Daily Papers

This paper addresses the challenge of creating a neural architecture for very long sequences that requires constant time for processing new information at each time step. Our approach, Associative Recurrent Memory Transformer (ARMT), is based on transformer self-attention for local context and segment-level recurrence for storage of task specific information distributed over a long context. We demonstrate that ARMT outperfors existing alternatives in associative retrieval tasks and sets a new performance record in the recent BABILong multi-task long-context benchmark by answering single-fact questions over 50 million tokens with an accuracy of 79.9%. The source code for training and evaluation is available on github.

Designing efficient and effective architectural backbones has been in the core of research efforts to enhance the capability of foundation models. Inspired by the human cognitive phenomenon of attentional bias-the natural tendency to prioritize certain events or stimuli-we reconceptualize neural architectures, including Transformers, Titans, and modern linear recurrent neural networks as associative memory modules that learn a mapping of keys and values using an internal objective, referred to as attentional bias. Surprisingly, we observed that most existing sequence models leverage either (1) dot-product similarity, or (2) L2 regression objectives as their attentional bias. Going beyond these objectives, we present a set of alternative attentional bias configurations along with their effective approximations to stabilize their training procedure. We then reinterpret forgetting mechanisms in modern deep learning architectures as a form of retention regularization, providing a novel set of forget gates for sequence models. Building upon these insights, we present Miras, a general framework to design deep learning architectures based on four choices of: (i) associative memory architecture, (ii) attentional bias objective, (iii) retention gate, and (iv) memory learning algorithm. We present three novel sequence models-Moneta, Yaad, and Memora-that go beyond the power of existing linear RNNs while maintaining a fast parallelizable training process. Our experiments show different design choices in Miras yield models with varying strengths. For example, certain instances of Miras achieve exceptional performance in special tasks such as language modeling, commonsense reasoning, and recall intensive tasks, even outperforming Transformers and other modern linear recurrent models.

Transformer-based models show their effectiveness across multiple domains and tasks. The self-attention allows to combine information from all sequence elements into context-aware representations. However, global and local information has to be stored mostly in the same element-wise representations. Moreover, the length of an input sequence is limited by quadratic computational complexity of self-attention. In this work, we propose and study a memory-augmented segment-level recurrent Transformer (RMT). Memory allows to store and process local and global information as well as to pass information between segments of the long sequence with the help of recurrence. We implement a memory mechanism with no changes to Transformer model by adding special memory tokens to the input or output sequence. Then the model is trained to control both memory operations and sequence representations processing. Results of experiments show that RMT performs on par with the Transformer-XL on language modeling for smaller memory sizes and outperforms it for tasks that require longer sequence processing. We show that adding memory tokens to Tr-XL is able to improve its performance. This makes Recurrent Memory Transformer a promising architecture for applications that require learning of long-term dependencies and general purpose in memory processing, such as algorithmic tasks and reasoning.

Increasing the size of a Transformer model does not always lead to enhanced performance. This phenomenon cannot be explained by the empirical scaling laws. Furthermore, improved generalization ability occurs as the model memorizes the training samples. We present a theoretical framework that sheds light on the memorization process and performance dynamics of transformer-based language models. We model the behavior of Transformers with associative memories using Hopfield networks, such that each transformer block effectively conducts an approximate nearest-neighbor search. Based on this, we design an energy function analogous to that in the modern continuous Hopfield network which provides an insightful explanation for the attention mechanism. Using the majorization-minimization technique, we construct a global energy function that captures the layered architecture of the Transformer. Under specific conditions, we show that the minimum achievable cross-entropy loss is bounded from below by a constant approximately equal to 1. We substantiate our theoretical results by conducting experiments with GPT-2 on various data sizes, as well as training vanilla Transformers on a dataset of 2M tokens.

Transformers have been established as the most popular backbones in sequence modeling, mainly due to their effectiveness in in-context retrieval tasks and the ability to learn at scale. Their quadratic memory and time complexity, however, bound their applicability in longer sequences and so has motivated researchers to explore effective alternative architectures such as modern recurrent neural networks (a.k.a long-term recurrent memory module). Despite their recent success in diverse downstream tasks, they struggle in tasks that requires long context understanding and extrapolation to longer sequences. We observe that these shortcomings come from three disjoint aspects in their design: (1) limited memory capacity that is bounded by the architecture of memory and feature mapping of the input; (2) online nature of update, i.e., optimizing the memory only with respect to the last input; and (3) less expressive management of their fixed-size memory. To enhance all these three aspects, we present ATLAS, a long-term memory module with high capacity that learns to memorize the context by optimizing the memory based on the current and past tokens, overcoming the online nature of long-term memory models. Building on this insight, we present a new family of Transformer-like architectures, called DeepTransformers, that are strict generalizations of the original Transformer architecture. Our experimental results on language modeling, common-sense reasoning, recall-intensive, and long-context understanding tasks show that ATLAS surpasses the performance of Transformers and recent linear recurrent models. ATLAS further improves the long context performance of Titans, achieving +80\% accuracy in 10M context length of BABILong benchmark.

Large Language Models (LLMs) struggle to handle long input sequences due to high memory and runtime costs. Memory-augmented models have emerged as a promising solution to this problem, but current methods are hindered by limited memory capacity and require costly re-training to integrate with a new LLM. In this work, we introduce an associative memory module which can be coupled to any pre-trained (frozen) attention-based LLM without re-training, enabling it to handle arbitrarily long input sequences. Unlike previous methods, our associative memory module consolidates representations of individual tokens into a non-parametric distribution model, dynamically managed by properly balancing the novelty and recency of the incoming data. By retrieving information from this consolidated associative memory, the base LLM can achieve significant (up to 29.7% on Arxiv) perplexity reduction in long-context modeling compared to other baselines evaluated on standard benchmarks. This architecture, which we call CAMELoT (Consolidated Associative Memory Enhanced Long Transformer), demonstrates superior performance even with a tiny context window of 128 tokens, and also enables improved in-context learning with a much larger set of demonstrations.

Memory is fundamental to intelligence, enabling learning, reasoning, and adaptability across biological and artificial systems. While Transformer architectures excel at sequence modeling, they face critical limitations in long-range context retention, continual learning, and knowledge integration. This review presents a unified framework bridging neuroscience principles, including dynamic multi-timescale memory, selective attention, and consolidation, with engineering advances in Memory-Augmented Transformers. We organize recent progress through three taxonomic dimensions: functional objectives (context extension, reasoning, knowledge integration, adaptation), memory representations (parameter-encoded, state-based, explicit, hybrid), and integration mechanisms (attention fusion, gated control, associative retrieval). Our analysis of core memory operations (reading, writing, forgetting, and capacity management) reveals a shift from static caches toward adaptive, test-time learning systems. We identify persistent challenges in scalability and interference, alongside emerging solutions including hierarchical buffering and surprise-gated updates. This synthesis provides a roadmap toward cognitively-inspired, lifelong-learning Transformer architectures.

Learning arguably involves the discovery and memorization of abstract rules. The aim of this paper is to study associative memory mechanisms. Our model is based on high-dimensional matrices consisting of outer products of embeddings, which relates to the inner layers of transformer language models. We derive precise scaling laws with respect to sample size and parameter size, and discuss the statistical efficiency of different estimators, including optimization-based algorithms. We provide extensive numerical experiments to validate and interpret theoretical results, including fine-grained visualizations of the stored memory associations.

In this paper, we share our reflections and insights on understanding Transformer architectures through the lens of associative memory--a classic psychological concept inspired by human cognition. We start with the basics of associative memory (think simple linear attention) and then dive into two dimensions: Memory Capacity: How much can a Transformer really remember, and how well? We introduce retrieval SNR to measure this and use a kernel perspective to mathematically reveal why Softmax Attention is so effective. We also show how FFNs can be seen as a type of associative memory, leading to insights on their design and potential improvements. Memory Update: How do these memories learn and evolve? We present a unified framework for understanding how different Transformer variants (like DeltaNet and Softmax Attention) update their "knowledge base". This leads us to tackle two provocative questions: 1. Are Transformers fundamentally limited in what they can express, and can we break these barriers? 2. If a Transformer had infinite context, would it become infinitely intelligent? We want to demystify Transformer architecture, offering a clearer understanding of existing designs. This exploration aims to provide fresh insights and spark new avenues for Transformer innovation.

Transformer models struggle with long-context inference due to their quadratic time and linear memory complexity. Recurrent Memory Transformers (RMTs) offer a solution by reducing the asymptotic cost to linear time and constant memory usage. However, their memory update mechanism leads to sequential execution, causing a performance bottleneck. We introduce Diagonal Batching, a scheduling scheme that unlocks parallelism across segments in RMTs while preserving exact recurrence. This approach eliminates the sequential constraint, enabling efficient GPU inference even for single long-context inputs without complex batching and pipelining techniques. Because the technique is purely a run-time computation reordering, existing RMT models adopt it with no retraining. Applied to a LLaMA-1B ARMT model, Diagonal Batching yields a 3.3x speedup over standard full-attention LLaMA-1B and a 1.8x speedup over the sequential RMT implementation on 131,072-token sequences. By removing sequential bottleneck, Diagonal Batching reduces inference cost and latency, thereby strengthening RMTs as a practical solution for real-world, long-context applications.

This paper investigates the gap in representation powers of Recurrent Neural Networks (RNNs) and Transformers in the context of solving algorithmic problems. We focus on understanding whether RNNs, known for their memory efficiency in handling long sequences, can match the performance of Transformers, particularly when enhanced with Chain-of-Thought (CoT) prompting. Our theoretical analysis reveals that CoT improves RNNs but is insufficient to close the gap with Transformers. A key bottleneck lies in the inability of RNNs to perfectly retrieve information from the context, even with CoT: for several tasks that explicitly or implicitly require this capability, such as associative recall and determining if a graph is a tree, we prove that RNNs are not expressive enough to solve the tasks while Transformers can solve them with ease. Conversely, we prove that adopting techniques to enhance the in-context retrieval capability of RNNs, including Retrieval-Augmented Generation (RAG) and adding a single Transformer layer, can elevate RNNs to be capable of solving all polynomial-time solvable problems with CoT, hence closing the representation gap with Transformers.

In recent years, Transformers have become the de-facto architecture for sequence modeling on text and a variety of multi-dimensional data, such as images and video. However, the use of self-attention layers in a Transformer incurs prohibitive compute and memory complexity that scales quadratically w.r.t. the sequence length. A recent architecture, Mamba, based on state space models has been shown to achieve comparable performance for modeling text sequences, while scaling linearly with the sequence length. In this work, we present Mamba-ND, a generalized design extending the Mamba architecture to arbitrary multi-dimensional data. Our design alternatively unravels the input data across different dimensions following row-major orderings. We provide a systematic comparison of Mamba-ND with several other alternatives, based on prior multi-dimensional extensions such as Bi-directional LSTMs and S4ND. Empirically, we show that Mamba-ND demonstrates performance competitive with the state-of-the-art on a variety of multi-dimensional benchmarks, including ImageNet-1K classification, HMDB-51 action recognition, and ERA5 weather forecasting.

This technical report presents the application of a recurrent memory to extend the context length of BERT, one of the most effective Transformer-based models in natural language processing. By leveraging the Recurrent Memory Transformer architecture, we have successfully increased the model's effective context length to an unprecedented two million tokens, while maintaining high memory retrieval accuracy. Our method allows for the storage and processing of both local and global information and enables information flow between segments of the input sequence through the use of recurrence. Our experiments demonstrate the effectiveness of our approach, which holds significant potential to enhance long-term dependency handling in natural language understanding and generation tasks as well as enable large-scale context processing for memory-intensive applications.

