized variable after considering the molar volume variation or the den Broeder's method expressed with respect to the concentration (composition divided by the molar volume) normalized variable. On the other hand, the relations for estimation of the intrinsic diffusion coefficients of components as established by van Loo and integrated diffusion coefficients in a phase with narrow homogeneity range as established by Wagner are currently available with respect to the composition normalized variable only. In this study, we have first derived the relation proposed by den Broeder following the line of treatment proposed by Wagner. Further, the relations for estimation of the intrinsic diffusion coefficients of the components and integrated interdiffusion coefficient are established with respect to the concentration normalized variable, which were not available earlier. The veracity of these methods is examined based on the estimation of data in Ni-Pd, Ni-Al and Cu-Sn systems. Our analysis indicates that both the approaches are logically correct and there is small difference in the estimated data in these systems although a higher difference could be found in other systems. The integrated interdiffusion coefficients with respect to the concentration (or concentration normalized variable) can only be estimated considering the ideal molar volume variation. This might be drawback in certain practical systems.

Recent progress in neural rendering has brought forth pioneering methods, such as NeRF and Gaussian Splatting, which revolutionize view rendering across various domains like AR/VR, gaming, and content creation. While these methods excel at interpolating {\em within the training data}, the challenge of generalizing to new scenes and objects from very sparse views persists. Specifically, modeling 3D humans from sparse views presents formidable hurdles due to the inherent complexity of human geometry, resulting in inaccurate reconstructions of geometry and textures. To tackle this challenge, this paper leverages recent advancements in Gaussian Splatting and introduces a new method to learn generalizable human Gaussians that allows photorealistic and accurate view-rendering of a new human subject from a limited set of sparse views in a feed-forward manner. A pivotal innovation of our approach involves reformulating the learning of 3D Gaussian parameters into a regression process defined on the 2D UV space of a human template, which allows leveraging the strong geometry prior and the advantages of 2D convolutions. In addition, a multi-scaffold is proposed to effectively represent the offset details. Our method outperforms recent methods on both within-dataset generalization as well as cross-dataset generalization settings.

In deep learning, often the training process finds an interpolator (a solution with 0 training loss), but the test loss is still low. This phenomenon, known as benign overfitting, is a major mystery that received a lot of recent attention. One common mechanism for benign overfitting is implicit regularization, where the training process leads to additional properties for the interpolator, often characterized by minimizing certain norms. However, even for a simple sparse linear regression problem y = beta^{*top} x +xi with sparse beta^*, neither minimum ell_1 or ell_2 norm interpolator gives the optimal test loss. In this work, we give a different parametrization of the model which leads to a new implicit regularization effect that combines the benefit of ell_1 and ell_2 interpolators. We show that training our new model via gradient descent leads to an interpolator with near-optimal test loss. Our result is based on careful analysis of the training dynamics and provides another example of implicit regularization effect that goes beyond norm minimization.

Polar slice sampling (Roberts & Rosenthal, 2002) is a Markov chain approach for approximate sampling of distributions that is difficult, if not impossible, to implement efficiently, but behaves provably well with respect to the dimension. By updating the directional and radial components of chain iterates separately, we obtain a family of samplers that mimic polar slice sampling, and yet can be implemented efficiently. Numerical experiments in a variety of settings indicate that our proposed algorithm outperforms the two most closely related approaches, elliptical slice sampling (Murray et al., 2010) and hit-and-run uniform slice sampling (MacKay, 2003). We prove the well-definedness and convergence of our methods under suitable assumptions on the target distribution.

Mixup is a powerful data augmentation method that interpolates between two or more examples in the input or feature space and between the corresponding target labels. Many recent mixup methods focus on cutting and pasting two or more objects into one image, which is more about efficient processing than interpolation. However, how to best interpolate images is not well defined. In this sense, mixup has been connected to autoencoders, because often autoencoders "interpolate well", for instance generating an image that continuously deforms into another. In this work, we revisit mixup from the interpolation perspective and introduce AlignMix, where we geometrically align two images in the feature space. The correspondences allow us to interpolate between two sets of features, while keeping the locations of one set. Interestingly, this gives rise to a situation where mixup retains mostly the geometry or pose of one image and the texture of the other, connecting it to style transfer. More than that, we show that an autoencoder can still improve representation learning under mixup, without the classifier ever seeing decoded images. AlignMix outperforms state-of-the-art mixup methods on five different benchmarks.

Many problems in astrophysics cover multiple orders of magnitude in spatial and temporal scales. While simulating systems that experience rapid changes in these conditions, it is essential to adapt the (time-) step size to capture the behavior of the system during those rapid changes and use a less accurate time step at other, less demanding, moments. We encounter three problems with traditional methods. Firstly, making such changes requires expert knowledge of the astrophysics as well as of the details of the numerical implementation. Secondly, some parameters that determine the time-step size are fixed throughout the simulation, which means that they do not adapt to the rapidly changing conditions of the problem. Lastly, we would like the choice of time-step size to balance accuracy and computation effort. We address these challenges with Reinforcement Learning by training it to select the time-step size dynamically. We use the integration of a system of three equal-mass bodies that move due to their mutual gravity as an example of its application. With our method, the selected integration parameter adapts to the specific requirements of the problem, both in terms of computation time and accuracy while eliminating the expert knowledge needed to set up these simulations. Our method produces results competitive to existing methods and improve the results found with the most commonly-used values of time-step parameter. This method can be applied to other integrators without further retraining. We show that this extrapolation works for variable time-step integrators but does not perform to the desired accuracy for fixed time-step integrators.

Diffusion models have demonstrated remarkable generation quality but at the cost of numerous function evaluations. Recently, advanced ODE-based solvers have been developed to mitigate the substantial computational demands of reverse-diffusion solving under limited sampling steps. However, these solvers, heavily inspired by Adams-like multistep methods, rely solely on t-related Lagrange interpolation. We show that t-related Lagrange interpolation is suboptimal for diffusion model and reveal a compact search space comprised of time steps and solver coefficients. Building on our analysis, we propose a novel differentiable solver search algorithm to identify more optimal solver. Equipped with the searched solver, rectified-flow models, e.g., SiT-XL/2 and FlowDCN-XL/2, achieve FID scores of 2.40 and 2.35, respectively, on ImageNet256 with only 10 steps. Meanwhile, DDPM model, DiT-XL/2, reaches a FID score of 2.33 with only 10 steps. Notably, our searched solver outperforms traditional solvers by a significant margin. Moreover, our searched solver demonstrates generality across various model architectures, resolutions, and model sizes.

We discuss the numerical solution of initial value problems for varepsilon^2,varphi''+a(x),varphi=0 in the highly oscillatory regime, i.e., with a(x)>0 and 0<varepsilonll 1. We analyze and implement an approximate solution based on the well-known WKB-ansatz. The resulting approximation error is of magnitude O(varepsilon^{N}) where N refers to the truncation order of the underlying asymptotic series. When the optimal truncation order N_{opt} is chosen, the error behaves like O(varepsilon^{-2}exp(-cvarepsilon^{-1})) with some c>0.

In this paper we provide a new method to certify that a nearby polynomial system has a singular isolated root with a prescribed multiplicity structure. More precisely, given a polynomial system f =(f_1, ldots, f_N)in C[x_1, ldots, x_n]^N, we present a Newton iteration on an extended deflated system that locally converges, under regularity conditions, to a small deformation of f such that this deformed system has an exact singular root. The iteration simultaneously converges to the coordinates of the singular root and the coefficients of the so called inverse system that describes the multiplicity structure at the root. We use $alpha$-theory test to certify the quadratic convergence, and togive bounds on the size of the deformation and on the approximation error. The approach relies on an analysis of the punctual Hilbert scheme, for which we provide a new description. We show in particular that some of its strata can be rationally parametrized and exploit these parametrizations in the certification. We show in numerical experimentation how the approximate inverse system can be computed as a starting point of the Newton iterations and the fast numerical convergence to the singular root with its multiplicity structure, certified by our criteria.

Denoising diffusion models have enabled high-quality image generation and editing. We present a method to localize the desired edit region implicit in a text instruction. We leverage InstructPix2Pix (IP2P) and identify the discrepancy between IP2P predictions with and without the instruction. This discrepancy is referred to as the relevance map. The relevance map conveys the importance of changing each pixel to achieve the edits, and is used to to guide the modifications. This guidance ensures that the irrelevant pixels remain unchanged. Relevance maps are further used to enhance the quality of text-guided editing of 3D scenes in the form of neural radiance fields. A field is trained on relevance maps of training views, denoted as the relevance field, defining the 3D region within which modifications should be made. We perform iterative updates on the training views guided by rendered relevance maps from the relevance field. Our method achieves state-of-the-art performance on both image and NeRF editing tasks. Project page: https://ashmrz.github.io/WatchYourSteps/

Diffusion inversion is the problem of taking an image and a text prompt that describes it and finding a noise latent that would generate the image. Most current inversion techniques operate by approximately solving an implicit equation and may converge slowly or yield poor reconstructed images. Here, we formulate the problem as finding the roots of an implicit equation and design a method to solve it efficiently. Our solution is based on Newton-Raphson (NR), a well-known technique in numerical analysis. A naive application of NR may be computationally infeasible and tends to converge to incorrect solutions. We describe an efficient regularized formulation that converges quickly to a solution that provides high-quality reconstructions. We also identify a source of inconsistency stemming from prompt conditioning during the inversion process, which significantly degrades the inversion quality. To address this, we introduce a prompt-aware adjustment of the encoding, effectively correcting this issue. Our solution, Regularized Newton-Raphson Inversion, inverts an image within 0.5 sec for latent consistency models, opening the door for interactive image editing. We further demonstrate improved results in image interpolation and generation of rare objects.

We present a novel deep learning approach to approximate the solution of large, sparse, symmetric, positive-definite linear systems of equations. These systems arise from many problems in applied science, e.g., in numerical methods for partial differential equations. Algorithms for approximating the solution to these systems are often the bottleneck in problems that require their solution, particularly for modern applications that require many millions of unknowns. Indeed, numerical linear algebra techniques have been investigated for many decades to alleviate this computational burden. Recently, data-driven techniques have also shown promise for these problems. Motivated by the conjugate gradients algorithm that iteratively selects search directions for minimizing the matrix norm of the approximation error, we design an approach that utilizes a deep neural network to accelerate convergence via data-driven improvement of the search directions. Our method leverages a carefully chosen convolutional network to approximate the action of the inverse of the linear operator up to an arbitrary constant. We train the network using unsupervised learning with a loss function equal to the L^2 difference between an input and the system matrix times the network evaluation, where the unspecified constant in the approximate inverse is accounted for. We demonstrate the efficacy of our approach on spatially discretized Poisson equations with millions of degrees of freedom arising in computational fluid dynamics applications. Unlike state-of-the-art learning approaches, our algorithm is capable of reducing the linear system residual to a given tolerance in a small number of iterations, independent of the problem size. Moreover, our method generalizes effectively to various systems beyond those encountered during training.