State space models (SSMs) for language modelling promise an efficient and performant alternative to quadratic-attention Transformers, yet show variable performance on recalling basic information from the context. While performance on synthetic tasks like Associative Recall (AR) can point to this deficiency, behavioural metrics provide little information as to why--on a mechanistic level--certain architectures fail and others succeed. To address this, we conduct experiments on AR and find that only Transformers and Based SSM models fully succeed at AR, with Mamba a close third, whereas the other SSMs (H3, Hyena) fail. We then use causal interventions to explain why. We find that Transformers and Based learn to store key-value associations in-context using induction heads. By contrast, the SSMs compute these associations only at the last state, with only Mamba succeeding because of its short convolution component. To extend and deepen these findings, we introduce Associative Treecall (ATR), a synthetic task similar to AR based on PCFG induction. ATR introduces language-like hierarchical structure into the AR setting. We find that all architectures learn the same mechanism as they did for AR, and the same three models succeed at the task. These results reveal that architectures with similar accuracy may still have substantive differences, motivating the adoption of mechanistic evaluations.

The scalability limitations of Transformers regarding sequence length have renewed interest in recurrent sequence models that are parallelizable during training. As a result, many novel recurrent architectures, such as S4, Mamba, and Aaren, have been proposed that achieve comparable performance. In this work, we revisit traditional recurrent neural networks (RNNs) from over a decade ago: LSTMs (1997) and GRUs (2014). While these models were slow due to requiring to backpropagate through time (BPTT), we show that by removing their hidden state dependencies from their input, forget, and update gates, LSTMs and GRUs no longer need to BPTT and can be efficiently trained in parallel. Building on this, we introduce minimal versions (minLSTMs and minGRUs) that (1) use significantly fewer parameters than their traditional counterparts and (2) are fully parallelizable during training (175x faster for a sequence of length 512). Lastly, we show that these stripped-down versions of decade-old RNNs match the empirical performance of recent sequence models.

Transformers achieve remarkable performance in several tasks but due to their quadratic complexity, with respect to the input's length, they are prohibitively slow for very long sequences. To address this limitation, we express the self-attention as a linear dot-product of kernel feature maps and make use of the associativity property of matrix products to reduce the complexity from Oleft(N^2right) to Oleft(Nright), where N is the sequence length. We show that this formulation permits an iterative implementation that dramatically accelerates autoregressive transformers and reveals their relationship to recurrent neural networks. Our linear transformers achieve similar performance to vanilla transformers and they are up to 4000x faster on autoregressive prediction of very long sequences.

The advent of Transformers marked a significant breakthrough in sequence modelling, providing a highly performant architecture capable of leveraging GPU parallelism. However, Transformers are computationally expensive at inference time, limiting their applications, particularly in low-resource settings (e.g., mobile and embedded devices). Addressing this, we (1) begin by showing that attention can be viewed as a special Recurrent Neural Network (RNN) with the ability to compute its many-to-one RNN output efficiently. We then (2) show that popular attention-based models such as Transformers can be viewed as RNN variants. However, unlike traditional RNNs (e.g., LSTMs), these models cannot be updated efficiently with new tokens, an important property in sequence modelling. Tackling this, we (3) introduce a new efficient method of computing attention's many-to-many RNN output based on the parallel prefix scan algorithm. Building on the new attention formulation, we (4) introduce Aaren, an attention-based module that can not only (i) be trained in parallel (like Transformers) but also (ii) be updated efficiently with new tokens, requiring only constant memory for inferences (like traditional RNNs). Empirically, we show Aarens achieve comparable performance to Transformers on 38 datasets spread across four popular sequential problem settings: reinforcement learning, event forecasting, time series classification, and time series forecasting tasks while being more time and memory-efficient.

MEGA is a recent transformer-based architecture, which utilizes a linear recurrent operator whose parallel computation, based on the FFT, scales as O(LlogL), with L being the sequence length. We build upon their approach by replacing the linear recurrence with a special temporal convolutional network which permits larger receptive field size with shallower networks, and reduces the computational complexity to O(L). The resulting model is called TCNCA, a Temporal Convolutional Network with Chunked Attention. We evaluate TCNCA on EnWik8 language modeling, long-range-arena (LRA) sequence classification, as well as a synthetic reasoning benchmark associative recall. On EnWik8, TCNCA outperforms MEGA, reaching a lower loss with 1.37times/1.24times faster forward/backward pass during training. The dilated convolutions used in TCNCA are consistently and significantly faster operations than the FFT-based parallelized recurrence in GPUs, making them a scalable candidate for handling very large sequence lengths: they are up to 7.07times/2.86times faster in the forward/backward pass for sequences up to 131k. Further on LRA, TCNCA achieves, on average, 1.28times speed-up during inference with similar accuracy to what MEGA achieves. On associative recall, we find that even a simplified version of TCNCA, without excessive multiplicative and additive interactions, remains superior or competitive to MEGA on a range of sequence lengths and vocabulary sizes.

Recurrent neural networks are effective models to process sequences. However, they are unable to learn long-term dependencies because of their inherent sequential nature. As a solution, Vaswani et al. introduced the Transformer, a model solely based on the attention mechanism that is able to relate any two positions of the input sequence, hence modelling arbitrary long dependencies. The Transformer has improved the state-of-the-art across numerous sequence modelling tasks. However, its effectiveness comes at the expense of a quadratic computational and memory complexity with respect to the sequence length, hindering its adoption. Fortunately, the deep learning community has always been interested in improving the models' efficiency, leading to a plethora of solutions such as parameter sharing, pruning, mixed-precision, and knowledge distillation. Recently, researchers have directly addressed the Transformer's limitation by designing lower-complexity alternatives such as the Longformer, Reformer, Linformer, and Performer. However, due to the wide range of solutions, it has become challenging for researchers and practitioners to determine which methods to apply in practice in order to meet the desired trade-off between capacity, computation, and memory. This survey addresses this issue by investigating popular approaches to make Transformers faster and lighter and by providing a comprehensive explanation of the methods' strengths, limitations, and underlying assumptions.

We introduce a neural network with a recurrent attention model over a possibly large external memory. The architecture is a form of Memory Network (Weston et al., 2015) but unlike the model in that work, it is trained end-to-end, and hence requires significantly less supervision during training, making it more generally applicable in realistic settings. It can also be seen as an extension of RNNsearch to the case where multiple computational steps (hops) are performed per output symbol. The flexibility of the model allows us to apply it to tasks as diverse as (synthetic) question answering and to language modeling. For the former our approach is competitive with Memory Networks, but with less supervision. For the latter, on the Penn TreeBank and Text8 datasets our approach demonstrates comparable performance to RNNs and LSTMs. In both cases we show that the key concept of multiple computational hops yields improved results.

We introduce the Block-Recurrent Transformer, which applies a transformer layer in a recurrent fashion along a sequence, and has linear complexity with respect to sequence length. Our recurrent cell operates on blocks of tokens rather than single tokens during training, and leverages parallel computation within a block in order to make efficient use of accelerator hardware. The cell itself is strikingly simple. It is merely a transformer layer: it uses self-attention and cross-attention to efficiently compute a recurrent function over a large set of state vectors and tokens. Our design was inspired in part by LSTM cells, and it uses LSTM-style gates, but it scales the typical LSTM cell up by several orders of magnitude. Our implementation of recurrence has the same cost in both computation time and parameter count as a conventional transformer layer, but offers dramatically improved perplexity in language modeling tasks over very long sequences. Our model out-performs a long-range Transformer XL baseline by a wide margin, while running twice as fast. We demonstrate its effectiveness on PG19 (books), arXiv papers, and GitHub source code. Our code has been released as open source.

Recently, the use of transformers in offline reinforcement learning has become a rapidly developing area. This is due to their ability to treat the agent's trajectory in the environment as a sequence, thereby reducing the policy learning problem to sequence modeling. In environments where the agent's decisions depend on past events, it is essential to capture both the event itself and the decision point in the context of the model. However, the quadratic complexity of the attention mechanism limits the potential for context expansion. One solution to this problem is to enhance transformers with memory mechanisms. In this paper, we propose the Recurrent Action Transformer with Memory (RATE) - a model that incorporates recurrent memory. To evaluate our model, we conducted extensive experiments on both memory-intensive environments (VizDoom-Two-Color, T-Maze) and classic Atari games and MuJoCo control environments. The results show that the use of memory can significantly improve performance in memory-intensive environments while maintaining or improving results in classic environments. We hope that our findings will stimulate research on memory mechanisms for transformers applicable to offline reinforcement learning.

We introduce an Outlier-Efficient Modern Hopfield Model (termed OutEffHop) and use it to address the outlier-induced challenge of quantizing gigantic transformer-based models. Our main contribution is a novel associative memory model facilitating outlier-efficient associative memory retrievals. Interestingly, this memory model manifests a model-based interpretation of an outlier-efficient attention mechanism (Softmax_1): it is an approximation of the memory retrieval process of OutEffHop. Methodologically, this allows us to debut novel outlier-efficient Hopfield layers a powerful attention alternative with superior post-quantization performance. Theoretically, the Outlier-Efficient Modern Hopfield Model retains and improves the desirable properties of the standard modern Hopfield models, including fixed point convergence and exponential storage capacity. Empirically, we demonstrate the proposed model's efficacy across large-scale transformer-based and Hopfield-based models (including BERT, OPT, ViT and STanHop-Net), benchmarking against state-of-the-art methods including Clipped_Softmax and Gated_Attention. Notably, OutEffHop achieves on average sim22+\% reductions in both average kurtosis and maximum infinity norm of model outputs accross 4 models.

Recent architectural developments have enabled recurrent neural networks (RNNs) to reach and even surpass the performance of Transformers on certain sequence modeling tasks. These modern RNNs feature a prominent design pattern: linear recurrent layers interconnected by feedforward paths with multiplicative gating. Here, we show how RNNs equipped with these two design elements can exactly implement (linear) self-attention, the main building block of Transformers. By reverse-engineering a set of trained RNNs, we find that gradient descent in practice discovers our construction. In particular, we examine RNNs trained to solve simple in-context learning tasks on which Transformers are known to excel and find that gradient descent instills in our RNNs the same attention-based in-context learning algorithm used by Transformers. Our findings highlight the importance of multiplicative interactions in neural networks and suggest that certain RNNs might be unexpectedly implementing attention under the hood.

Transformer models have demonstrated high accuracy in numerous applications but have high complexity and lack sequential processing capability making them ill-suited for many streaming applications at the edge where devices are heavily resource-constrained. Thus motivated, many researchers have proposed reformulating the transformer models as RNN modules which modify the self-attention computation with explicit states. However, these approaches often incur significant performance degradation. The ultimate goal is to develop a model that has the following properties: parallel training, streaming and low-cost inference, and SOTA performance. In this paper, we propose a new direction to achieve this goal. We show how architectural modifications to a recurrent model can help push its performance toward Transformer models while retaining its sequential processing capability. Specifically, inspired by the recent success of Legendre Memory Units (LMU) in sequence learning tasks, we propose LMUFormer, which augments the LMU with convolutional patch embedding and convolutional channel mixer. Moreover, we present a spiking version of this architecture, which introduces the benefit of states within the patch embedding and channel mixer modules while simultaneously reducing the computing complexity. We evaluated our architectures on multiple sequence datasets. In comparison to SOTA transformer-based models within the ANN domain on the SCv2 dataset, our LMUFormer demonstrates comparable performance while necessitating a remarkable 53 times reduction in parameters and a substantial 65 times decrement in FLOPs. Additionally, owing to our model's proficiency in real-time data processing, we can achieve a 32.03% reduction in sequence length, all while incurring an inconsequential decline in performance. Our code is publicly available at https://github.com/zeyuliu1037/LMUFormer.git.

This work introduces a new Transformer model called Cached Transformer, which uses Gated Recurrent Cached (GRC) attention to extend the self-attention mechanism with a differentiable memory cache of tokens. GRC attention enables attending to both past and current tokens, increasing the receptive field of attention and allowing for exploring long-range dependencies. By utilizing a recurrent gating unit to continuously update the cache, our model achieves significant advancements in six language and vision tasks, including language modeling, machine translation, ListOPs, image classification, object detection, and instance segmentation. Furthermore, our approach surpasses previous memory-based techniques in tasks such as language modeling and displays the ability to be applied to a broader range of situations.

Large language models based on transformers have achieved great empirical successes. However, as they are deployed more widely, there is a growing need to better understand their internal mechanisms in order to make them more reliable. These models appear to store vast amounts of knowledge from their training data, and to adapt quickly to new information provided in their context or prompt. We study how transformers balance these two types of knowledge by considering a synthetic setup where tokens are generated from either global or context-specific bigram distributions. By a careful empirical analysis of the training process on a simplified two-layer transformer, we illustrate the fast learning of global bigrams and the slower development of an "induction head" mechanism for the in-context bigrams. We highlight the role of weight matrices as associative memories, provide theoretical insights on how gradients enable their learning during training, and study the role of data-distributional properties.

Transformers have revolutionized almost all natural language processing (NLP) tasks but suffer from memory and computational complexity that scales quadratically with sequence length. In contrast, recurrent neural networks (RNNs) exhibit linear scaling in memory and computational requirements but struggle to match the same performance as Transformers due to limitations in parallelization and scalability. We propose a novel model architecture, Receptance Weighted Key Value (RWKV), that combines the efficient parallelizable training of Transformers with the efficient inference of RNNs. Our approach leverages a linear attention mechanism and allows us to formulate the model as either a Transformer or an RNN, which parallelizes computations during training and maintains constant computational and memory complexity during inference, leading to the first non-transformer architecture to be scaled to tens of billions of parameters. Our experiments reveal that RWKV performs on par with similarly sized Transformers, suggesting that future work can leverage this architecture to create more efficient models. This work presents a significant step towards reconciling the trade-offs between computational efficiency and model performance in sequence processing tasks.

Transformers have demonstrated their success in various domains and tasks. However, Transformers struggle with long input sequences due to their limited capacity. While one solution is to increase input length, endlessly stretching the length is unrealistic. Furthermore, humans selectively remember and use only relevant information from inputs, unlike Transformers which process all raw data from start to end. We introduce Memoria, a general memory network that applies Hebbian theory which is a major theory explaining human memory formulation to enhance long-term dependencies in neural networks. Memoria stores and retrieves information called engram at multiple memory levels of working memory, short-term memory, and long-term memory, using connection weights that change according to Hebb's rule. Through experiments with popular Transformer-based models like BERT and GPT, we present that Memoria significantly improves the ability to consider long-term dependencies in various tasks. Results show that Memoria outperformed existing methodologies in sorting and language modeling, and long text classification.

Although Transformers with fully connected self-attentions are powerful to model long-term dependencies, they are struggling to scale to long texts with thousands of words in language modeling. One of the solutions is to equip the model with a recurrence memory. However, existing approaches directly reuse hidden states from the previous segment that encodes contexts in a uni-directional way. As a result, this prohibits the memory to dynamically interact with the current context that provides up-to-date information for token prediction. To remedy this issue, we propose Look-Ahead Memory (LaMemo) that enhances the recurrence memory by incrementally attending to the right-side tokens, and interpolating with the old memory states to maintain long-term information in the history. LaMemo embraces bi-directional attention and segment recurrence with an additional computation overhead only linearly proportional to the memory length. Experiments on widely used language modeling benchmarks demonstrate its superiority over the baselines equipped with different types of memory.

When predicting the next token in a sequence, vanilla transformers compute attention over all previous tokens, resulting in quadratic scaling of compute with sequence length. State-space models compress the entire sequence of tokens into a fixed-dimensional representation to improve efficiency, while other architectures achieve sub-quadratic complexity via low-rank projections or sparse attention patterns over the sequence. In this paper, we introduce Attamba, a novel architecture that uses state-space models to compress chunks of tokens and applies attention on these compressed key-value representations. We find that replacing key and value projections in a transformer with SSMs can improve model quality and enable flexible token chunking, resulting in 24% improved perplexity with transformer of similar KV-Cache and attention footprint, and ~4 times smaller KV-Cache and Attention FLOPs for 5% perplexity trade-off. Attamba can perform attention on chunked-sequences of variable length, enabling a smooth transition between quadratic and linear scaling, offering adaptable efficiency gains.

Zero-shot and in-context learning enable solving tasks without model fine-tuning, making them essential for developing generative model solutions. Therefore, it is crucial to understand whether a pretrained model can be prompted to approximate any function, i.e., whether it is a universal in-context approximator. While it was recently shown that transformer models do possess this property, these results rely on their attention mechanism. Hence, these findings do not apply to fully recurrent architectures like RNNs, LSTMs, and the increasingly popular SSMs. We demonstrate that RNNs, LSTMs, GRUs, Linear RNNs, and linear gated architectures such as Mamba and Hawk/Griffin can also serve as universal in-context approximators. To streamline our argument, we introduce a programming language called LSRL that compiles to these fully recurrent architectures. LSRL may be of independent interest for further studies of fully recurrent models, such as constructing interpretability benchmarks. We also study the role of multiplicative gating and observe that architectures incorporating such gating (e.g., LSTMs, GRUs, Hawk/Griffin) can implement certain operations more stably, making them more viable candidates for practical in-context universal approximation.

Modern recurrent architectures, such as xLSTM and Mamba, have recently challenged the Transformer in language modeling. However, their structure constrains their applicability to sequences only or requires processing multi-dimensional data structures, such as images or molecular graphs, in a pre-defined sequential order. In contrast, Multi-Dimensional RNNs (MDRNNs) are well suited for data with a higher level structure, like 2D grids, trees, and directed acyclic graphs (DAGs). In this work, we extend the notion of multi-dimensionality to linear RNNs. We introduce parallelizable Linear Source Transition Mark networks (pLSTMs) using Source, Transition, and Mark gates that act on the line graph of a general DAG. This enables parallelization in analogy to parallel associative scans and the chunkwise-recurrent form of sequential linear RNNs, but for DAGs. For regular grids (1D and 2D), like images, this scheme can be efficiently implemented using einsum operations, concatenations, and padding in logarithmic time. pLSTMs tackle the vanishing/exploding activation/gradient problem for long distances in DAGs via two distinct modes: a directed propagation mode (P-mode) and a diffusive distribution mode (D-mode). To showcase the long-range capabilities of pLSTM, we introduce arrow-pointing extrapolation as a synthetic computer vision task that contains long-distance directional information. We demonstrate that pLSTMs generalize well to larger image sizes, whereas Transformers struggle to extrapolate. On established molecular graph and computer vision benchmarks, pLSTMs also show strong performance. Code and Datasets are available at: https://github.com/ml-jku/plstm_experiments.

Sequence modeling plays a vital role across various domains, with recurrent neural networks being historically the predominant method of performing these tasks. However, the emergence of transformers has altered this paradigm due to their superior performance. Built upon these advances, transformers have conjoined CNNs as two leading foundational models for learning visual representations. However, transformers are hindered by the O(N^2) complexity of their attention mechanisms, while CNNs lack global receptive fields and dynamic weight allocation. State Space Models (SSMs), specifically the \textbf{Mamba} model with selection mechanisms and hardware-aware architecture, have garnered immense interest lately in sequential modeling and visual representation learning, challenging the dominance of transformers by providing infinite context lengths and offering substantial efficiency maintaining linear complexity in the input sequence. Capitalizing on the advances in computer vision, medical imaging has heralded a new epoch with Mamba models. Intending to help researchers navigate the surge, this survey seeks to offer an encyclopedic review of Mamba models in medical imaging. Specifically, we start with a comprehensive theoretical review forming the basis of SSMs, including Mamba architecture and its alternatives for sequence modeling paradigms in this context. Next, we offer a structured classification of Mamba models in the medical field and introduce a diverse categorization scheme based on their application, imaging modalities, and targeted organs. Finally, we summarize key challenges, discuss different future research directions of the SSMs in the medical domain, and propose several directions to fulfill the demands of this field. In addition, we have compiled the studies discussed in this paper along with their open-source implementations on our GitHub repository.

Foundation models, now powering most of the exciting applications in deep learning, are almost universally based on the Transformer architecture and its core attention module. Many subquadratic-time architectures such as linear attention, gated convolution and recurrent models, and structured state space models (SSMs) have been developed to address Transformers' computational inefficiency on long sequences, but they have not performed as well as attention on important modalities such as language. We identify that a key weakness of such models is their inability to perform content-based reasoning, and make several improvements. First, simply letting the SSM parameters be functions of the input addresses their weakness with discrete modalities, allowing the model to selectively propagate or forget information along the sequence length dimension depending on the current token. Second, even though this change prevents the use of efficient convolutions, we design a hardware-aware parallel algorithm in recurrent mode. We integrate these selective SSMs into a simplified end-to-end neural network architecture without attention or even MLP blocks (Mamba). Mamba enjoys fast inference (5times higher throughput than Transformers) and linear scaling in sequence length, and its performance improves on real data up to million-length sequences. As a general sequence model backbone, Mamba achieves state-of-the-art performance across several modalities such as language, audio, and genomics. On language modeling, our Mamba-3B model outperforms Transformers of the same size and matches Transformers twice its size, both in pretraining and downstream evaluation.

Linear transformers have emerged as a subquadratic-time alternative to softmax attention and have garnered significant interest due to their fixed-size recurrent state that lowers inference cost. However, their original formulation suffers from poor scaling and underperforms compute-matched transformers. Recent linear models such as RWKV and Mamba have attempted to address these shortcomings by proposing novel time-mixing and gating architectures, but pre-training large language models requires significant data and compute investments. Thus, the search for subquadratic architectures is limited by the availability of compute and quality pre-training datasets. As a cost-effective alternative to pre-training linear transformers, we propose Scalable UPtraining for Recurrent Attention (SUPRA). We present a method to uptrain existing large pre-trained transformers into Recurrent Neural Networks (RNNs) with a modest compute budget. This allows us to leverage the strong pre-training data and performance of existing transformer LLMs, while requiring 5% of the training cost. We find that our linearization technique leads to competitive performance on standard benchmarks, but we identify persistent in-context learning and long-context modeling shortfalls for even the largest linear models. Our code and models can be found at https://github.com/TRI-ML/linear_open_lm.

Transformers provide a class of expressive architectures that are extremely effective for sequence modeling. However, the key limitation of transformers is their quadratic memory and time complexity O(L^2) with respect to the sequence length in attention layers, which restricts application in extremely long sequences. Most existing approaches leverage sparsity or low-rank assumptions in the attention matrix to reduce cost, but sacrifice expressiveness. Instead, we propose Combiner, which provides full attention capability in each attention head while maintaining low computation and memory complexity. The key idea is to treat the self-attention mechanism as a conditional expectation over embeddings at each location, and approximate the conditional distribution with a structured factorization. Each location can attend to all other locations, either via direct attention, or through indirect attention to abstractions, which are again conditional expectations of embeddings from corresponding local regions. We show that most sparse attention patterns used in existing sparse transformers are able to inspire the design of such factorization for full attention, resulting in the same sub-quadratic cost (O(Llog(L)) or O(LL)). Combiner is a drop-in replacement for attention layers in existing transformers and can be easily implemented in common frameworks. An experimental evaluation on both autoregressive and bidirectional sequence tasks demonstrates the effectiveness of this approach, yielding state-of-the-art results on several image and text modeling tasks.