We investigate the use of a stratified sampling approach for LIME Image, a popular model-agnostic explainable AI method for computer vision tasks, in order to reduce the artifacts generated by typical Monte Carlo sampling. Such artifacts are due to the undersampling of the dependent variable in the synthetic neighborhood around the image being explained, which may result in inadequate explanations due to the impossibility of fitting a linear regressor on the sampled data. We then highlight a connection with the Shapley theory, where similar arguments about undersampling and sample relevance were suggested in the past. We derive all the formulas and adjustment factors required for an unbiased stratified sampling estimator. Experiments show the efficacy of the proposed approach.

The combination of deep learning, artist-curated scans, and Implicit Functions (IF), is enabling the creation of detailed, clothed, 3D humans from images. However, existing methods are far from perfect. IF-based methods recover free-form geometry, but produce disembodied limbs or degenerate shapes for novel poses or clothes. To increase robustness for these cases, existing work uses an explicit parametric body model to constrain surface reconstruction, but this limits the recovery of free-form surfaces such as loose clothing that deviates from the body. What we want is a method that combines the best properties of implicit representation and explicit body regularization. To this end, we make two key observations: (1) current networks are better at inferring detailed 2D maps than full-3D surfaces, and (2) a parametric model can be seen as a "canvas" for stitching together detailed surface patches. Based on these, our method, ECON, has three main steps: (1) It infers detailed 2D normal maps for the front and back side of a clothed person. (2) From these, it recovers 2.5D front and back surfaces, called d-BiNI, that are equally detailed, yet incomplete, and registers these w.r.t. each other with the help of a SMPL-X body mesh recovered from the image. (3) It "inpaints" the missing geometry between d-BiNI surfaces. If the face and hands are noisy, they can optionally be replaced with the ones of SMPL-X. As a result, ECON infers high-fidelity 3D humans even in loose clothes and challenging poses. This goes beyond previous methods, according to the quantitative evaluation on the CAPE and Renderpeople datasets. Perceptual studies also show that ECON's perceived realism is better by a large margin. Code and models are available for research purposes at econ.is.tue.mpg.de

Text-driven image generation methods have shown impressive results recently, allowing casual users to generate high quality images by providing textual descriptions. However, similar capabilities for editing existing images are still out of reach. Text-driven image editing methods usually need edit masks, struggle with edits that require significant visual changes and cannot easily keep specific details of the edited portion. In this paper we make the observation that image-generation models can be converted to image-editing models simply by fine-tuning them on a single image. We also show that initializing the stochastic sampler with a noised version of the base image before the sampling and interpolating relevant details from the base image after sampling further increase the quality of the edit operation. Combining these observations, we propose UniTune, a novel image editing method. UniTune gets as input an arbitrary image and a textual edit description, and carries out the edit while maintaining high fidelity to the input image. UniTune does not require additional inputs, like masks or sketches, and can perform multiple edits on the same image without retraining. We test our method using the Imagen model in a range of different use cases. We demonstrate that it is broadly applicable and can perform a surprisingly wide range of expressive editing operations, including those requiring significant visual changes that were previously impossible.

We present a generalizable novel view synthesis method which enables modifying the visual appearance of an observed scene so rendered views match a target weather or lighting condition without any scene specific training or access to reference views at the target condition. Our method is based on a pretrained generalizable transformer architecture and is fine-tuned on synthetically generated scenes under different appearance conditions. This allows for rendering novel views in a consistent manner for 3D scenes that were not included in the training set, along with the ability to (i) modify their appearance to match the target condition and (ii) smoothly interpolate between different conditions. Experiments on real and synthetic scenes show that our method is able to generate 3D consistent renderings while making realistic appearance changes, including qualitative and quantitative comparisons. Please refer to our project page for video results: https://ava-nvs.github.io/

The past few years have witnessed the great success of Diffusion models~(DMs) in generating high-fidelity samples in generative modeling tasks. A major limitation of the DM is its notoriously slow sampling procedure which normally requires hundreds to thousands of time discretization steps of the learned diffusion process to reach the desired accuracy. Our goal is to develop a fast sampling method for DMs with a much less number of steps while retaining high sample quality. To this end, we systematically analyze the sampling procedure in DMs and identify key factors that affect the sample quality, among which the method of discretization is most crucial. By carefully examining the learned diffusion process, we propose Diffusion Exponential Integrator Sampler~(DEIS). It is based on the Exponential Integrator designed for discretizing ordinary differential equations (ODEs) and leverages a semilinear structure of the learned diffusion process to reduce the discretization error. The proposed method can be applied to any DMs and can generate high-fidelity samples in as few as 10 steps. In our experiments, it takes about 3 minutes on one A6000 GPU to generate 50k images from CIFAR10. Moreover, by directly using pre-trained DMs, we achieve the state-of-art sampling performance when the number of score function evaluation~(NFE) is limited, e.g., 4.17 FID with 10 NFEs, 3.37 FID, and 9.74 IS with only 15 NFEs on CIFAR10. Code is available at https://github.com/qsh-zh/deis

We investigate the problem of automatically placing an object into a background image for image compositing. Given a background image and a segmented object, the goal is to train a model to predict plausible placements (location and scale) of the object for compositing. The quality of the composite image highly depends on the predicted location/scale. Existing works either generate candidate bounding boxes or apply sliding-window search using global representations from background and object images, which fail to model local information in background images. However, local clues in background images are important to determine the compatibility of placing the objects with certain locations/scales. In this paper, we propose to learn the correlation between object features and all local background features with a transformer module so that detailed information can be provided on all possible location/scale configurations. A sparse contrastive loss is further proposed to train our model with sparse supervision. Our new formulation generates a 3D heatmap indicating the plausibility of all location/scale combinations in one network forward pass, which is over 10 times faster than the previous sliding-window method. It also supports interactive search when users provide a pre-defined location or scale. The proposed method can be trained with explicit annotation or in a self-supervised manner using an off-the-shelf inpainting model, and it outperforms state-of-the-art methods significantly. The user study shows that the trained model generalizes well to real-world images with diverse challenging scenes and object categories.

A popular approach to sample a diffusion-based generative model is to solve an ordinary differential equation (ODE). In existing samplers, the coefficients of the ODE solvers are pre-determined by the ODE formulation, the reverse discrete timesteps, and the employed ODE methods. In this paper, we consider accelerating several popular ODE-based sampling processes (including EDM, DDIM, and DPM-Solver) by optimizing certain coefficients via improved integration approximation (IIA). We propose to minimize, for each time step, a mean squared error (MSE) function with respect to the selected coefficients. The MSE is constructed by applying the original ODE solver for a set of fine-grained timesteps, which in principle provides a more accurate integration approximation in predicting the next diffusion state. The proposed IIA technique does not require any change of a pre-trained model, and only introduces a very small computational overhead for solving a number of quadratic optimization problems. Extensive experiments show that considerably better FID scores can be achieved by using IIA-EDM, IIA-DDIM, and IIA-DPM-Solver than the original counterparts when the neural function evaluation (NFE) is small (i.e., less than 25).

We extend Textual Inversion to learn pseudo-words that represent a concept at different resolutions. This allows us to generate images that use the concept with different levels of detail and also to manipulate different resolutions using language. Once learned, the user can generate images at different levels of agreement to the original concept; "A photo of S^*(0)" produces the exact object while the prompt "A photo of S^*(0.8)" only matches the rough outlines and colors. Our framework allows us to generate images that use different resolutions of an image (e.g. details, textures, styles) as separate pseudo-words that can be composed in various ways. We open-soure our code in the following URL: https://github.com/giannisdaras/multires_textual_inversion

We derive a minimalist but powerful deterministic denoising-diffusion model. While denoising diffusion has shown great success in many domains, its underlying theory remains largely inaccessible to non-expert users. Indeed, an understanding of graduate-level concepts such as Langevin dynamics or score matching appears to be required to grasp how it works. We propose an alternative approach that requires no more than undergrad calculus and probability. We consider two densities and observe what happens when random samples from these densities are blended (linearly interpolated). We show that iteratively blending and deblending samples produces random paths between the two densities that converge toward a deterministic mapping. This mapping can be evaluated with a neural network trained to deblend samples. We obtain a model that behaves like deterministic denoising diffusion: it iteratively maps samples from one density (e.g., Gaussian noise) to another (e.g., cat images). However, compared to the state-of-the-art alternative, our model is simpler to derive, simpler to implement, more numerically stable, achieves higher quality results in our experiments, and has interesting connections to computer graphics.

Traditional image detail enhancement is local filter-based or global filter-based. In both approaches, the original image is first divided into the base layer and the detail layer, and then the enhanced image is obtained by amplifying the detail layer. Our method is different, and its innovation lies in the special way to get the image detail layer. The detail layer in our method is obtained by updating the residual features, and the updating mechanism is usually based on searching and matching similar patches. However, due to the diversity of image texture features, perfect matching is often not possible. In this paper, the process of searching and matching is treated as a thermodynamic process, where the Metropolis theorem can minimize the internal energy and get the global optimal solution of this task, that is, to find a more suitable feature for a better detail enhancement performance. Extensive experiments have proven that our algorithm can achieve better results in quantitative metrics testing and visual effects evaluation. The source code can be obtained from the link.

Given a set of K probability densities, we consider the multimarginal generative modeling problem of learning a joint distribution that recovers these densities as marginals. The structure of this joint distribution should identify multi-way correspondences among the prescribed marginals. We formalize an approach to this task within a generalization of the stochastic interpolant framework, leading to efficient learning algorithms built upon dynamical transport of measure. Our generative models are defined by velocity and score fields that can be characterized as the minimizers of simple quadratic objectives, and they are defined on a simplex that generalizes the time variable in the usual dynamical transport framework. The resulting transport on the simplex is influenced by all marginals, and we show that multi-way correspondences can be extracted. The identification of such correspondences has applications to style transfer, algorithmic fairness, and data decorruption. In addition, the multimarginal perspective enables an efficient algorithm for reducing the dynamical transport cost in the ordinary two-marginal setting. We demonstrate these capacities with several numerical examples.