The Transformer has become the de facto standard for large language models and a wide range of downstream tasks across various domains. Despite its numerous advantages like inherent training parallelism, the Transformer still faces key challenges due to its inability to effectively process sequences beyond a fixed context window and the quadratic complexity of its attention mechanism. These challenges have renewed interest in RNN-like architectures, which offer linear scaling with sequence length and improved handling of long-range dependencies, albeit with limited parallelism due to their inherently recurrent nature. In this paper, we propose Avey, a new neural foundational architecture that breaks away from both attention and recurrence. Avey comprises a ranker and an autoregressive neural processor, which collaboratively identify and contextualize only the most relevant tokens for any given token, regardless of their positions in the sequence. Specifically, Avey decouples sequence length from context width, thus enabling effective processing of arbitrarily long sequences. Experimental results show that Avey compares favorably to the Transformer across a variety of standard short-range NLP benchmarks, while notably excelling at capturing long-range dependencies.

In recent years, there has been a trend in the field of Reinforcement Learning (RL) towards large action models trained offline on large-scale datasets via sequence modeling. Existing models are primarily based on the Transformer architecture, which result in powerful agents. However, due to slow inference times, Transformer-based approaches are impractical for real-time applications, such as robotics. Recently, modern recurrent architectures, such as xLSTM and Mamba, have been proposed that exhibit parallelization benefits during training similar to the Transformer architecture while offering fast inference. In this work, we study the aptitude of these modern recurrent architectures for large action models. Consequently, we propose a Large Recurrent Action Model (LRAM) with an xLSTM at its core that comes with linear-time inference complexity and natural sequence length extrapolation abilities. Experiments on 432 tasks from 6 domains show that LRAM compares favorably to Transformers in terms of performance and speed.

An essential component of modern recurrent sequence models is the forget gate. While Transformers do not have an explicit recurrent form, we show that a forget gate can be naturally incorporated into Transformers by down-weighting the unnormalized attention scores in a data-dependent way. We name this attention mechanism the Forgetting Attention and the resulting model the Forgetting Transformer (FoX). We show that FoX outperforms the Transformer on long-context language modeling, length extrapolation, and short-context downstream tasks, while performing on par with the Transformer on long-context downstream tasks. Moreover, it is compatible with the FlashAttention algorithm and does not require any positional embeddings. Several analyses, including the needle-in-the-haystack test, show that FoX also retains the Transformer's superior long-context capabilities over recurrent sequence models such as Mamba-2, HGRN2, and DeltaNet. We also introduce a "Pro" block design that incorporates some common architectural components in recurrent sequence models and find it significantly improves the performance of both FoX and the Transformer. Our code is available at https://github.com/zhixuan-lin/forgetting-transformer.

Transformer is a deep neural network that employs a self-attention mechanism to comprehend the contextual relationships within sequential data. Unlike conventional neural networks or updated versions of Recurrent Neural Networks (RNNs) such as Long Short-Term Memory (LSTM), transformer models excel in handling long dependencies between input sequence elements and enable parallel processing. As a result, transformer-based models have attracted substantial interest among researchers in the field of artificial intelligence. This can be attributed to their immense potential and remarkable achievements, not only in Natural Language Processing (NLP) tasks but also in a wide range of domains, including computer vision, audio and speech processing, healthcare, and the Internet of Things (IoT). Although several survey papers have been published highlighting the transformer's contributions in specific fields, architectural differences, or performance evaluations, there is still a significant absence of a comprehensive survey paper encompassing its major applications across various domains. Therefore, we undertook the task of filling this gap by conducting an extensive survey of proposed transformer models from 2017 to 2022. Our survey encompasses the identification of the top five application domains for transformer-based models, namely: NLP, Computer Vision, Multi-Modality, Audio and Speech Processing, and Signal Processing. We analyze the impact of highly influential transformer-based models in these domains and subsequently classify them based on their respective tasks using a proposed taxonomy. Our aim is to shed light on the existing potential and future possibilities of transformers for enthusiastic researchers, thus contributing to the broader understanding of this groundbreaking technology.

In this work, we explore whether modeling recurrence into the Transformer architecture can both be beneficial and efficient, by building an extremely simple recurrent module into the Transformer. We compare our model to baselines following the training and evaluation recipe of BERT. Our results confirm that recurrence can indeed improve Transformer models by a consistent margin, without requiring low-level performance optimizations, and while keeping the number of parameters constant. For example, our base model achieves an absolute improvement of 2.1 points averaged across 10 tasks and also demonstrates increased stability in fine-tuning over a range of learning rates.

Transformer-based large language models (LLMs) excel in modeling complex language patterns but face significant computational costs during inference, especially with long inputs due to the attention mechanism's memory overhead. We observe that certain attention heads exhibit a distribution where the attention weights concentrate on tokens near the query token, termed as recency aware, which focuses on local and short-range dependencies. Leveraging this insight, we propose RecurFormer, a novel architecture that replaces these attention heads with linear recurrent neural networks (RNNs), specifically the Mamba architecture. This replacement reduces the cache size without evicting tokens, thus maintaining generation quality. RecurFormer retains the ability to model long-range dependencies through the remaining attention heads and allows for reusing pre-trained Transformer-based LLMs weights with continual training. Experiments demonstrate that RecurFormer matches the original model's performance while significantly enhancing inference efficiency. Our approach provides a practical solution to the computational challenges of Transformer-based LLMs inference, making it highly attractive for tasks involving long inputs.

This paper explores the potential of recurrent neural networks (RNNs) and other subquadratic architectures as competitive alternatives to transformer-based models in low-resource language modeling scenarios. We utilize HGRN2 (Qin et al., 2024), a recently proposed RNN-based architecture, and comparatively evaluate its effectiveness against transformer-based baselines and other subquadratic architectures (LSTM, xLSTM, Mamba). Our experimental results show that BABYHGRN, our HGRN2 language model, outperforms transformer-based models in both the 10M and 100M word tracks of the challenge, as measured by their performance on the BLiMP, EWoK, GLUE and BEAR benchmarks. Further, we show the positive impact of knowledge distillation. Our findings challenge the prevailing focus on transformer architectures and indicate the viability of RNN-based models, particularly in resource-constrained environments.

Recent advances in recurrent neural network architectures, such as Mamba and RWKV, have enabled RNNs to match or exceed the performance of equal-size transformers in terms of language modeling perplexity and downstream evaluations, suggesting that future systems may be built on completely new architectures. In this paper, we examine if selected interpretability methods originally designed for transformer language models will transfer to these up-and-coming recurrent architectures. Specifically, we focus on steering model outputs via contrastive activation addition, on eliciting latent predictions via the tuned lens, and eliciting latent knowledge from models fine-tuned to produce false outputs under certain conditions. Our results show that most of these techniques are effective when applied to RNNs, and we show that it is possible to improve some of them by taking advantage of RNNs' compressed state.

Transformer-based large language models (LLM) have been widely used in language processing applications. However, most of them restrict the context window that permits the model to attend to every token in the inputs. Previous works in recurrent models can memorize past tokens to enable unlimited context and maintain effectiveness. However, they have "flat" memory architectures, which have limitations in selecting and filtering information. Since humans are good at learning and self-adjustment, we speculate that imitating brain memory hierarchy is beneficial for model memorization. We propose the Hierarchical Memory Transformer (HMT), a novel framework that enables and improves models' long-context processing ability by imitating human memorization behavior. Leveraging memory-augmented segment-level recurrence, we organize the memory hierarchy by preserving tokens from early input token segments, passing memory embeddings along the sequence, and recalling relevant information from history. Evaluating general language modeling (Wikitext-103, PG-19) and question-answering tasks (PubMedQA), we show that HMT steadily improves the long-context processing ability of context-constrained and long-context models. With an additional 0.5% - 2% of parameters, HMT can easily plug in and augment future LLMs to handle long context effectively. Our code is open-sourced on Github: https://github.com/OswaldHe/HMT-pytorch.

Current large language models (LLMs) often perform poorly on simple fact retrieval tasks. Here we investigate if coupling a dynamically adaptable external memory to a LLM can alleviate this problem. For this purpose, we test Larimar, a recently proposed language model architecture which uses an external associative memory, on long-context recall tasks including passkey and needle-in-the-haystack tests. We demonstrate that the external memory of Larimar, which allows fast write and read of an episode of text samples, can be used at test time to handle contexts much longer than those seen during training. We further show that the latent readouts from the memory (to which long contexts are written) control the decoder towards generating correct outputs, with the memory stored off of the GPU. Compared to existing transformer-based LLM architectures for long-context recall tasks that use larger parameter counts or modified attention mechanisms, a relatively smaller size Larimar is able to maintain strong performance without any task-specific training or training on longer contexts.

This paper introduces the Large Memory Model (LM2), a decoder-only Transformer architecture enhanced with an auxiliary memory module that aims to address the limitations of standard Transformers in multi-step reasoning, relational argumentation, and synthesizing information distributed over long contexts. The proposed LM2 incorporates a memory module that acts as a contextual representation repository, interacting with input tokens via cross attention and updating through gating mechanisms. To preserve the Transformers general-purpose capabilities, LM2 maintains the original information flow while integrating a complementary memory pathway. Experimental results on the BABILong benchmark demonstrate that the LM2model outperforms both the memory-augmented RMT model by 37.1% and the baseline Llama-3.2 model by 86.3% on average across tasks. LM2 exhibits exceptional capabilities in multi-hop inference, numerical reasoning, and large-context question-answering. On the MMLU dataset, it achieves a 5.0% improvement over a pre-trained vanilla model, demonstrating that its memory module does not degrade performance on general tasks. Further, in our analysis, we explore the memory interpretability, effectiveness of memory modules, and test-time behavior. Our findings emphasize the importance of explicit memory in enhancing Transformer architectures.

Over more than a decade there has been an extensive research effort on how to effectively utilize recurrent models and attention. While recurrent models aim to compress the data into a fixed-size memory (called hidden state), attention allows attending to the entire context window, capturing the direct dependencies of all tokens. This more accurate modeling of dependencies, however, comes with a quadratic cost, limiting the model to a fixed-length context. We present a new neural long-term memory module that learns to memorize historical context and helps attention to attend to the current context while utilizing long past information. We show that this neural memory has the advantage of fast parallelizable training while maintaining a fast inference. From a memory perspective, we argue that attention due to its limited context but accurate dependency modeling performs as a short-term memory, while neural memory due to its ability to memorize the data, acts as a long-term, more persistent, memory. Based on these two modules, we introduce a new family of architectures, called Titans, and present three variants to address how one can effectively incorporate memory into this architecture. Our experimental results on language modeling, common-sense reasoning, genomics, and time series tasks show that Titans are more effective than Transformers and recent modern linear recurrent models. They further can effectively scale to larger than 2M context window size with higher accuracy in needle-in-haystack tasks compared to baselines.

Transformers have reached remarkable success in sequence modeling. However, these models have efficiency issues as they need to store all the history token-level representations as memory. We present Memformer, an efficient neural network for sequence modeling, that utilizes an external dynamic memory to encode and retrieve past information. Our model achieves linear time complexity and constant memory space complexity when processing long sequences. We also propose a new optimization scheme, memory replay back-propagation (MRBP), which promotes long-range back-propagation through time with a significantly reduced memory requirement. Experimental results show that Memformer has achieved comparable performance compared to the baselines by using 8.1x less memory space and 3.2x faster on inference. Analysis of the attention pattern shows that our external memory slots can encode and retain important information through timesteps.

In order to reduce the computational complexity of large language models, great efforts have been made to to improve the efficiency of transformer models such as linear attention and flash-attention. However, the model size and corresponding computational complexity are constantly scaled up in pursuit of higher performance. In this work, we present MemoryFormer, a novel transformer architecture which significantly reduces the computational complexity (FLOPs) from a new perspective. We eliminate nearly all the computations of the transformer model except for the necessary computation required by the multi-head attention operation. This is made possible by utilizing an alternative method for feature transformation to replace the linear projection of fully-connected layers. Specifically, we first construct a group of in-memory lookup tables that store a large amount of discrete vectors to replace the weight matrix used in linear projection. We then use a hash algorithm to retrieve a correlated subset of vectors dynamically based on the input embedding. The retrieved vectors combined together will form the output embedding, which provides an estimation of the result of matrix multiplication operation in a fully-connected layer. Compared to conducting matrix multiplication, retrieving data blocks from memory is a much cheaper operation which requires little computations. We train MemoryFormer from scratch and conduct extensive experiments on various benchmarks to demonstrate the effectiveness of the proposed model.

Transformers with linear attention (i.e., linear transformers) and state-space models have recently been suggested as a viable linear-time alternative to transformers with softmax attention. However, these models still underperform transformers especially on tasks that require in-context retrieval. While more expressive variants of linear transformers which replace the additive outer-product update in linear transformers with the delta rule have been found to be more effective at associative recall, existing algorithms for training such models do not parallelize over sequence length and are thus inefficient to train on modern hardware. This work describes a hardware-efficient algorithm for training linear transformers with the delta rule, which exploits a memory-efficient representation for computing products of Householder matrices. This algorithm allows us to scale up DeltaNet to standard language modeling settings. We train a 1.3B model for 100B tokens and find that it outperforms recent linear-time baselines such as Mamba and GLA in terms of perplexity and zero-shot performance on downstream tasks (including on tasks that focus on recall). We also experiment with two hybrid models which combine DeltaNet layers with (1) sliding-window attention layers every other layer or (2) two global attention layers, and find that these hybrid models outperform strong transformer baselines.

Countless learning tasks require dealing with sequential data. Image captioning, speech synthesis, and music generation all require that a model produce outputs that are sequences. In other domains, such as time series prediction, video analysis, and musical information retrieval, a model must learn from inputs that are sequences. Interactive tasks, such as translating natural language, engaging in dialogue, and controlling a robot, often demand both capabilities. Recurrent neural networks (RNNs) are connectionist models that capture the dynamics of sequences via cycles in the network of nodes. Unlike standard feedforward neural networks, recurrent networks retain a state that can represent information from an arbitrarily long context window. Although recurrent neural networks have traditionally been difficult to train, and often contain millions of parameters, recent advances in network architectures, optimization techniques, and parallel computation have enabled successful large-scale learning with them. In recent years, systems based on long short-term memory (LSTM) and bidirectional (BRNN) architectures have demonstrated ground-breaking performance on tasks as varied as image captioning, language translation, and handwriting recognition. In this survey, we review and synthesize the research that over the past three decades first yielded and then made practical these powerful learning models. When appropriate, we reconcile conflicting notation and nomenclature. Our goal is to provide a self-contained explication of the state of the art together with a historical perspective and references to primary research.

Deep learning employs multi-layer neural networks trained via the backpropagation algorithm. This approach has achieved success across many domains and relies on adaptive gradient methods such as the Adam optimizer. Sequence modeling evolved from recurrent neural networks to attention-based models, culminating in the Transformer architecture. Transformers have achieved state-of-the-art performance in natural language processing (for example, BERT and GPT-3) and have been applied in computer vision and computational biology. However, theoretical understanding of these models remains limited. In this paper, we examine the mathematical foundations of deep learning and Transformers and present a novel theoretical result. We review key concepts from linear algebra, probability, and optimization that underpin deep learning, and we analyze the multi-head self-attention mechanism and the backpropagation algorithm in detail. Our main contribution is a universal approximation theorem for Transformers: we prove that a single-layer Transformer, comprising one self-attention layer followed by a position-wise feed-forward network with ReLU activation, can approximate any continuous sequence-to-sequence mapping on a compact domain to arbitrary precision. We provide a formal statement and a complete proof. Finally, we present case studies that demonstrate the practical implications of this result. Our findings advance the theoretical understanding of Transformer models and help bridge the gap between theory and practice.

Linear Recurrence has proven to be a powerful tool for modeling long sequences efficiently. In this work, we show that existing models fail to take full advantage of its potential. Motivated by this finding, we develop GateLoop, a foundational sequence model that generalizes linear recurrent models such as S4, S5, LRU and RetNet, by employing data-controlled state transitions. Utilizing this theoretical advance, GateLoop empirically outperforms existing models for auto-regressive language modeling. Our method comes with a low-cost O(l) recurrent mode and an efficient O(l log_{2} l) parallel mode making use of highly optimized associative scan implementations. Furthermore, we derive an O(l^2) surrogate attention mode, revealing remarkable implications for Transformer and recently proposed architectures. Specifically, we prove that our approach can be interpreted as providing data-controlled relative-positional information to Attention. While many existing models solely rely on data-controlled cumulative sums for context aggregation, our findings suggest that incorporating data-controlled complex cumulative products may be a crucial step towards more powerful sequence models.

Recently, recurrent models based on linear state space models (SSMs) have shown promising performance in language modeling (LM), competititve with transformers. However, there is little understanding of the in-principle abilities of such models, which could provide useful guidance to the search for better LM architectures. We present a comprehensive theoretical study of the capacity of such SSMs as it compares to that of transformers and traditional RNNs. We find that SSMs and transformers have overlapping but distinct strengths. In star-free state tracking, SSMs implement straightforward and exact solutions to problems that transformers struggle to represent exactly. They can also model bounded hierarchical structure with optimal memory even without simulating a stack. On the other hand, we identify a design choice in current SSMs that limits their expressive power. We discuss implications for SSM and LM research, and verify results empirically on a recent SSM, Mamba.

Transformers are considered conceptually different compared to the previous generation of state-of-the-art NLP models - recurrent neural networks (RNNs). In this work, we demonstrate that decoder-only transformers can in fact be conceptualized as infinite multi-state RNNs - an RNN variant with unlimited hidden state size. We further show that pretrained transformers can be converted into finite multi-state RNNs by fixing the size of their hidden state. We observe that several existing transformers cache compression techniques can be framed as such conversion policies, and introduce a novel policy, TOVA, which is simpler compared to these policies. Our experiments with several long range tasks indicate that TOVA outperforms all other baseline policies, while being nearly on par with the full (infinite) model, and using in some cases only 1{8} of the original cache size. Our results indicate that transformer decoder LLMs often behave in practice as RNNs. They also lay out the option of mitigating one of their most painful computational bottlenecks - the size of their cache memory. We publicly release our code at https://github.com/schwartz-lab-NLP/TOVA.

We present the Compressive Transformer, an attentive sequence model which compresses past memories for long-range sequence learning. We find the Compressive Transformer obtains state-of-the-art language modelling results in the WikiText-103 and Enwik8 benchmarks, achieving 17.1 ppl and 0.97 bpc respectively. We also find it can model high-frequency speech effectively and can be used as a memory mechanism for RL, demonstrated on an object matching task. To promote the domain of long-range sequence learning, we propose a new open-vocabulary language modelling benchmark derived from books, PG-19.

Video Captioning and Summarization have become very popular in the recent years due to advancements in Sequence Modelling, with the resurgence of Long-Short Term Memory networks (LSTMs) and introduction of Gated Recurrent Units (GRUs). Existing architectures extract spatio-temporal features using CNNs and utilize either GRUs or LSTMs to model dependencies with soft attention layers. These attention layers do help in attending to the most prominent features and improve upon the recurrent units, however, these models suffer from the inherent drawbacks of the recurrent units themselves. The introduction of the Transformer model has driven the Sequence Modelling field into a new direction. In this project, we implement a Transformer-based model for Video captioning, utilizing 3D CNN architectures like C3D and Two-stream I3D for video extraction. We also apply certain dimensionality reduction techniques so as to keep the overall size of the model within limits. We finally present our results on the MSVD and ActivityNet datasets for Single and Dense video captioning tasks respectively.

In multi-source sequence-to-sequence tasks, the attention mechanism can be modeled in several ways. This topic has been thoroughly studied on recurrent architectures. In this paper, we extend the previous work to the encoder-decoder attention in the Transformer architecture. We propose four different input combination strategies for the encoder-decoder attention: serial, parallel, flat, and hierarchical. We evaluate our methods on tasks of multimodal translation and translation with multiple source languages. The experiments show that the models are able to use multiple sources and improve over single source baselines.

The transformer architecture and variants presented remarkable success across many machine learning tasks in recent years. This success is intrinsically related to the capability of handling long sequences and the presence of context-dependent weights from the attention mechanism. We argue that these capabilities suit the central role of a Meta-Reinforcement Learning algorithm. Indeed, a meta-RL agent needs to infer the task from a sequence of trajectories. Furthermore, it requires a fast adaptation strategy to adapt its policy for a new task -- which can be achieved using the self-attention mechanism. In this work, we present TrMRL (Transformers for Meta-Reinforcement Learning), a meta-RL agent that mimics the memory reinstatement mechanism using the transformer architecture. It associates the recent past of working memories to build an episodic memory recursively through the transformer layers. We show that the self-attention computes a consensus representation that minimizes the Bayes Risk at each layer and provides meaningful features to compute the best actions. We conducted experiments in high-dimensional continuous control environments for locomotion and dexterous manipulation. Results show that TrMRL presents comparable or superior asymptotic performance, sample efficiency, and out-of-distribution generalization compared to the baselines in these environments.

We introduce the Autoregressive Block-Based Iterative Encoder (AbbIE), a novel recursive generalization of the encoder-only Transformer architecture, which achieves better perplexity than a standard Transformer and allows for the dynamic scaling of compute resources at test time. This simple, recursive approach is a complement to scaling large language model (LLM) performance through parameter and token counts. AbbIE performs its iterations in latent space, but unlike latent reasoning models, does not require a specialized dataset or training protocol. We show that AbbIE upward generalizes (ability to generalize to arbitrary iteration lengths) at test time by only using 2 iterations during train time, far outperforming alternative iterative methods. AbbIE's ability to scale its computational expenditure based on the complexity of the task gives it an up to 12\% improvement in zero-shot in-context learning tasks versus other iterative and standard methods and up to 5\% improvement in language perplexity. The results from this study open a new avenue to Transformer performance scaling. We perform all of our evaluations on model sizes up to 350M parameters.