The success of image generative models has enabled us to build methods that can edit images based on text or other user input. However, these methods are bespoke, imprecise, require additional information, or are limited to only 2D image edits. We present GeoDiffuser, a zero-shot optimization-based method that unifies common 2D and 3D image-based object editing capabilities into a single method. Our key insight is to view image editing operations as geometric transformations. We show that these transformations can be directly incorporated into the attention layers in diffusion models to implicitly perform editing operations. Our training-free optimization method uses an objective function that seeks to preserve object style but generate plausible images, for instance with accurate lighting and shadows. It also inpaints disoccluded parts of the image where the object was originally located. Given a natural image and user input, we segment the foreground object using SAM and estimate a corresponding transform which is used by our optimization approach for editing. GeoDiffuser can perform common 2D and 3D edits like object translation, 3D rotation, and removal. We present quantitative results, including a perceptual study, that shows how our approach is better than existing methods. Visit https://ivl.cs.brown.edu/research/geodiffuser.html for more information.

Recent years have witnessed significant progress in developing efficient training and fast sampling approaches for diffusion models. A recent remarkable advancement is the use of stochastic differential equations (SDEs) to describe data perturbation and generative modeling in a unified mathematical framework. In this paper, we reveal several intriguing geometric structures of diffusion models and contribute a simple yet powerful interpretation to their sampling dynamics. Through carefully inspecting a popular variance-exploding SDE and its marginal-preserving ordinary differential equation (ODE) for sampling, we discover that the data distribution and the noise distribution are smoothly connected with an explicit, quasi-linear sampling trajectory, and another implicit denoising trajectory, which even converges faster in terms of visual quality. We also establish a theoretical relationship between the optimal ODE-based sampling and the classic mean-shift (mode-seeking) algorithm, with which we can characterize the asymptotic behavior of diffusion models and identify the score deviation. These new geometric observations enable us to improve previous sampling algorithms, re-examine latent interpolation, as well as re-explain the working principles of distillation-based fast sampling techniques.

Lebesgue curve is a space-filling curve that fills the unit square through linear interpolation. In this study, we generalise Lebesgue's construction to generate space-filling curves from any given planar substitution satisfying a mild condition. The generated space-filling curves for some known substitutions are elucidated. Some of those substitutions further induce relatively dense fractal-like sets in the plane, whenever some additional assumptions are met.

Photorealistic image stylization concerns transferring style of a reference photo to a content photo with the constraint that the stylized photo should remain photorealistic. While several photorealistic image stylization methods exist, they tend to generate spatially inconsistent stylizations with noticeable artifacts. In this paper, we propose a method to address these issues. The proposed method consists of a stylization step and a smoothing step. While the stylization step transfers the style of the reference photo to the content photo, the smoothing step ensures spatially consistent stylizations. Each of the steps has a closed-form solution and can be computed efficiently. We conduct extensive experimental validations. The results show that the proposed method generates photorealistic stylization outputs that are more preferred by human subjects as compared to those by the competing methods while running much faster. Source code and additional results are available at https://github.com/NVIDIA/FastPhotoStyle .

Given a sample of size N, it is often useful to select a subsample of smaller size n<N to be used for statistical estimation or learning. Such a data selection step is useful to reduce the requirements of data labeling and the computational complexity of learning. We assume to be given N unlabeled samples {{boldsymbol x}_i}_{ile N}, and to be given access to a `surrogate model' that can predict labels y_i better than random guessing. Our goal is to select a subset of the samples, to be denoted by {{boldsymbol x}_i}_{iin G}, of size |G|=n<N. We then acquire labels for this set and we use them to train a model via regularized empirical risk minimization. By using a mixture of numerical experiments on real and synthetic data, and mathematical derivations under low- and high- dimensional asymptotics, we show that: (i)~Data selection can be very effective, in particular beating training on the full sample in some cases; (ii)~Certain popular choices in data selection methods (e.g. unbiased reweighted subsampling, or influence function-based subsampling) can be substantially suboptimal.

In this paper, we consider the problem of Iterative Machine Teaching (IMT), where the teacher provides examples to the learner iteratively such that the learner can achieve fast convergence to a target model. However, existing IMT algorithms are solely based on parameterized families of target models. They mainly focus on convergence in the parameter space, resulting in difficulty when the target models are defined to be functions without dependency on parameters. To address such a limitation, we study a more general task -- Nonparametric Iterative Machine Teaching (NIMT), which aims to teach nonparametric target models to learners in an iterative fashion. Unlike parametric IMT that merely operates in the parameter space, we cast NIMT as a functional optimization problem in the function space. To solve it, we propose both random and greedy functional teaching algorithms. We obtain the iterative teaching dimension (ITD) of the random teaching algorithm under proper assumptions, which serves as a uniform upper bound of ITD in NIMT. Further, the greedy teaching algorithm has a significantly lower ITD, which reaches a tighter upper bound of ITD in NIMT. Finally, we verify the correctness of our theoretical findings with extensive experiments in nonparametric scenarios.

We introduce infty-Diff, a generative diffusion model which directly operates on infinite resolution data. By randomly sampling subsets of coordinates during training and learning to denoise the content at those coordinates, a continuous function is learned that allows sampling at arbitrary resolutions. In contrast to other recent infinite resolution generative models, our approach operates directly on the raw data, not requiring latent vector compression for context, using hypernetworks, nor relying on discrete components. As such, our approach achieves significantly higher sample quality, as evidenced by lower FID scores, as well as being able to effectively scale to higher resolutions than the training data while retaining detail.

We explore the integration of Kolmogorov Networks (KANs) into molecular dynamics (MD) simulations to improve interatomic potentials. We propose that widely used potentials, such as the Lennard-Jones (LJ) potential, the embedded atom model (EAM), and artificial neural network (ANN) potentials, can be interpreted within the KAN framework. Specifically, we demonstrate that the descriptors for ANN potentials, typically constructed using polynomials, can be redefined using KAN's non-linear functions. By employing linear or cubic spline interpolations for these KAN functions, we show that the computational cost of evaluating ANN potentials and their derivatives is reduced.

Textured 3D morphing creates smooth and plausible interpolation sequences between two 3D objects, focusing on transitions in both shape and texture. This is important for creative applications like visual effects in filmmaking. Previous methods rely on establishing point-to-point correspondences and determining smooth deformation trajectories, which inherently restrict them to shape-only morphing on untextured, topologically aligned datasets. This restriction leads to labor-intensive preprocessing and poor generalization. To overcome these challenges, we propose a method for 3D regenerative morphing using a 3D diffusion prior. Unlike previous methods that depend on explicit correspondences and deformations, our method eliminates the additional need for obtaining correspondence and uses the 3D diffusion prior to generate morphing. Specifically, we introduce a 3D diffusion model and interpolate the source and target information at three levels: initial noise, model parameters, and condition features. We then explore an Attention Fusion strategy to generate more smooth morphing sequences. To further improve the plausibility of semantic interpolation and the generated 3D surfaces, we propose two strategies: (a) Token Reordering, where we match approximate tokens based on semantic analysis to guide implicit correspondences in the denoising process of the diffusion model, and (b) Low-Frequency Enhancement, where we enhance low-frequency signals in the tokens to improve the quality of generated surfaces. Experimental results show that our method achieves superior smoothness and plausibility in 3D morphing across diverse cross-category object pairs, offering a novel regenerative method for 3D morphing with textured representations.

With the emergence of diffusion models and rapid development in image processing, it has become effortless to generate fancy images in tasks such as style transfer and image editing. However, these impressive image processing approaches face consistency issues in video processing. In this paper, we propose a powerful model-free toolkit called FastBlend to address the consistency problem for video processing. Based on a patch matching algorithm, we design two inference modes, including blending and interpolation. In the blending mode, FastBlend eliminates video flicker by blending the frames within a sliding window. Moreover, we optimize both computational efficiency and video quality according to different application scenarios. In the interpolation mode, given one or more keyframes rendered by diffusion models, FastBlend can render the whole video. Since FastBlend does not modify the generation process of diffusion models, it exhibits excellent compatibility. Extensive experiments have demonstrated the effectiveness of FastBlend. In the blending mode, FastBlend outperforms existing methods for video deflickering and video synthesis. In the interpolation mode, FastBlend surpasses video interpolation and model-based video processing approaches. The source codes have been released on GitHub.

We study the problem of extrapolative controlled generation, i.e., generating sequences with attribute values beyond the range seen in training. This task is of significant importance in automated design, especially drug discovery, where the goal is to design novel proteins that are better (e.g., more stable) than existing sequences. Thus, by definition, the target sequences and their attribute values are out of the training distribution, posing challenges to existing methods that aim to directly generate the target sequence. Instead, in this work, we propose Iterative Controlled Extrapolation (ICE) which iteratively makes local edits to a sequence to enable extrapolation. We train the model on synthetically generated sequence pairs that demonstrate small improvement in the attribute value. Results on one natural language task (sentiment analysis) and two protein engineering tasks (ACE2 stability and AAV fitness) show that ICE considerably outperforms state-of-the-art approaches despite its simplicity. Our code and models are available at: https://github.com/vishakhpk/iter-extrapolation.

Diffusion-weighted magnetic resonance imaging (DW-MRI) can be used to characterise the microstructure of the nervous tissue, e.g. to delineate brain white matter connections in a non-invasive manner via fibre tracking. Magnetic Resonance Imaging (MRI) in high spatial resolution would play an important role in visualising such fibre tracts in a superior manner. However, obtaining an image of such resolution comes at the expense of longer scan time. Longer scan time can be associated with the increase of motion artefacts, due to the patient's psychological and physical conditions. Single Image Super-Resolution (SISR), a technique aimed to obtain high-resolution (HR) details from one single low-resolution (LR) input image, achieved with Deep Learning, is the focus of this study. Compared to interpolation techniques or sparse-coding algorithms, deep learning extracts prior knowledge from big datasets and produces superior MRI images from the low-resolution counterparts. In this research, a deep learning based super-resolution technique is proposed and has been applied for DW-MRI. Images from the IXI dataset have been used as the ground-truth and were artificially downsampled to simulate the low-resolution images. The proposed method has shown statistically significant improvement over the baselines and achieved an SSIM of 0.913pm0.045.

Recent ODE/SDE-based generative models, such as diffusion models, rectified flows, and flow matching, define a generative process as a time reversal of a fixed forward process. Even though these models show impressive performance on large-scale datasets, numerical simulation requires multiple evaluations of a neural network, leading to a slow sampling speed. We attribute the reason to the high curvature of the learned generative trajectories, as it is directly related to the truncation error of a numerical solver. Based on the relationship between the forward process and the curvature, here we present an efficient method of training the forward process to minimize the curvature of generative trajectories without any ODE/SDE simulation. Experiments show that our method achieves a lower curvature than previous models and, therefore, decreased sampling costs while maintaining competitive performance. Code is available at https://github.com/sangyun884/fast-ode.