Sequence modeling is a crucial area across various domains, including Natural Language Processing (NLP), speech recognition, time series forecasting, music generation, and bioinformatics. Recurrent Neural Networks (RNNs) and Long Short Term Memory Networks (LSTMs) have historically dominated sequence modeling tasks like Machine Translation, Named Entity Recognition (NER), etc. However, the advancement of transformers has led to a shift in this paradigm, given their superior performance. Yet, transformers suffer from O(N^2) attention complexity and challenges in handling inductive bias. Several variations have been proposed to address these issues which use spectral networks or convolutions and have performed well on a range of tasks. However, they still have difficulty in dealing with long sequences. State Space Models(SSMs) have emerged as promising alternatives for sequence modeling paradigms in this context, especially with the advent of S4 and its variants, such as S4nd, Hippo, Hyena, Diagnol State Spaces (DSS), Gated State Spaces (GSS), Linear Recurrent Unit (LRU), Liquid-S4, Mamba, etc. In this survey, we categorize the foundational SSMs based on three paradigms namely, Gating architectures, Structural architectures, and Recurrent architectures. This survey also highlights diverse applications of SSMs across domains such as vision, video, audio, speech, language (especially long sequence modeling), medical (including genomics), chemical (like drug design), recommendation systems, and time series analysis, including tabular data. Moreover, we consolidate the performance of SSMs on benchmark datasets like Long Range Arena (LRA), WikiText, Glue, Pile, ImageNet, Kinetics-400, sstv2, as well as video datasets such as Breakfast, COIN, LVU, and various time series datasets. The project page for Mamba-360 work is available on this webpage.https://github.com/badripatro/mamba360.

Advancing the frontier of subquadratic architectures for Language Models (LMs) is crucial in the rapidly evolving field of natural language processing. Current innovations, including State Space Models, were initially celebrated for surpassing Transformer performance on language modeling tasks. However, these models have revealed deficiencies in essential In-Context Learning capabilities - a domain where the Transformer traditionally shines. The Based model emerged as a hybrid solution, blending a Linear Transformer with a kernel inspired by the Taylor expansion of exponential functions, augmented by convolutional networks. Mirroring the Transformer's in-context adeptness, it became a strong contender in the field. In our work, we present a singular, elegant alteration to the Based kernel that amplifies its In-Context Learning abilities evaluated with the Multi-Query Associative Recall task and overall language modeling process, as demonstrated on the Pile dataset.

Contextual memory integration remains a high challenge in the development of language models, particularly in tasks that require maintaining coherence over extended sequences. Traditional approaches, such as self-attention mechanisms and memory-augmented architectures, often prioritize short-term dependencies, leading to fragmentation and inconsistency in long-range contextual understanding. Inspired by principles of synaptic plasticity observed in biological neural systems, a novel mechanism, Synaptic Resonance, is introduced to dynamically reinforce relevant memory pathways during training and inference. Unlike static memory representations, this mechanism continuously adjusts synaptic weight matrices based on contextual relevance, allowing for improved information retention without excessive computational overhead. Evaluations conducted on an open-source language model demonstrate reductions in perplexity, enhancements in contextual coherence, and increased robustness against input noise, highlighting the effectiveness of reinforcement-driven memory modulation. Comparative analysis against baseline models further reveals that the proposed approach achieves higher memory retention efficiency while maintaining computational feasibility. The architectural modifications integrate seamlessly into existing transformer-based frameworks, ensuring stable convergence and efficient inference without sacrificing scalability. Applications benefiting from improved long-term contextual consistency, such as dialogue systems and document summarization, stand to gain from this approach. Empirical findings suggest that dynamically reinforced memory pathways offer a promising alternative to conventional memory mechanisms, addressing longstanding limitations in extended sequence modeling.

The self-attention mechanism in the transformer architecture is capable of capturing long-range dependencies and it is the main reason behind its effectiveness in processing sequential data. Nevertheless, despite their success, transformers have two significant drawbacks that still limit their broader applicability: (1) In order to remember past information, the self-attention mechanism requires access to the whole history to be provided as context. (2) The inference cost in transformers is expensive. In this paper we introduce recurrent alternatives to the transformer self-attention mechanism that offer a context-independent inference cost, leverage long-range dependencies effectively, and perform well in practice. We evaluate our approaches in reinforcement learning problems where the aforementioned computational limitations make the application of transformers nearly infeasible. We quantify the impact of the different components of our architecture in a diagnostic environment and assess performance gains in 2D and 3D pixel-based partially-observable environments. When compared to a state-of-the-art architecture, GTrXL, inference in our approach is at least 40% cheaper while reducing memory use in more than 50%. Our approach either performs similarly or better than GTrXL, improving more than 37% upon GTrXL performance on harder tasks.

Transformers have emerged as the architecture of choice for many state-of-the-art AI models, showcasing exceptional performance across a wide range of AI applications. However, the memory demands imposed by Transformers limit their ability to handle long sequences, thereby creating challenges for tasks involving extended sequences or long-term dependencies. We present a distinct approach, Ring Attention, which leverages blockwise computation of self-attention to distribute long sequences across multiple devices while concurrently overlapping the communication of key-value blocks with the computation of blockwise attention. By processing longer input sequences while maintaining memory efficiency, Ring Attention enables training and inference of sequences that are device count times longer than those of prior memory-efficient Transformers, effectively eliminating the memory constraints imposed by individual devices. Extensive experiments on language modeling tasks demonstrate the effectiveness of Ring Attention in allowing large sequence input size and improving performance.

A recent trend in LLMs is developing recurrent sub-quadratic models that improve long-context processing efficiency. We investigate leading large long-context models, focusing on how their fixed-size recurrent memory affects their performance. Our experiments reveal that, even when these models are trained for extended contexts, their use of long contexts remains underutilized. Specifically, we demonstrate that a chunk-based inference procedure, which identifies and processes only the most relevant portion of the input can mitigate recurrent memory failures and be effective for many long-context tasks: On LongBench, our method improves the overall performance of Falcon3-Mamba-Inst-7B by 14%, Falcon-Mamba-Inst-7B by 28%, RecurrentGemma-IT-9B by 50%, and RWKV6-Finch-7B by 51%. Surprisingly, this simple approach also leads to state-of-the-art results in the challenging LongBench v2 benchmark, showing competitive performance with equivalent size Transformers. Furthermore, our findings raise questions about whether recurrent models genuinely exploit long-range dependencies, as our single-chunk strategy delivers stronger performance - even in tasks that presumably require cross-context relations.

Neural architecture search (NAS) has allowed for the automatic creation of new and effective neural network architectures, offering an alternative to the laborious process of manually designing complex architectures. However, traditional NAS algorithms are slow and require immense amounts of computing power. Recent research has investigated training-free NAS metrics for image classification architectures, drastically speeding up search algorithms. In this paper, we investigate training-free NAS metrics for recurrent neural network (RNN) and BERT-based transformer architectures, targeted towards language modeling tasks. First, we develop a new training-free metric, named hidden covariance, that predicts the trained performance of an RNN architecture and significantly outperforms existing training-free metrics. We experimentally evaluate the effectiveness of the hidden covariance metric on the NAS-Bench-NLP benchmark. Second, we find that the current search space paradigm for transformer architectures is not optimized for training-free neural architecture search. Instead, a simple qualitative analysis can effectively shrink the search space to the best performing architectures. This conclusion is based on our investigation of existing training-free metrics and new metrics developed from recent transformer pruning literature, evaluated on our own benchmark of trained BERT architectures. Ultimately, our analysis shows that the architecture search space and the training-free metric must be developed together in order to achieve effective results.

Attention mechanisms have revolutionized sequence learning but suffer from quadratic computational complexity. This paper introduces Lattice, a novel recurrent neural network (RNN) mechanism that leverages the inherent low-rank structure of K-V matrices to efficiently compress the cache into a fixed number of memory slots, achieving sub-quadratic complexity. We formulate this compression as an online optimization problem and derive a dynamic memory update rule based on a single gradient descent step. The resulting recurrence features a state- and input-dependent gating mechanism, offering an interpretable memory update process. The core innovation is the orthogonal update: each memory slot is updated exclusively with information orthogonal to its current state hence incorporation of only novel, non-redundant data, which minimizes the interference with previously stored information. The experimental results show that Lattice achieves the best perplexity compared to all baselines across diverse context lengths, with performance improvement becoming more pronounced as the context length increases.

Several variants of the Long Short-Term Memory (LSTM) architecture for recurrent neural networks have been proposed since its inception in 1995. In recent years, these networks have become the state-of-the-art models for a variety of machine learning problems. This has led to a renewed interest in understanding the role and utility of various computational components of typical LSTM variants. In this paper, we present the first large-scale analysis of eight LSTM variants on three representative tasks: speech recognition, handwriting recognition, and polyphonic music modeling. The hyperparameters of all LSTM variants for each task were optimized separately using random search, and their importance was assessed using the powerful fANOVA framework. In total, we summarize the results of 5400 experimental runs (approx 15 years of CPU time), which makes our study the largest of its kind on LSTM networks. Our results show that none of the variants can improve upon the standard LSTM architecture significantly, and demonstrate the forget gate and the output activation function to be its most critical components. We further observe that the studied hyperparameters are virtually independent and derive guidelines for their efficient adjustment.

Transformers have emerged as the cornerstone of state-of-the-art natural language processing models, showcasing exceptional performance across a wide range of AI applications. However, the memory demands posed by the self-attention mechanism and the large feedforward network in Transformers limit their ability to handle long sequences, thereby creating challenges for tasks involving multiple long sequences or long-term dependencies. We present a distinct approach, Blockwise Parallel Transformer (BPT), that leverages blockwise computation of self-attention and feedforward network fusion to minimize memory costs. By processing longer input sequences while maintaining memory efficiency, BPT enables training sequences up to 32 times longer than vanilla Transformers and 2 to 4 times longer than previous memory-efficient methods. Extensive experiments on language modeling and reinforcement learning tasks demonstrate the effectiveness of BPT in reducing memory requirements and improving performance.

The Transformer is a sequence model that forgoes traditional recurrent architectures in favor of a fully attention-based approach. Besides improving performance, an advantage of using attention is that it can also help to interpret a model by showing how the model assigns weight to different input elements. However, the multi-layer, multi-head attention mechanism in the Transformer model can be difficult to decipher. To make the model more accessible, we introduce an open-source tool that visualizes attention at multiple scales, each of which provides a unique perspective on the attention mechanism. We demonstrate the tool on BERT and OpenAI GPT-2 and present three example use cases: detecting model bias, locating relevant attention heads, and linking neurons to model behavior.

Managing long texts is challenging for large language models (LLMs) due to limited context window sizes. This study introduces UIO-LLMs, an unbiased incremental optimization approach for memory-enhanced transformers under long-context settings. We initially conceptualize the process as a streamlined encoder-decoder framework where the weights-shared encoder and decoder respectively encapsulate a context segment into memories and leverage these memories to predict outputs of the subsequent segment. Subsequently, by treating our memory-enhanced transformers as fully-connected recurrent neural networks (RNNs), we refine the training process using the Truncated Backpropagation Through Time (TBPTT) algorithm, which incorporates innovative incremental optimization techniques. These techniques not only diminish time complexity but also address the bias in gradient computation through an unbiased optimization process. UIO-LLMs successfully handle long context, such as extending the context window of Llama2-7b-chat from 4K to 100K tokens with minimal 2% additional parameters, while keeping the inference cost nearly linear as context length increases.

With the advancement of RNN models with linear complexity, the quadratic complexity challenge of transformers has the potential to be overcome. Notably, the emerging Mamba-2 has demonstrated competitive performance, bridging the gap between RNN models and transformers. However, due to sequential processing and vanishing gradients, RNN models struggle to capture long-range dependencies, limiting contextual understanding. This results in slow convergence, high resource demands, and poor performance on downstream understanding and complex reasoning tasks. In this work, we present a hybrid model MaTVLM by substituting a portion of the transformer decoder layers in a pre-trained VLM with Mamba-2 layers. Leveraging the inherent relationship between attention and Mamba-2, we initialize Mamba-2 with corresponding attention weights to accelerate convergence. Subsequently, we employ a single-stage distillation process, using the pre-trained VLM as the teacher model to transfer knowledge to the MaTVLM, further enhancing convergence speed and performance. Furthermore, we investigate the impact of differential distillation loss within our training framework. We evaluate the MaTVLM on multiple benchmarks, demonstrating competitive performance against the teacher model and existing VLMs while surpassing both Mamba-based VLMs and models of comparable parameter scales. Remarkably, the MaTVLM achieves up to 3.6x faster inference than the teacher model while reducing GPU memory consumption by 27.5%, all without compromising performance. Code and models are released at http://github.com/hustvl/MaTVLM.

Transformers are powerful sequence models, but require time and memory that grows quadratically with the sequence length. In this paper we introduce sparse factorizations of the attention matrix which reduce this to O(n n). We also introduce a) a variation on architecture and initialization to train deeper networks, b) the recomputation of attention matrices to save memory, and c) fast attention kernels for training. We call networks with these changes Sparse Transformers, and show they can model sequences tens of thousands of timesteps long using hundreds of layers. We use the same architecture to model images, audio, and text from raw bytes, setting a new state of the art for density modeling of Enwik8, CIFAR-10, and ImageNet-64. We generate unconditional samples that demonstrate global coherence and great diversity, and show it is possible in principle to use self-attention to model sequences of length one million or more.

Efficient long-context modeling remains a critical challenge for natural language processing (NLP), as the time complexity of the predominant Transformer architecture scales quadratically with the sequence length. While state-space models (SSMs) offer alternative sub-quadratic solutions, they struggle to capture long-range dependencies effectively. In this work, we focus on analyzing and improving the long-context modeling capabilities of SSMs. We show that the widely used synthetic task, associative recall, which requires a model to recall a value associated with a single key without context, insufficiently represents the complexities of real-world long-context modeling. To address this limitation, we extend the associative recall to a novel synthetic task, joint recall, which requires a model to recall the value associated with a key given in a specified context. Theoretically, we prove that SSMs do not have the expressiveness to solve multi-query joint recall in sub-quadratic time complexity. To resolve this issue, we propose a solution based on integrating SSMs with Context-Dependent Sparse Attention (CDSA), which has the expressiveness to solve multi-query joint recall with sub-quadratic computation. To bridge the gap between theoretical analysis and real-world applications, we propose locality-sensitive Hashing Attention with sparse Key Selection (HAX), which instantiates the theoretical solution and is further tailored to natural language domains. Extensive experiments on both synthetic and real-world long-context benchmarks show that HAX consistently outperforms SSM baselines and SSMs integrated with context-independent sparse attention (CISA).

Transformer-based models have emerged as one of the most widely used architectures for natural language processing, natural language generation, and image generation. The size of the state-of-the-art models has increased steadily reaching billions of parameters. These huge models are memory hungry and incur significant inference latency even on cutting edge AI-accelerators, such as GPUs. Specifically, the time and memory complexity of the attention operation is quadratic in terms of the total context length, i.e., prompt and output tokens. Thus, several optimizations such as key-value tensor caching and FlashAttention computation have been proposed to deliver the low latency demands of applications relying on such large models. However, these techniques do not cater to the computationally distinct nature of different phases during inference. To that end, we propose LeanAttention, a scalable technique of computing self-attention for the token-generation phase (decode-phase) of decoder-only transformer models. LeanAttention enables scaling the attention mechanism implementation for the challenging case of long context lengths by re-designing the execution flow for the decode-phase. We identify that the associative property of online softmax can be treated as a reduction operation thus allowing us to parallelize the attention computation over these large context lengths. We extend the "stream-K" style reduction of tiled calculation to self-attention to enable parallel computation resulting in an average of 2.6x attention execution speedup over FlashAttention-2 and up to 8.33x speedup for 512k context lengths.

Owing to their ability to both effectively integrate information over long time horizons and scale to massive amounts of data, self-attention architectures have recently shown breakthrough success in natural language processing (NLP), achieving state-of-the-art results in domains such as language modeling and machine translation. Harnessing the transformer's ability to process long time horizons of information could provide a similar performance boost in partially observable reinforcement learning (RL) domains, but the large-scale transformers used in NLP have yet to be successfully applied to the RL setting. In this work we demonstrate that the standard transformer architecture is difficult to optimize, which was previously observed in the supervised learning setting but becomes especially pronounced with RL objectives. We propose architectural modifications that substantially improve the stability and learning speed of the original Transformer and XL variant. The proposed architecture, the Gated Transformer-XL (GTrXL), surpasses LSTMs on challenging memory environments and achieves state-of-the-art results on the multi-task DMLab-30 benchmark suite, exceeding the performance of an external memory architecture. We show that the GTrXL, trained using the same losses, has stability and performance that consistently matches or exceeds a competitive LSTM baseline, including on more reactive tasks where memory is less critical. GTrXL offers an easy-to-train, simple-to-implement but substantially more expressive architectural alternative to the standard multi-layer LSTM ubiquitously used for RL agents in partially observable environments.

Ever since their conception, Transformers have taken over traditional sequence models in many tasks, such as NLP, image classification, and video/audio processing, for their fast training and superior performance. Much of the merit is attributable to positional encoding and multi-head attention. However, Transformers fall short in learning long-range dependencies mainly due to the quadratic complexity scaled with context length, in terms of both time and space. Consequently, over the past five years, a myriad of methods has been proposed to make Transformers more efficient. In this work, we first take a step back, study and compare existing solutions to long-sequence modeling in terms of their pure mathematical formulation. Specifically, we summarize them using a unified template, given their shared nature of token mixing. Through benchmarks, we then demonstrate that long context length does yield better performance, albeit application-dependent, and traditional Transformer models fall short in taking advantage of long-range dependencies. Next, inspired by emerging sparse models of huge capacity, we propose a machine learning system for handling million-scale dependencies. As a proof of concept, we evaluate the performance of one essential component of this system, namely, the distributed multi-head attention. We show that our algorithm can scale up attention computation by almost 40times using four GeForce RTX 4090 GPUs, compared to vanilla multi-head attention mechanism. We believe this study is an instrumental step towards modeling million-scale dependencies.

Vision Transformers (ViTs) have attracted a lot of popularity in recent years, due to their exceptional capabilities in modeling long-range spatial dependencies and scalability for large scale training. Although the training parallelism of self-attention mechanism plays an important role in retaining great performance, its quadratic complexity baffles the application of ViTs in many scenarios which demand fast inference. This effect is even more pronounced in applications in which autoregressive modeling of input features is required. In Natural Language Processing (NLP), a new stream of efforts have proposed parallelizable models with recurrent formulation that allows for efficient inference in generative applications. Inspired by this trend, we propose a new class of computer vision models, dubbed Vision Retention Networks (ViR), with dual parallel and recurrent formulations, which strike an optimal balance between fast inference and parallel training with competitive performance. In particular, ViR scales favorably for image throughput and memory consumption in tasks that require higher-resolution images due to its flexible formulation in processing large sequence lengths. The ViR is the first attempt to realize dual parallel and recurrent equivalency in a general vision backbone for recognition tasks. We have validated the effectiveness of ViR through extensive experiments with different dataset sizes and various image resolutions and achieved competitive performance. Our code and pretrained models will be made publicly available.

Effective representation learning from text has been an active area of research in the fields of NLP and text mining. Attention mechanisms have been at the forefront in order to learn contextual sentence representations. Current state-of-the-art approaches for many NLP tasks use large pre-trained language models such as BERT, XLNet and so on for learning representations. These models are based on the Transformer architecture that involves recurrent blocks of computation consisting of multi-head self-attention and feedforward networks. One of the major bottlenecks largely contributing to the computational complexity of the Transformer models is the self-attention layer, that is both computationally expensive and parameter intensive. In this work, we introduce a novel multi-head self-attention mechanism operating on GRUs that is shown to be computationally cheaper and more parameter efficient than self-attention mechanism proposed in Transformers for text classification tasks. The efficiency of our approach mainly stems from two optimizations; 1) we use low-rank matrix factorization of the affinity matrix to efficiently get multiple attention distributions instead of having separate parameters for each head 2) attention scores are obtained by querying a global context vector instead of densely querying all the words in the sentence. We evaluate the performance of the proposed model on tasks such as sentiment analysis from movie reviews, predicting business ratings from reviews and classifying news articles into topics. We find that the proposed approach matches or outperforms a series of strong baselines and is more parameter efficient than comparable multi-head approaches. We also perform qualitative analyses to verify that the proposed approach is interpretable and captures context-dependent word importance.

Sequence models like Transformers and RNNs often overallocate attention to irrelevant context, leading to noisy intermediate representations. This degrades LLM capabilities by promoting hallucinations, weakening long-range and retrieval abilities, and reducing robustness. Recent work has shown that differential design can mitigate this issue in Transformers, improving their effectiveness across various applications. In this paper, we explore whether these techniques, originally developed for Transformers, can be applied to Mamba, a recent architecture based on selective state-space layers that achieves Transformer-level performance with greater efficiency. We show that a naive adaptation of differential design to Mamba is insufficient and requires careful architectural modifications. To address this, we introduce a novel differential mechanism for Mamba, empirically validated on language modeling benchmarks, demonstrating improved retrieval capabilities and superior performance over vanilla Mamba. Finally, we conduct extensive ablation studies and empirical analyses to justify our design choices and provide evidence that our approach effectively mitigates the overallocation problem in Mamba-based models. Our code is publicly available.

In this paper, we present a novel approach for incorporating external knowledge in Recurrent Neural Networks (RNNs). We propose the integration of lexicon features into the self-attention mechanism of RNN-based architectures. This form of conditioning on the attention distribution, enforces the contribution of the most salient words for the task at hand. We introduce three methods, namely attentional concatenation, feature-based gating and affine transformation. Experiments on six benchmark datasets show the effectiveness of our methods. Attentional feature-based gating yields consistent performance improvement across tasks. Our approach is implemented as a simple add-on module for RNN-based models with minimal computational overhead and can be adapted to any deep neural architecture.

Self-attention performs well in long context but has quadratic complexity. Existing RNN layers have linear complexity, but their performance in long context is limited by the expressive power of their hidden state. We propose a new class of sequence modeling layers with linear complexity and an expressive hidden state. The key idea is to make the hidden state a machine learning model itself, and the update rule a step of self-supervised learning. Since the hidden state is updated by training even on test sequences, our layers are called Test-Time Training (TTT) layers. We consider two instantiations: TTT-Linear and TTT-MLP, whose hidden state is a linear model and a two-layer MLP respectively. We evaluate our instantiations at the scale of 125M to 1.3B parameters, comparing with a strong Transformer and Mamba, a modern RNN. Both TTT-Linear and TTT-MLP match or exceed the baselines. Similar to Transformer, they can keep reducing perplexity by conditioning on more tokens, while Mamba cannot after 16k context. With preliminary systems optimization, TTT-Linear is already faster than Transformer at 8k context and matches Mamba in wall-clock time. TTT-MLP still faces challenges in memory I/O, but shows larger potential in long context, pointing to a promising direction for future research.