We show how to obtain improved active learning methods in the agnostic (adversarial noise) setting by combining marginal leverage score sampling with non-independent sampling strategies that promote spatial coverage. In particular, we propose an easily implemented method based on the pivotal sampling algorithm, which we test on problems motivated by learning-based methods for parametric PDEs and uncertainty quantification. In comparison to independent sampling, our method reduces the number of samples needed to reach a given target accuracy by up to 50%. We support our findings with two theoretical results. First, we show that any non-independent leverage score sampling method that obeys a weak one-sided ell_{infty} independence condition (which includes pivotal sampling) can actively learn d dimensional linear functions with O(dlog d) samples, matching independent sampling. This result extends recent work on matrix Chernoff bounds under ell_{infty} independence, and may be of interest for analyzing other sampling strategies beyond pivotal sampling. Second, we show that, for the important case of polynomial regression, our pivotal method obtains an improved bound of O(d) samples.

Despite recent advances in large-scale text-to-image generative models, manipulating real images with these models remains a challenging problem. The main limitations of existing editing methods are that they either fail to perform with consistent quality on a wide range of image edits or require time-consuming hyperparameter tuning or fine-tuning of the diffusion model to preserve the image-specific appearance of the input image. We propose a novel approach that is built upon a modified diffusion sampling process via the guidance mechanism. In this work, we explore the self-guidance technique to preserve the overall structure of the input image and its local regions appearance that should not be edited. In particular, we explicitly introduce layout-preserving energy functions that are aimed to save local and global structures of the source image. Additionally, we propose a noise rescaling mechanism that allows to preserve noise distribution by balancing the norms of classifier-free guidance and our proposed guiders during generation. Such a guiding approach does not require fine-tuning the diffusion model and exact inversion process. As a result, the proposed method provides a fast and high-quality editing mechanism. In our experiments, we show through human evaluation and quantitative analysis that the proposed method allows to produce desired editing which is more preferable by humans and also achieves a better trade-off between editing quality and preservation of the original image. Our code is available at https://github.com/FusionBrainLab/Guide-and-Rescale.

This paper introduces a LArge-scale Video Interpolation Benchmark (LAVIB) for the low-level video task of Video Frame Interpolation (VFI). LAVIB comprises a large collection of high-resolution videos sourced from the web through an automated pipeline with minimal requirements for human verification. Metrics are computed for each video's motion magnitudes, luminance conditions, frame sharpness, and contrast. The collection of videos and the creation of quantitative challenges based on these metrics are under-explored by current low-level video task datasets. In total, LAVIB includes 283K clips from 17K ultra-HD videos, covering 77.6 hours. Benchmark train, val, and test sets maintain similar video metric distributions. Further splits are also created for out-of-distribution (OOD) challenges, with train and test splits including videos of dissimilar attributes.

Hyperparameter optimization (HPO) is concerned with the automated search for the most appropriate hyperparameter configuration (HPC) of a parameterized machine learning algorithm. A state-of-the-art HPO method is Hyperband, which, however, has its own parameters that influence its performance. One of these parameters, the maximal budget, is especially problematic: If chosen too small, the budget needs to be increased in hindsight and, as Hyperband is not incremental by design, the entire algorithm must be re-run. This is not only costly but also comes with a loss of valuable knowledge already accumulated. In this paper, we propose incremental variants of Hyperband that eliminate these drawbacks, and show that these variants satisfy theoretical guarantees qualitatively similar to those for the original Hyperband with the "right" budget. Moreover, we demonstrate their practical utility in experiments with benchmark data sets.

We propose a new approach for generative modeling based on training a neural network to be idempotent. An idempotent operator is one that can be applied sequentially without changing the result beyond the initial application, namely f(f(z))=f(z). The proposed model f is trained to map a source distribution (e.g, Gaussian noise) to a target distribution (e.g. realistic images) using the following objectives: (1) Instances from the target distribution should map to themselves, namely f(x)=x. We define the target manifold as the set of all instances that f maps to themselves. (2) Instances that form the source distribution should map onto the defined target manifold. This is achieved by optimizing the idempotence term, f(f(z))=f(z) which encourages the range of f(z) to be on the target manifold. Under ideal assumptions such a process provably converges to the target distribution. This strategy results in a model capable of generating an output in one step, maintaining a consistent latent space, while also allowing sequential applications for refinement. Additionally, we find that by processing inputs from both target and source distributions, the model adeptly projects corrupted or modified data back to the target manifold. This work is a first step towards a ``global projector'' that enables projecting any input into a target data distribution.

We present a new algorithm to optimize distributions defined implicitly by parameterized stochastic diffusions. Doing so allows us to modify the outcome distribution of sampling processes by optimizing over their parameters. We introduce a general framework for first-order optimization of these processes, that performs jointly, in a single loop, optimization and sampling steps. This approach is inspired by recent advances in bilevel optimization and automatic implicit differentiation, leveraging the point of view of sampling as optimization over the space of probability distributions. We provide theoretical guarantees on the performance of our method, as well as experimental results demonstrating its effectiveness in real-world settings.

Neural fields have become widely used in various fields, from shape representation to neural rendering, and for solving partial differential equations (PDEs). With the advent of hybrid neural field representations like Instant NGP that leverage small MLPs and explicit representations, these models train quickly and can fit large scenes. Yet in many applications like rendering and simulation, hybrid neural fields can cause noticeable and unreasonable artifacts. This is because they do not yield accurate spatial derivatives needed for these downstream applications. In this work, we propose two ways to circumvent these challenges. Our first approach is a post hoc operator that uses local polynomial fitting to obtain more accurate derivatives from pre-trained hybrid neural fields. Additionally, we also propose a self-supervised fine-tuning approach that refines the hybrid neural field to yield accurate derivatives directly while preserving the initial signal. We show applications of our method to rendering, collision simulation, and solving PDEs. We observe that using our approach yields more accurate derivatives, reducing artifacts and leading to more accurate simulations in downstream applications.

Grid-based structures are commonly used to encode explicit features for graphics primitives such as images, signed distance functions (SDF), and neural radiance fields (NeRF) due to their simple implementation. However, in n-dimensional space, calculating the value of a sampled point requires interpolating the values of its 2^n neighboring vertices. The exponential scaling with dimension leads to significant computational overheads. To address this issue, we propose a simplex-based approach for encoding graphics primitives. The number of vertices in a simplex-based structure increases linearly with dimension, making it a more efficient and generalizable alternative to grid-based representations. Using the non-axis-aligned simplicial structure property, we derive and prove a coordinate transformation, simplicial subdivision, and barycentric interpolation scheme for efficient sampling, which resembles transformation procedures in the simplex noise algorithm. Finally, we use hash tables to store multiresolution features of all interest points in the simplicial grid, which are passed into a tiny fully connected neural network to parameterize graphics primitives. We implemented a detailed simplex-based structure encoding algorithm in C++ and CUDA using the methods outlined in our approach. In the 2D image fitting task, the proposed method is capable of fitting a giga-pixel image with 9.4% less time compared to the baseline method proposed by instant-ngp, while maintaining the same quality and compression rate. In the volumetric rendering setup, we observe a maximum 41.2% speedup when the samples are dense enough.

Recent advancements in visualizing deep neural networks provide insights into their structures and mesh extraction from Continuous Piecewise Affine (CPWA) functions. Meanwhile, developments in neural surface representation learning incorporate non-linear positional encoding, addressing issues like spectral bias; however, this poses challenges in applying mesh extraction techniques based on CPWA functions. Focusing on trilinear interpolating methods as positional encoding, we present theoretical insights and an analytical mesh extraction, showing the transformation of hypersurfaces to flat planes within the trilinear region under the eikonal constraint. Moreover, we introduce a method for approximating intersecting points among three hypersurfaces contributing to broader applications. We empirically validate correctness and parsimony through chamfer distance and efficiency, and angular distance, while examining the correlation between the eikonal loss and the planarity of the hypersurfaces.

We present a neural network emulator to constrain the thermal parameters of the intergalactic medium (IGM) at 5.4z6.0 using the Lyman-displaystylealpha (Lydisplaystylealpha) forest flux auto-correlation function. Our auto-differentiable JAX-based framework accelerates the surrogate model generation process using approximately 100 sparsely sampled Nyx hydrodynamical simulations with varying combinations of thermal parameters, i.e., the temperature at mean density T_{{0}}, the slope of the temperaturedisplaystyle-density relation displaystylegamma, and the mean transmission flux langle{F}{rangle}. We show that this emulator has a typical accuracy of 1.0% across the specified redshift range. Bayesian inference of the IGM thermal parameters, incorporating emulator uncertainty propagation, is further expedited using NumPyro Hamiltonian Monte Carlo. We compare both the inference results and computational cost of our framework with the traditional nearest-neighbor interpolation approach applied to the same set of mock Lyalpha flux. By examining the credibility contours of the marginalized posteriors for T_{{0}},gamma,and{langle}{F}{rangle} obtained using the emulator, the statistical reliability of measurements is established through inference on 100 realistic mock data sets of the auto-correlation function.

This work presents CLIPDraw, an algorithm that synthesizes novel drawings based on natural language input. CLIPDraw does not require any training; rather a pre-trained CLIP language-image encoder is used as a metric for maximizing similarity between the given description and a generated drawing. Crucially, CLIPDraw operates over vector strokes rather than pixel images, a constraint that biases drawings towards simpler human-recognizable shapes. Results compare between CLIPDraw and other synthesis-through-optimization methods, as well as highlight various interesting behaviors of CLIPDraw, such as satisfying ambiguous text in multiple ways, reliably producing drawings in diverse artistic styles, and scaling from simple to complex visual representations as stroke count is increased. Code for experimenting with the method is available at: https://colab.research.google.com/github/kvfrans/clipdraw/blob/main/clipdraw.ipynb

In this paper, we introduce FITS, a lightweight yet powerful model for time series analysis. Unlike existing models that directly process raw time-domain data, FITS operates on the principle that time series can be manipulated through interpolation in the complex frequency domain. By discarding high-frequency components with negligible impact on time series data, FITS achieves performance comparable to state-of-the-art models for time series forecasting and anomaly detection tasks, while having a remarkably compact size of only approximately 10k parameters. Such a lightweight model can be easily trained and deployed in edge devices, creating opportunities for various applications. The code is available in: https://github.com/VEWOXIC/FITS

While score-based generative models are the model of choice across diverse domains, there are limited tools available for controlling inference-time behavior in a principled manner, e.g. for composing multiple pretrained models. Existing classifier-free guidance methods use a simple heuristic to mix conditional and unconditional scores to approximately sample from conditional distributions. However, such methods do not approximate the intermediate distributions, necessitating additional 'corrector' steps. In this work, we provide an efficient and principled method for sampling from a sequence of annealed, geometric-averaged, or product distributions derived from pretrained score-based models. We derive a weighted simulation scheme which we call Feynman-Kac Correctors (FKCs) based on the celebrated Feynman-Kac formula by carefully accounting for terms in the appropriate partial differential equations (PDEs). To simulate these PDEs, we propose Sequential Monte Carlo (SMC) resampling algorithms that leverage inference-time scaling to improve sampling quality. We empirically demonstrate the utility of our methods by proposing amortized sampling via inference-time temperature annealing, improving multi-objective molecule generation using pretrained models, and improving classifier-free guidance for text-to-image generation. Our code is available at https://github.com/martaskrt/fkc-diffusion.

Recently large-scale language-image models (e.g., text-guided diffusion models) have considerably improved the image generation capabilities to generate photorealistic images in various domains. Based on this success, current image editing methods use texts to achieve intuitive and versatile modification of images. To edit a real image using diffusion models, one must first invert the image to a noisy latent from which an edited image is sampled with a target text prompt. However, most methods lack one of the following: user-friendliness (e.g., additional masks or precise descriptions of the input image are required), generalization to larger domains, or high fidelity to the input image. In this paper, we design an accurate and quick inversion technique, Prompt Tuning Inversion, for text-driven image editing. Specifically, our proposed editing method consists of a reconstruction stage and an editing stage. In the first stage, we encode the information of the input image into a learnable conditional embedding via Prompt Tuning Inversion. In the second stage, we apply classifier-free guidance to sample the edited image, where the conditional embedding is calculated by linearly interpolating between the target embedding and the optimized one obtained in the first stage. This technique ensures a superior trade-off between editability and high fidelity to the input image of our method. For example, we can change the color of a specific object while preserving its original shape and background under the guidance of only a target text prompt. Extensive experiments on ImageNet demonstrate the superior editing performance of our method compared to the state-of-the-art baselines.

Recent surge in large-scale generative models has spurred the development of vast fields in computer vision. In particular, text-to-image diffusion models have garnered widespread adoption across diverse domain due to their potential for high-fidelity image generation. Nonetheless, existing large-scale diffusion models are confined to generate images of up to 1K resolution, which is far from meeting the demands of contemporary commercial applications. Directly sampling higher-resolution images often yields results marred by artifacts such as object repetition and distorted shapes. Addressing the aforementioned issues typically necessitates training or fine-tuning models on higher resolution datasets. However, this undertaking poses a formidable challenge due to the difficulty in collecting large-scale high-resolution contents and substantial computational resources. While several preceding works have proposed alternatives, they often fail to produce convincing results. In this work, we probe the generative ability of diffusion models at higher resolution beyond its original capability and propose a novel progressive approach that fully utilizes generated low-resolution image to guide the generation of higher resolution image. Our method obviates the need for additional training or fine-tuning which significantly lowers the burden of computational costs. Extensive experiments and results validate the efficiency and efficacy of our method. Project page: https://yhyun225.github.io/DiffuseHigh/

A very recent trend in generative modeling is building 3D-aware generators from 2D image collections. To induce the 3D bias, such models typically rely on volumetric rendering, which is expensive to employ at high resolutions. During the past months, there appeared more than 10 works that address this scaling issue by training a separate 2D decoder to upsample a low-resolution image (or a feature tensor) produced from a pure 3D generator. But this solution comes at a cost: not only does it break multi-view consistency (i.e. shape and texture change when the camera moves), but it also learns the geometry in a low fidelity. In this work, we show that it is possible to obtain a high-resolution 3D generator with SotA image quality by following a completely different route of simply training the model patch-wise. We revisit and improve this optimization scheme in two ways. First, we design a location- and scale-aware discriminator to work on patches of different proportions and spatial positions. Second, we modify the patch sampling strategy based on an annealed beta distribution to stabilize training and accelerate the convergence. The resulted model, named EpiGRAF, is an efficient, high-resolution, pure 3D generator, and we test it on four datasets (two introduced in this work) at 256^2 and 512^2 resolutions. It obtains state-of-the-art image quality, high-fidelity geometry and trains {approx} 2.5 times faster than the upsampler-based counterparts. Project website: https://universome.github.io/epigraf.

Novel architectures have recently improved generative image synthesis leading to excellent visual quality in various tasks. Much of this success is due to the scalability of these architectures and hence caused by a dramatic increase in model complexity and in the computational resources invested in training these models. Our work questions the underlying paradigm of compressing large training data into ever growing parametric representations. We rather present an orthogonal, semi-parametric approach. We complement comparably small diffusion or autoregressive models with a separate image database and a retrieval strategy. During training we retrieve a set of nearest neighbors from this external database for each training instance and condition the generative model on these informative samples. While the retrieval approach is providing the (local) content, the model is focusing on learning the composition of scenes based on this content. As demonstrated by our experiments, simply swapping the database for one with different contents transfers a trained model post-hoc to a novel domain. The evaluation shows competitive performance on tasks which the generative model has not been trained on, such as class-conditional synthesis, zero-shot stylization or text-to-image synthesis without requiring paired text-image data. With negligible memory and computational overhead for the external database and retrieval we can significantly reduce the parameter count of the generative model and still outperform the state-of-the-art.

Machine learning has demonstrated remarkable performance over finite datasets, yet whether the scores over the fixed benchmarks can sufficiently indicate the model's performance in the real world is still in discussion. In reality, an ideal robust model will probably behave similarly to the oracle (e.g., the human users), thus a good evaluation protocol is probably to evaluate the models' behaviors in comparison to the oracle. In this paper, we introduce a new robustness measurement that directly measures the image classification model's performance compared with a surrogate oracle (i.e., a foundation model). Besides, we design a simple method that can accomplish the evaluation beyond the scope of the benchmarks. Our method extends the image datasets with new samples that are sufficiently perturbed to be distinct from the ones in the original sets, but are still bounded within the same image-label structure the original test image represents, constrained by a foundation model pretrained with a large amount of samples. As a result, our new method will offer us a new way to evaluate the models' robustness performance, free of limitations of fixed benchmarks or constrained perturbations, although scoped by the power of the oracle. In addition to the evaluation results, we also leverage our generated data to understand the behaviors of the model and our new evaluation strategies.

Recent advancements in text-guided diffusion models have unlocked powerful image manipulation capabilities. However, applying these methods to real images necessitates the inversion of the images into the domain of the pretrained diffusion model. Achieving faithful inversion remains a challenge, particularly for more recent models trained to generate images with a small number of denoising steps. In this work, we introduce an inversion method with a high quality-to-operation ratio, enhancing reconstruction accuracy without increasing the number of operations. Building on reversing the diffusion sampling process, our method employs an iterative renoising mechanism at each inversion sampling step. This mechanism refines the approximation of a predicted point along the forward diffusion trajectory, by iteratively applying the pretrained diffusion model, and averaging these predictions. We evaluate the performance of our ReNoise technique using various sampling algorithms and models, including recent accelerated diffusion models. Through comprehensive evaluations and comparisons, we show its effectiveness in terms of both accuracy and speed. Furthermore, we confirm that our method preserves editability by demonstrating text-driven image editing on real images.

Singly-TASE operators for the numerical solution of stiff differential equations were proposed by Calvo et al. in J.Sci. Comput. 2023 to reduce the computational cost of Runge-Kutta-TASE (RKTASE) methods when the involved linear systems are solved by some LU factorization. In this paper we propose a modification of these methods to improve the efficiency by considering different TASE operators for each stage of the Runge-Kutta. We prove that the resulting RKTASE methods are equivalent to W-methods (Steihaug and Wolfbrandt, Mathematics of Computation,1979) and this allows us to obtain the order conditions of the proposed Modified Singly-RKTASE methods (MSRKTASE) through the theory developed for the W-methods. We construct new MSRKTASE methods of order two and three and demonstrate their effectiveness through numerical experiments on both linear and nonlinear stiff systems. The results show that the MSRKTASE schemes significantly enhance efficiency and accuracy compared to previous Singly-RKTASE schemes.

We study the joint image of lines incident to points, meaning the set of image tuples obtained from fixed cameras observing a varying 3D point-line incidence. We prove a formula for the number of complex critical points of the triangulation problem that aims to compute a 3D point-line incidence from noisy images. Our formula works for an arbitrary number of images and measures the intrinsic difficulty of this triangulation. Additionally, we conduct numerical experiments using homotopy continuation methods, comparing different approaches of triangulation of such incidences. In our setup, exploiting the incidence relations gives both a faster point reconstruction and in three views more accurate.

Computing the matrix square root or its inverse in a differentiable manner is important in a variety of computer vision tasks. Previous methods either adopt the Singular Value Decomposition (SVD) to explicitly factorize the matrix or use the Newton-Schulz iteration (NS iteration) to derive the approximate solution. However, both methods are not computationally efficient enough in either the forward pass or in the backward pass. In this paper, we propose two more efficient variants to compute the differentiable matrix square root. For the forward propagation, one method is to use Matrix Taylor Polynomial (MTP), and the other method is to use Matrix Pad\'e Approximants (MPA). The backward gradient is computed by iteratively solving the continuous-time Lyapunov equation using the matrix sign function. Both methods yield considerable speed-up compared with the SVD or the Newton-Schulz iteration. Experimental results on the de-correlated batch normalization and second-order vision transformer demonstrate that our methods can also achieve competitive and even slightly better performances. The code is available at https://github.com/KingJamesSong/FastDifferentiableMatSqrt{https://github.com/KingJamesSong/FastDifferentiableMatSqrt}.

Zero-shot models like CLIP are often fine-tuned on a target dataset to improve its accuracy further, but this can compromise out-of-distribution (OOD) robustness. Robust Fine-Tuning (RFT )~wortsman2021robust, which interpolates between the zero-shot and fine-tuned models, has been proposed to address this issue. However, understanding when RFT actually improves OOD error remains limited. In this work, we empirically investigate the robustness of RFT in CLIP models, with a focus on the sharpness of the CLIP model during interpolation. First, we demonstrate that while sharpness may not serve as a reliable indicator for predicting the generalization of modern architectures like CLIP on OOD data, this challenges the conventional belief in the generalization benefits of flat minima in foundation models. However, by examining the role of the straggler layer phenomenon, we show that, unlike overall sharpness, the layer-wise sharpness of straggler layers can reliably capture the generalization performance of interpolated CLIP models on OOD data. Our extensive experiments reveal that layer-wise sharpness correlates with generalization in OOD accuracy for RFT. Furthermore, we demonstrate that by inducing sparsity in the straggler layers, we can mitigate the failure mode phenomenon in RFT. To the best of our knowledge, this is the first work to study the role of sharpness in the success of interpolation in the weight space of CLIP foundation models. Our code is available at https://github.com/alirezaabdollahpour/CLIP_Mode_Connectivity.

We address the computational challenges of solving parametric PDEs with non parametrized geometric variations and non-reducible problems, such as those involving shocks and discontinuities of variable positions. Traditional dimensionality reduction methods like POD struggle with these scenarios due to slowly decaying Kolmogorov widths. To overcome this, we propose a novel non-linear dimensionality reduction technique to reduce the required modes for representation. The non-linear reduction is obtained through a POD after applying a transformation on the fields, which we call optimal mappings, and is a solution to an optimization problem in infinite dimension. The proposed learning framework combines morphing techniques, non-linear dimensionality reduction, and Gaussian Process Regression (GPR). The problem is reformulated on a reference geometry before applying the dimensionality reduction. Our method learns both the optimal mapping, and the solution fields, using a series of GPR models, enabling efficient and accurate modeling of complex parametric PDEs with geometrical variability. The results obtained concur with current state-of-the-art models. We mainly compare our method with the winning solution of the ML4CFD NeurIPS 2024 competition.

In large scale machine learning, random sampling is a popular way to approximate datasets by a small representative subset of examples. In particular, sensitivity sampling is an intensely studied technique which provides provable guarantees on the quality of approximation, while reducing the number of examples to the product of the VC dimension d and the total sensitivity mathfrak S in remarkably general settings. However, guarantees going beyond this general bound of mathfrak S d are known in perhaps only one setting, for ell_2 subspace embeddings, despite intense study of sensitivity sampling in prior work. In this work, we show the first bounds for sensitivity sampling for ell_p subspace embeddings for pneq 2 that improve over the general mathfrak S d bound, achieving a bound of roughly mathfrak S^{2/p} for 1leq p<2 and mathfrak S^{2-2/p} for 2<p<infty. For 1leq p<2, we show that this bound is tight, in the sense that there exist matrices for which mathfrak S^{2/p} samples is necessary. Furthermore, our techniques yield further new results in the study of sampling algorithms, showing that the root leverage score sampling algorithm achieves a bound of roughly d for 1leq p<2, and that a combination of leverage score and sensitivity sampling achieves an improved bound of roughly d^{2/p}mathfrak S^{2-4/p} for 2<p<infty. Our sensitivity sampling results yield the best known sample complexity for a wide class of structured matrices that have small ell_p sensitivity.

We develop a spacetime neural network method with second order optimization for solving quantum dynamics from the high dimensional Schr\"{o}dinger equation. In contrast to the standard iterative first order optimization and the time-dependent variational principle, our approach utilizes the implicit mid-point method and generates the solution for all spatial and temporal values simultaneously after optimization. We demonstrate the method in the Schr\"{o}dinger equation with a self-normalized autoregressive spacetime neural network construction. Future explorations for solving different high dimensional differential equations are discussed.

Iterative methods are ubiquitous in large-scale scientific computing applications, and a number of approaches based on meta-learning have been recently proposed to accelerate them. However, a systematic study of these approaches and how they differ from meta-learning is lacking. In this paper, we propose a framework to analyze such learning-based acceleration approaches, where one can immediately identify a departure from classical meta-learning. We show that this departure may lead to arbitrary deterioration of model performance. Based on our analysis, we introduce a novel training method for learning-based acceleration of iterative methods. Furthermore, we theoretically prove that the proposed method improves upon the existing methods, and demonstrate its significant advantage and versatility through various numerical applications.

We introduced a novel method to solve Bayesian inverse problems governed by PDE equations with a hybrid two-level MCMC where we took advantage of the AI surrogate model speed and the accuracy of numerical models. We show theoretically the potential to solve Bayesian inverse problems accurately with only a small number of numerical samples when the AI surrogate model error is small. Several numerical experiment results are included which demonstrates the advantage of the hybrid method.

We present a novel generative 3D modeling system, coined CraftsMan, which can generate high-fidelity 3D geometries with highly varied shapes, regular mesh topologies, and detailed surfaces, and, notably, allows for refining the geometry in an interactive manner. Despite the significant advancements in 3D generation, existing methods still struggle with lengthy optimization processes, irregular mesh topologies, noisy surfaces, and difficulties in accommodating user edits, consequently impeding their widespread adoption and implementation in 3D modeling software. Our work is inspired by the craftsman, who usually roughs out the holistic figure of the work first and elaborates the surface details subsequently. Specifically, we employ a 3D native diffusion model, which operates on latent space learned from latent set-based 3D representations, to generate coarse geometries with regular mesh topology in seconds. In particular, this process takes as input a text prompt or a reference image and leverages a powerful multi-view (MV) diffusion model to generate multiple views of the coarse geometry, which are fed into our MV-conditioned 3D diffusion model for generating the 3D geometry, significantly improving robustness and generalizability. Following that, a normal-based geometry refiner is used to significantly enhance the surface details. This refinement can be performed automatically, or interactively with user-supplied edits. Extensive experiments demonstrate that our method achieves high efficacy in producing superior-quality 3D assets compared to existing methods. HomePage: https://craftsman3d.github.io/, Code: https://github.com/wyysf-98/CraftsMan

The field of novel view synthesis has made significant strides thanks to the development of radiance field methods. However, most radiance field techniques are far better at novel view interpolation than novel view extrapolation where the synthesis novel views are far beyond the observed training views. We design ViewExtrapolator, a novel view synthesis approach that leverages the generative priors of Stable Video Diffusion (SVD) for realistic novel view extrapolation. By redesigning the SVD denoising process, ViewExtrapolator refines the artifact-prone views rendered by radiance fields, greatly enhancing the clarity and realism of the synthesized novel views. ViewExtrapolator is a generic novel view extrapolator that can work with different types of 3D rendering such as views rendered from point clouds when only a single view or monocular video is available. Additionally, ViewExtrapolator requires no fine-tuning of SVD, making it both data-efficient and computation-efficient. Extensive experiments demonstrate the superiority of ViewExtrapolator in novel view extrapolation. Project page: https://kunhao-liu.github.io/ViewExtrapolator/.

We introduce BM25S, an efficient Python-based implementation of BM25 that only depends on Numpy and Scipy. BM25S achieves up to a 500x speedup compared to the most popular Python-based framework by eagerly computing BM25 scores during indexing and storing them into sparse matrices. It also achieves considerable speedups compared to highly optimized Java-based implementations, which are used by popular commercial products. Finally, BM25S reproduces the exact implementation of five BM25 variants based on Kamphuis et al. (2020) by extending eager scoring to non-sparse variants using a novel score shifting method. The code can be found at https://github.com/xhluca/bm25s

Text-to-image models give rise to workflows which often begin with an exploration step, where users sift through a large collection of generated images. The global nature of the text-to-image generation process prevents users from narrowing their exploration to a particular object in the image. In this paper, we present a technique to generate a collection of images that depicts variations in the shape of a specific object, enabling an object-level shape exploration process. Creating plausible variations is challenging as it requires control over the shape of the generated object while respecting its semantics. A particular challenge when generating object variations is accurately localizing the manipulation applied over the object's shape. We introduce a prompt-mixing technique that switches between prompts along the denoising process to attain a variety of shape choices. To localize the image-space operation, we present two techniques that use the self-attention layers in conjunction with the cross-attention layers. Moreover, we show that these localization techniques are general and effective beyond the scope of generating object variations. Extensive results and comparisons demonstrate the effectiveness of our method in generating object variations, and the competence of our localization techniques.

We tackle the problem of estimating a Manhattan frame, i.e. three orthogonal vanishing points, and the unknown focal length of the camera, leveraging a prior vertical direction. The direction can come from an Inertial Measurement Unit that is a standard component of recent consumer devices, e.g., smartphones. We provide an exhaustive analysis of minimal line configurations and derive two new 2-line solvers, one of which does not suffer from singularities affecting existing solvers. Additionally, we design a new non-minimal method, running on an arbitrary number of lines, to boost the performance in local optimization. Combining all solvers in a hybrid robust estimator, our method achieves increased accuracy even with a rough prior. Experiments on synthetic and real-world datasets demonstrate the superior accuracy of our method compared to the state of the art, while having comparable runtimes. We further demonstrate the applicability of our solvers for relative rotation estimation. The code is available at https://github.com/cvg/VP-Estimation-with-Prior-Gravity.

In this paper, we first present the character texture generation system Minecraft-ify, specified to Minecraft video game toward in-game application. Ours can generate face-focused image for texture mapping tailored to 3D virtual character having cube manifold. While existing projects or works only generate texture, proposed system can inverse the user-provided real image, or generate average/random appearance from learned distribution. Moreover, it can be manipulated with text-guidance using StyleGAN and StyleCLIP. These features provide a more extended user experience with enlarged freedom as a user-friendly AI-tool. Project page can be found at https://gh-bumsookim.github.io/Minecraft-ify/

Seven years ago, researchers proposed a postprocessing method to equalize the error rates of a model across different demographic groups. The work launched hundreds of papers purporting to improve over the postprocessing baseline. We empirically evaluate these claims through thousands of model evaluations on several tabular datasets. We find that the fairness-accuracy Pareto frontier achieved by postprocessing contains all other methods we were feasibly able to evaluate. In doing so, we address two common methodological errors that have confounded previous observations. One relates to the comparison of methods with different unconstrained base models. The other concerns methods achieving different levels of constraint relaxation. At the heart of our study is a simple idea we call unprocessing that roughly corresponds to the inverse of postprocessing. Unprocessing allows for a direct comparison of methods using different underlying models and levels of relaxation.

We propose a new method for solving imaging inverse problems using text-to-image latent diffusion models as general priors. Existing methods using latent diffusion models for inverse problems typically rely on simple null text prompts, which can lead to suboptimal performance. To address this limitation, we introduce a method for prompt tuning, which jointly optimizes the text embedding on-the-fly while running the reverse diffusion process. This allows us to generate images that are more faithful to the diffusion prior. In addition, we propose a method to keep the evolution of latent variables within the range space of the encoder, by projection. This helps to reduce image artifacts, a major problem when using latent diffusion models instead of pixel-based diffusion models. Our combined method, called P2L, outperforms both image- and latent-diffusion model-based inverse problem solvers on a variety of tasks, such as super-resolution, deblurring, and inpainting.

The Maximal Update Parametrization (muP) aims to make the optimal hyperparameters (HPs) of a model independent of its size, allowing them to be swept using a cheap proxy model rather than the full-size target model. We present a new scheme, u-muP, which improves upon muP by combining it with Unit Scaling, a method for designing models that makes them easy to train in low-precision. The two techniques have a natural affinity: muP ensures that the scale of activations is independent of model size, and Unit Scaling ensures that activations, weights and gradients begin training with a scale of one. This synthesis opens the door to a simpler scheme, whose default values are near-optimal. This in turn facilitates a more efficient sweeping strategy, with u-muP models reaching a lower loss than comparable muP models and working out-of-the-box in FP8.

In this manuscript we consider the problem of generalized linear estimation on Gaussian mixture data with labels given by a single-index model. Our first result is a sharp asymptotic expression for the test and training errors in the high-dimensional regime. Motivated by the recent stream of results on the Gaussian universality of the test and training errors in generalized linear estimation, we ask ourselves the question: "when is a single Gaussian enough to characterize the error?". Our formula allow us to give sharp answers to this question, both in the positive and negative directions. More precisely, we show that the sufficient conditions for Gaussian universality (or lack of thereof) crucially depend on the alignment between the target weights and the means and covariances of the mixture clusters, which we precisely quantify. In the particular case of least-squares interpolation, we prove a strong universality property of the training error, and show it follows a simple, closed-form expression. Finally, we apply our results to real datasets, clarifying some recent discussion in the literature about Gaussian universality of the errors in this context.

Recently, diffusion models have made remarkable progress in text-to-image (T2I) generation, synthesizing images with high fidelity and diverse contents. Despite this advancement, latent space smoothness within diffusion models remains largely unexplored. Smooth latent spaces ensure that a perturbation on an input latent corresponds to a steady change in the output image. This property proves beneficial in downstream tasks, including image interpolation, inversion, and editing. In this work, we expose the non-smoothness of diffusion latent spaces by observing noticeable visual fluctuations resulting from minor latent variations. To tackle this issue, we propose Smooth Diffusion, a new category of diffusion models that can be simultaneously high-performing and smooth. Specifically, we introduce Step-wise Variation Regularization to enforce the proportion between the variations of an arbitrary input latent and that of the output image is a constant at any diffusion training step. In addition, we devise an interpolation standard deviation (ISTD) metric to effectively assess the latent space smoothness of a diffusion model. Extensive quantitative and qualitative experiments demonstrate that Smooth Diffusion stands out as a more desirable solution not only in T2I generation but also across various downstream tasks. Smooth Diffusion is implemented as a plug-and-play Smooth-LoRA to work with various community models. Code is available at https://github.com/SHI-Labs/Smooth-Diffusion.

We study the ranking of individuals, teams, or objects, based on pairwise comparisons between them, using the Bradley-Terry model. Estimates of rankings within this model are commonly made using a simple iterative algorithm first introduced by Zermelo almost a century ago. Here we describe an alternative and similarly simple iteration that provably returns identical results but does so much faster -- over a hundred times faster in some cases. We demonstrate this algorithm with applications to a range of example data sets and derive a number of results regarding its convergence.

Recently, using diffusion models for zero-shot image restoration (IR) has become a new hot paradigm. This type of method only needs to use the pre-trained off-the-shelf diffusion models, without any finetuning, and can directly handle various IR tasks. The upper limit of the restoration performance depends on the pre-trained diffusion models, which are in rapid evolution. However, current methods only discuss how to deal with fixed-size images, but dealing with images of arbitrary sizes is very important for practical applications. This paper focuses on how to use those diffusion-based zero-shot IR methods to deal with any size while maintaining the excellent characteristics of zero-shot. A simple way to solve arbitrary size is to divide it into fixed-size patches and solve each patch independently. But this may yield significant artifacts since it neither considers the global semantics of all patches nor the local information of adjacent patches. Inspired by the Range-Null space Decomposition, we propose the Mask-Shift Restoration to address local incoherence and propose the Hierarchical Restoration to alleviate out-of-domain issues. Our simple, parameter-free approaches can be used not only for image restoration but also for image generation of unlimited sizes, with the potential to be a general tool for diffusion models. Code: https://github.com/wyhuai/DDNM/tree/main/hq_demo

In this paper, we develop and implement an efficient asymptotic-preserving (AP) scheme to solve the gas mixture of Boltzmann equations under the disparate mass scaling relevant to the so-called "epochal relaxation" phenomenon. The disparity in molecular masses, ranging across several orders of magnitude, leads to significant challenges in both the evaluation of collision operators and the designing of time-stepping schemes to capture the multi-scale nature of the dynamics. A direct implementation of the spectral method faces prohibitive computational costs as the mass ratio increases due to the need to resolve vastly different thermal velocities. Unlike [I. M. Gamba, S. Jin, and L. Liu, Commun. Math. Sci., 17 (2019), pp. 1257-1289], we propose an alternative approach based on proper truncation of asymptotic expansions of the collision operators, which significantly reduces the computational complexity and works well for small varepsilon. By incorporating the separation of three time scales in the model's relaxation process [P. Degond and B. Lucquin-Desreux, Math. Models Methods Appl. Sci., 6 (1996), pp. 405-436], we design an AP scheme that captures the specific dynamics of the disparate mass model while maintaining computational efficiency. Numerical experiments demonstrate the effectiveness of the proposed scheme in handling large mass ratios of heavy and light species, as well as capturing the epochal relaxation phenomenon.

In recent years, multiple notions of algorithmic fairness have arisen. One such notion is individual fairness (IF), which requires that individuals who are similar receive similar treatment. In parallel, matrix estimation (ME) has emerged as a natural paradigm for handling noisy data with missing values. In this work, we connect the two concepts. We show that pre-processing data using ME can improve an algorithm's IF without sacrificing performance. Specifically, we show that using a popular ME method known as singular value thresholding (SVT) to pre-process the data provides a strong IF guarantee under appropriate conditions. We then show that, under analogous conditions, SVT pre-processing also yields estimates that are consistent and approximately minimax optimal. As such, the ME pre-processing step does not, under the stated conditions, increase the prediction error of the base algorithm, i.e., does not impose a fairness-performance trade-off. We verify these results on synthetic and real data.

We propose a new learning paradigm called Deep Memory. It has the potential to completely revolutionize the Machine Learning field. Surprisingly, this paradigm has not been reinvented yet, unlike Deep Learning. At the core of this approach is the Learning By Heart principle, well studied in primary schools all over the world. Inspired by poem recitation, or by pi decimal memorization, we propose a concrete algorithm that mimics human behavior. We implement this paradigm on the task of generative modeling, and apply to images, natural language and even the pi decimals as long as one can print them as text. The proposed algorithm even generated this paper, in a one-shot learning setting. In carefully designed experiments, we show that the generated samples are indistinguishable from the training examples, as measured by any statistical tests or metrics.

We present a novel type of neural fields that uses general radial bases for signal representation. State-of-the-art neural fields typically rely on grid-based representations for storing local neural features and N-dimensional linear kernels for interpolating features at continuous query points. The spatial positions of their neural features are fixed on grid nodes and cannot well adapt to target signals. Our method instead builds upon general radial bases with flexible kernel position and shape, which have higher spatial adaptivity and can more closely fit target signals. To further improve the channel-wise capacity of radial basis functions, we propose to compose them with multi-frequency sinusoid functions. This technique extends a radial basis to multiple Fourier radial bases of different frequency bands without requiring extra parameters, facilitating the representation of details. Moreover, by marrying adaptive radial bases with grid-based ones, our hybrid combination inherits both adaptivity and interpolation smoothness. We carefully designed weighting schemes to let radial bases adapt to different types of signals effectively. Our experiments on 2D image and 3D signed distance field representation demonstrate the higher accuracy and compactness of our method than prior arts. When applied to neural radiance field reconstruction, our method achieves state-of-the-art rendering quality, with small model size and comparable training speed.

A great deal of effort has been devoted to reducing the risk of spurious scientific discoveries, from the use of sophisticated validation techniques, to deep statistical methods for controlling the false discovery rate in multiple hypothesis testing. However, there is a fundamental disconnect between the theoretical results and the practice of data analysis: the theory of statistical inference assumes a fixed collection of hypotheses to be tested, or learning algorithms to be applied, selected non-adaptively before the data are gathered, whereas in practice data is shared and reused with hypotheses and new analyses being generated on the basis of data exploration and the outcomes of previous analyses. In this work we initiate a principled study of how to guarantee the validity of statistical inference in adaptive data analysis. As an instance of this problem, we propose and investigate the question of estimating the expectations of m adaptively chosen functions on an unknown distribution given n random samples. We show that, surprisingly, there is a way to estimate an exponential in n number of expectations accurately even if the functions are chosen adaptively. This gives an exponential improvement over standard empirical estimators that are limited to a linear number of estimates. Our result follows from a general technique that counter-intuitively involves actively perturbing and coordinating the estimates, using techniques developed for privacy preservation. We give additional applications of this technique to our question.

We present an algorithm for minimizing an objective with hard-to-compute gradients by using a related, easier-to-access function as a proxy. Our algorithm is based on approximate proximal point iterations on the proxy combined with relatively few stochastic gradients from the objective. When the difference between the objective and the proxy is delta-smooth, our algorithm guarantees convergence at a rate matching stochastic gradient descent on a delta-smooth objective, which can lead to substantially better sample efficiency. Our algorithm has many potential applications in machine learning, and provides a principled means of leveraging synthetic data, physics simulators, mixed public and private data, and more.

In the realm of generative models for graphs, extensive research has been conducted. However, most existing methods struggle with large graphs due to the complexity of representing the entire joint distribution across all node pairs and capturing both global and local graph structures simultaneously. To overcome these issues, we introduce a method that generates a graph by progressively expanding a single node to a target graph. In each step, nodes and edges are added in a localized manner through denoising diffusion, building first the global structure, and then refining the local details. The local generation avoids modeling the entire joint distribution over all node pairs, achieving substantial computational savings with subquadratic runtime relative to node count while maintaining high expressivity through multiscale generation. Our experiments show that our model achieves state-of-the-art performance on well-established benchmark datasets while successfully scaling to graphs with at least 5000 nodes. Our method is also the first to successfully extrapolate to graphs outside of the training distribution, showcasing a much better generalization capability over existing methods.

Given a matrix Ain R^{ntimes d} and a vector bin R^n, we consider the regression problem with ell_infty guarantees: finding a vector x'in R^d such that |x'-x^*|_infty leq epsilon{d}cdot |Ax^*-b|_2cdot |A^dagger| where x^*=argmin_{xin R^d}|Ax-b|_2. One popular approach for solving such ell_2 regression problem is via sketching: picking a structured random matrix Sin R^{mtimes n} with mll n and SA can be quickly computed, solve the ``sketched'' regression problem argmin_{xin R^d} |SAx-Sb|_2. In this paper, we show that in order to obtain such ell_infty guarantee for ell_2 regression, one has to use sketching matrices that are dense. To the best of our knowledge, this is the first user case in which dense sketching matrices are necessary. On the algorithmic side, we prove that there exists a distribution of dense sketching matrices with m=epsilon^{-2}dlog^3(n/delta) such that solving the sketched regression problem gives the ell_infty guarantee, with probability at least 1-delta. Moreover, the matrix SA can be computed in time O(ndlog n). Our row count is nearly-optimal up to logarithmic factors, and significantly improves the result in [Price, Song and Woodruff, ICALP'17], in which a super-linear in d rows, m=Omega(epsilon^{-2}d^{1+gamma}) for gamma=Theta(frac{loglog n{log d}}) is required. We also develop a novel analytical framework for ell_infty guarantee regression that utilizes the Oblivious Coordinate-wise Embedding (OCE) property introduced in [Song and Yu, ICML'21]. Our analysis is arguably much simpler and more general than [Price, Song and Woodruff, ICALP'17], and it extends to dense sketches for tensor product of vectors.

We use tools from geometric statistics to analyze the usual estimation procedure of a template shape. This applies to shapes from landmarks, curves, surfaces, images etc. We demonstrate the asymptotic bias of the template shape estimation using the stratified geometry of the shape space. We give a Taylor expansion of the bias with respect to a parameter sigma describing the measurement error on the data. We propose two bootstrap procedures that quantify the bias and correct it, if needed. They are applicable for any type of shape data. We give a rule of thumb to provide intuition on whether the bias has to be corrected. This exhibits the parameters that control the bias' magnitude. We illustrate our results on simulated and real shape data.

Generative models have demonstrated remarkable success in domains such as text, image, and video synthesis. In this work, we explore the application of generative models to fluid dynamics, specifically for turbulence simulation, where classical numerical solvers are computationally expensive. We propose a novel stochastic generative model based on stochastic interpolants, which enables probabilistic forecasting while incorporating physical constraints such as energy stability and divergence-freeness. Unlike conventional stochastic generative models, which are often agnostic to underlying physical laws, our approach embeds energy consistency by making the parameters of the stochastic interpolant learnable coefficients. We evaluate our method on a benchmark turbulence problem - Kolmogorov flow - demonstrating superior accuracy and stability over state-of-the-art alternatives such as autoregressive conditional diffusion models (ACDMs) and PDE-Refiner. Furthermore, we achieve stable results for significantly longer roll-outs than standard stochastic interpolants. Our results highlight the potential of physics-aware generative models in accelerating and enhancing turbulence simulations while preserving fundamental conservation properties.

The largest experiments in machine learning now require resources far beyond the budget of all but a few institutions. Fortunately, it has recently been shown that the results of these huge experiments can often be extrapolated from the results of a sequence of far smaller, cheaper experiments. In this work, we show that not only can the extrapolation be done based on the size of the model, but on the size of the problem as well. By conducting a sequence of experiments using AlphaZero and Hex, we show that the performance achievable with a fixed amount of compute degrades predictably as the game gets larger and harder. Along with our main result, we further show that the test-time and train-time compute available to an agent can be traded off while maintaining performance.

Generating 3D models lies at the core of computer graphics and has been the focus of decades of research. With the emergence of advanced neural representations and generative models, the field of 3D content generation is developing rapidly, enabling the creation of increasingly high-quality and diverse 3D models. The rapid growth of this field makes it difficult to stay abreast of all recent developments. In this survey, we aim to introduce the fundamental methodologies of 3D generation methods and establish a structured roadmap, encompassing 3D representation, generation methods, datasets, and corresponding applications. Specifically, we introduce the 3D representations that serve as the backbone for 3D generation. Furthermore, we provide a comprehensive overview of the rapidly growing literature on generation methods, categorized by the type of algorithmic paradigms, including feedforward generation, optimization-based generation, procedural generation, and generative novel view synthesis. Lastly, we discuss available datasets, applications, and open challenges. We hope this survey will help readers explore this exciting topic and foster further advancements in the field of 3D content generation.

Knot diagrams are among the most common visual tools in topology. Computer programs now make it possible to draw, manipulate and render them digitally, which proves to be useful in knot theory teaching and research. Still, an openly available tool to manipulate knot diagrams in a real-time, interactive way is yet to be developed. We introduce a method of operating on the geometry of the knot diagram itself without any underlying three-dimensional structure that can underpin such an application. This allows us to directly interact with vector graphics knot diagrams while at the same time computing knot invariants in ways proposed by previous work. An implementation of this method is provided.

This paper develops a new mathematical-statistical approach to analyze a class of Flajolet-Martin algorithms (FMa), and provides analytical confidence intervals for the number F0 of distinct elements in a stream, based on Chernoff bounds. The class of FMa has reached a significant popularity in bigdata stream learning, and the attention of the literature has mainly been based on algorithmic aspects, basically complexity optimality, while the statistical analysis of these class of algorithms has been often faced heuristically. The analysis provided here shows deep connections with mathematical special functions and with extreme value theory. The latter connection may help in explaining heuristic considerations, while the first opens many numerical issues, faced at the end of the present paper. Finally, the algorithms are tested on an anonymized real data stream and MonteCarlo simulations are provided to support our analytical choice in this context.

Text-to-motion generation is a crucial task in computer vision, which generates the target 3D motion by the given text. The existing annotated datasets are limited in scale, resulting in most existing methods overfitting to the small datasets and unable to generalize to the motions of the open domain. Some methods attempt to solve the open-vocabulary motion generation problem by aligning to the CLIP space or using the Pretrain-then-Finetuning paradigm. However, the current annotated dataset's limited scale only allows them to achieve mapping from sub-text-space to sub-motion-space, instead of mapping between full-text-space and full-motion-space (full mapping), which is the key to attaining open-vocabulary motion generation. To this end, this paper proposes to leverage the atomic motion (simple body part motions over a short time period) as an intermediate representation, and leverage two orderly coupled steps, i.e., Textual Decomposition and Sub-motion-space Scattering, to address the full mapping problem. For Textual Decomposition, we design a fine-grained description conversion algorithm, and combine it with the generalization ability of a large language model to convert any given motion text into atomic texts. Sub-motion-space Scattering learns the compositional process from atomic motions to the target motions, to make the learned sub-motion-space scattered to form the full-motion-space. For a given motion of the open domain, it transforms the extrapolation into interpolation and thereby significantly improves generalization. Our network, DSO-Net, combines textual decomposition and sub-motion-space scattering to solve the open-vocabulary motion generation. Extensive experiments demonstrate that our DSO-Net achieves significant improvements over the state-of-the-art methods on open-vocabulary motion generation. Code is available at https://vankouf.github.io/DSONet/.

Stochastic gradient descent method and its variants constitute the core optimization algorithms that achieve good convergence rates for solving machine learning problems. These rates are obtained especially when these algorithms are fine-tuned for the application at hand. Although this tuning process can require large computational costs, recent work has shown that these costs can be reduced by line search methods that iteratively adjust the stepsize. We propose an alternative approach to stochastic line search by using a new algorithm based on forward step model building. This model building step incorporates second-order information that allows adjusting not only the stepsize but also the search direction. Noting that deep learning model parameters come in groups (layers of tensors), our method builds its model and calculates a new step for each parameter group. This novel diagonalization approach makes the selected step lengths adaptive. We provide convergence rate analysis, and experimentally show that the proposed algorithm achieves faster convergence and better generalization in well-known test problems. More precisely, SMB requires less tuning, and shows comparable performance to other adaptive methods.

Variational inference using the reparameterization trick has enabled large-scale approximate Bayesian inference in complex probabilistic models, leveraging stochastic optimization to sidestep intractable expectations. The reparameterization trick is applicable when we can simulate a random variable by applying a differentiable deterministic function on an auxiliary random variable whose distribution is fixed. For many distributions of interest (such as the gamma or Dirichlet), simulation of random variables relies on acceptance-rejection sampling. The discontinuity introduced by the accept-reject step means that standard reparameterization tricks are not applicable. We propose a new method that lets us leverage reparameterization gradients even when variables are outputs of a acceptance-rejection sampling algorithm. Our approach enables reparameterization on a larger class of variational distributions. In several studies of real and synthetic data, we show that the variance of the estimator of the gradient is significantly lower than other state-of-the-art methods. This leads to faster convergence of stochastic gradient variational inference.

We consider dense, associative neural-networks trained by a teacher (i.e., with supervision) and we investigate their computational capabilities analytically, via statistical-mechanics of spin glasses, and numerically, via Monte Carlo simulations. In particular, we obtain a phase diagram summarizing their performance as a function of the control parameters such as quality and quantity of the training dataset, network storage and noise, that is valid in the limit of large network size and structureless datasets: these networks may work in a ultra-storage regime (where they can handle a huge amount of patterns, if compared with shallow neural networks) or in a ultra-detection regime (where they can perform pattern recognition at prohibitive signal-to-noise ratios, if compared with shallow neural networks). Guided by the random theory as a reference framework, we also test numerically learning, storing and retrieval capabilities shown by these networks on structured datasets as MNist and Fashion MNist. As technical remarks, from the analytic side, we implement large deviations and stability analysis within Guerra's interpolation to tackle the not-Gaussian distributions involved in the post-synaptic potentials while, from the computational counterpart, we insert Plefka approximation in the Monte Carlo scheme, to speed up the evaluation of the synaptic tensors, overall obtaining a novel and broad approach to investigate supervised learning in neural networks, beyond the shallow limit, in general.

In this paper, we study the problem of principal component analysis with generative modeling assumptions, adopting a general model for the observed matrix that encompasses notable special cases, including spiked matrix recovery and phase retrieval. The key assumption is that the underlying signal lies near the range of an L-Lipschitz continuous generative model with bounded k-dimensional inputs. We propose a quadratic estimator, and show that it enjoys a statistical rate of order frac{klog L{m}}, where m is the number of samples. We also provide a near-matching algorithm-independent lower bound. Moreover, we provide a variant of the classic power method, which projects the calculated data onto the range of the generative model during each iteration. We show that under suitable conditions, this method converges exponentially fast to a point achieving the above-mentioned statistical rate. We perform experiments on various image datasets for spiked matrix and phase retrieval models, and illustrate performance gains of our method to the classic power method and the truncated power method devised for sparse principal component analysis.

We present Neural Spectral Methods, a technique to solve parametric Partial Differential Equations (PDEs), grounded in classical spectral methods. Our method uses orthogonal bases to learn PDE solutions as mappings between spectral coefficients. In contrast to current machine learning approaches which enforce PDE constraints by minimizing the numerical quadrature of the residuals in the spatiotemporal domain, we leverage Parseval's identity and introduce a new training strategy through a spectral loss. Our spectral loss enables more efficient differentiation through the neural network, and substantially reduces training complexity. At inference time, the computational cost of our method remains constant, regardless of the spatiotemporal resolution of the domain. Our experimental results demonstrate that our method significantly outperforms previous machine learning approaches in terms of speed and accuracy by one to two orders of magnitude on multiple different problems. When compared to numerical solvers of the same accuracy, our method demonstrates a 10times increase in performance speed.