In this work, we propose Retentive Network (RetNet) as a foundation architecture for large language models, simultaneously achieving training parallelism, low-cost inference, and good performance. We theoretically derive the connection between recurrence and attention. Then we propose the retention mechanism for sequence modeling, which supports three computation paradigms, i.e., parallel, recurrent, and chunkwise recurrent. Specifically, the parallel representation allows for training parallelism. The recurrent representation enables low-cost O(1) inference, which improves decoding throughput, latency, and GPU memory without sacrificing performance. The chunkwise recurrent representation facilitates efficient long-sequence modeling with linear complexity, where each chunk is encoded parallelly while recurrently summarizing the chunks. Experimental results on language modeling show that RetNet achieves favorable scaling results, parallel training, low-cost deployment, and efficient inference. The intriguing properties make RetNet a strong successor to Transformer for large language models. Code will be available at https://aka.ms/retnet.

In order to make the foundation model more efficient and effective, our idea is combining sequence transformation and state transformation. First, we prove the availability of rotary position embedding in the state space duality algorithm, which reduces the perplexity of the hybrid quadratic causal self-attention and state space duality by more than 4%, to ensure that the combining sequence transformation unifies position encoding. Second, we propose dynamic mask attention, which maintains 100% accuracy in the more challenging multi-query associative recall task, improving by more than 150% compared to quadratic causal self-attention and state space duality, to ensure that the combining sequence transformation selectively filters relevant information. Third, we design cross domain mixture of experts, which makes the computational speed of expert retrieval with more than 1024 experts 8 to 10 times faster than the mixture of experts, to ensure that the combining state transformation quickly retrieval mixture. Finally, we summarize these matrix algorithms that can form the foundation model: Wonderful Matrices, which can be a competitor to popular model architectures.

In recent years, transformer-based models have gained prominence in multivariate long-term time series forecasting (LTSF), demonstrating significant advancements despite facing challenges such as high computational demands, difficulty in capturing temporal dynamics, and managing long-term dependencies. The emergence of LTSF-Linear, with its straightforward linear architecture, has notably outperformed transformer-based counterparts, prompting a reevaluation of the transformer's utility in time series forecasting. In response, this paper presents an adaptation of a recent architecture termed extended LSTM (xLSTM) for LTSF. xLSTM incorporates exponential gating and a revised memory structure with higher capacity that has good potential for LTSF. Our adopted architecture for LTSF termed as xLSTMTime surpasses current approaches. We compare xLSTMTime's performance against various state-of-the-art models across multiple real-world da-tasets, demonstrating superior forecasting capabilities. Our findings suggest that refined recurrent architectures can offer competitive alternatives to transformer-based models in LTSF tasks, po-tentially redefining the landscape of time series forecasting.

The Transformer architecture consists of self-attention and feed-forward networks (FFNs) which can be viewed as key-value memories according to previous works. However, FFN and traditional memory utilize different activation functions (i.e., ReLU and Softmax respectively), which makes them not equivalent. In this paper, we first rebuild the connections between FFN and key-value memory by conducting extensive studies on ReLU and Softmax, and find they are equivalent when adding an additional layer normalization module on Softmax. In addition, ReLU outperforms Softmax on both FFN and key-value memory when the number of value slots is large. We analyze the reasons and then explore this good property of ReLU on the self-attention network where the original Softmax activation performs poorly on long input sequences. We then propose a full ReLU architecture named ReLUFormer which performs better than the baseline Transformer on long sequence tasks such as document translation. This paper sheds light on the following points: 1) Softmax and ReLU use different normalization methods over elements which lead to different variances of results, and ReLU is good at dealing with a large number of key-value slots; 2) FFN and key-value memory are equivalent, and thus the Transformer can be viewed as a memory network where FFNs and self-attention networks are both key-value memories.

In contrast to RNNs, which compress previous tokens into a single hidden state, Transformers can attend to all previous tokens directly. However, standard Transformers only use representations from the immediately preceding layer. In this paper, we show that this design choice causes representation collapse and leads to suboptimal performance. To address this issue, we introduce Layer-Integrated Memory (LIMe), a simple yet powerful approach that preserves the model's overall memory footprint while expanding its representational capacity by allowing access to hidden states from earlier layers. Through extensive experiments across various architectures and different lookup mechanisms, we demonstrate consistent performance improvements on a wide range of tasks. Moreover, our analysis of the learned representation dynamics and our exploration of depthwise circuits reveal how LIMe integrates information across layers, pointing to promising directions for future research.

In this paper we propose augmenting Vision Transformer models with learnable memory tokens. Our approach allows the model to adapt to new tasks, using few parameters, while optionally preserving its capabilities on previously learned tasks. At each layer we introduce a set of learnable embedding vectors that provide contextual information useful for specific datasets. We call these "memory tokens". We show that augmenting a model with just a handful of such tokens per layer significantly improves accuracy when compared to conventional head-only fine-tuning, and performs only slightly below the significantly more expensive full fine-tuning. We then propose an attention-masking approach that enables extension to new downstream tasks, with a computation reuse. In this setup in addition to being parameters efficient, models can execute both old and new tasks as a part of single inference at a small incremental cost.

While Attention has come to be an important mechanism in deep learning, there remains limited intuition for why it works so well. Here, we show that Transformer Attention can be closely related under certain data conditions to Kanerva's Sparse Distributed Memory (SDM), a biologically plausible associative memory model. We confirm that these conditions are satisfied in pre-trained GPT2 Transformer models. We discuss the implications of the Attention-SDM map and provide new computational and biological interpretations of Attention.

Models based on deep convolutional networks have dominated recent image interpretation tasks; we investigate whether models which are also recurrent, or "temporally deep", are effective for tasks involving sequences, visual and otherwise. We develop a novel recurrent convolutional architecture suitable for large-scale visual learning which is end-to-end trainable, and demonstrate the value of these models on benchmark video recognition tasks, image description and retrieval problems, and video narration challenges. In contrast to current models which assume a fixed spatio-temporal receptive field or simple temporal averaging for sequential processing, recurrent convolutional models are "doubly deep"' in that they can be compositional in spatial and temporal "layers". Such models may have advantages when target concepts are complex and/or training data are limited. Learning long-term dependencies is possible when nonlinearities are incorporated into the network state updates. Long-term RNN models are appealing in that they directly can map variable-length inputs (e.g., video frames) to variable length outputs (e.g., natural language text) and can model complex temporal dynamics; yet they can be optimized with backpropagation. Our recurrent long-term models are directly connected to modern visual convnet models and can be jointly trained to simultaneously learn temporal dynamics and convolutional perceptual representations. Our results show such models have distinct advantages over state-of-the-art models for recognition or generation which are separately defined and/or optimized.

Transformers are the cornerstone of modern large language models, but their quadratic computational complexity limits efficiency in long-sequence processing. Recent advancements in Mamba, a state space model (SSM) with linear complexity, offer promising efficiency gains but suffer from unstable contextual learning and multitask generalization. This paper proposes TransMamba, a novel framework that unifies Transformer and Mamba through shared parameter matrices (e.g., QKV and CBx), and thus could dynamically switch between attention and SSM mechanisms at different token lengths and layers. We design the Memory converter to bridge Transformer and Mamba by converting attention outputs into SSM-compatible states, ensuring seamless information flow at TransPoints where the transformation happens. The TransPoint scheduling is also thoroughly explored for further improvements. We conducted extensive experiments demonstrating that TransMamba achieves superior training efficiency and performance compared to baselines, and validated the deeper consistency between Transformer and Mamba paradigms, offering a scalable solution for next-generation sequence modeling.

While modern decoder-only LLMs achieve superior performance across various domains, hallucinations have risen to be a common problem in their generated text, hindering their application in knowledge-intensive tasks. Retriever-augmented generation (RAG) offers a solution, but the non-parametric nature of the retriever hinders its deep interaction with LLM. In this work, we propose to decouple memorization from the LLM decoder using a pretrained, differentiable external memory. The external memory is an MLP pretrained by imitating the behavior of a retriever on the entire pretraining dataset. Our resulting architecture, which comprises a transformer decoder and an external MLP memory pretrained on language modeling and retriever imitation respectively, demonstrates strong perplexity and performance on downstream tasks. Experiments show our architecture exhibits steeper power-law scaling with model size, achieving 17.5% and 24.1% improvement on WikiText-103 and Web datasets compared to decoder-only models while benefiting from added training without overfitting. We demonstrate superior performance on three hallucination benchmarks and nine memory-intensive tasks. Additionally, our approach delivers 80times speedup over kNN-LM (500M tokens) and 1.3times faster inference than decoder-only models. Unlike kNN-LM, which impairs reasoning, our MLP memory improves StrategyQA performance. We will open-source our code and models in the future.

In recent computer vision research, the advent of the Vision Transformer (ViT) has rapidly revolutionized various architectural design efforts: ViT achieved state-of-the-art image classification performance using self-attention found in natural language processing, and MLP-Mixer achieved competitive performance using simple multi-layer perceptrons. In contrast, several studies have also suggested that carefully redesigned convolutional neural networks (CNNs) can achieve advanced performance comparable to ViT without resorting to these new ideas. Against this background, there is growing interest in what inductive bias is suitable for computer vision. Here we propose Sequencer, a novel and competitive architecture alternative to ViT that provides a new perspective on these issues. Unlike ViTs, Sequencer models long-range dependencies using LSTMs rather than self-attention layers. We also propose a two-dimensional version of Sequencer module, where an LSTM is decomposed into vertical and horizontal LSTMs to enhance performance. Despite its simplicity, several experiments demonstrate that Sequencer performs impressively well: Sequencer2D-L, with 54M parameters, realizes 84.6% top-1 accuracy on only ImageNet-1K. Not only that, we show that it has good transferability and the robust resolution adaptability on double resolution-band.

Recent shifts in the space of large language model (LLM) research have shown an increasing focus on novel architectures to compete with prototypical Transformer-based models that have long dominated this space. Linear recurrent models have proven to be a viable competitor due to their computational efficiency. However, such models still demonstrate a sizable gap compared to Transformers in terms of in-context learning among other tasks that require recalling information from a context. In this work, we introduce __Resona__, a simple and scalable framework for augmenting linear recurrent models with retrieval. __Resona__~augments models with the ability to integrate retrieved information from the provided input context, enabling tailored behavior to diverse task requirements. Experiments on a variety of linear recurrent models demonstrate that __Resona__-augmented models observe significant performance gains on a variety of synthetic as well as real-world natural language tasks, highlighting its ability to act as a general purpose method to improve the in-context learning and language modeling abilities of linear recurrent LLMs.

Recent advances in efficient sequence modeling have introduced selective state-space layers, a key component of the Mamba architecture, which have demonstrated remarkable success in a wide range of NLP and vision tasks. While Mamba's empirical performance has matched or surpassed SoTA transformers on such diverse benchmarks, the theoretical foundations underlying its powerful representational capabilities remain less explored. In this work, we investigate the expressivity of selective state-space layers using multivariate polynomials, and prove that they surpass linear transformers in expressiveness. Consequently, our findings reveal that Mamba offers superior representational power over linear attention-based models for long sequences, while not sacrificing their generalization. Our theoretical insights are validated by a comprehensive set of empirical experiments on various datasets.

Our previously proposed MossFormer has achieved promising performance in monaural speech separation. However, it predominantly adopts a self-attention-based MossFormer module, which tends to emphasize longer-range, coarser-scale dependencies, with a deficiency in effectively modelling finer-scale recurrent patterns. In this paper, we introduce a novel hybrid model that provides the capabilities to model both long-range, coarse-scale dependencies and fine-scale recurrent patterns by integrating a recurrent module into the MossFormer framework. Instead of applying the recurrent neural networks (RNNs) that use traditional recurrent connections, we present a recurrent module based on a feedforward sequential memory network (FSMN), which is considered "RNN-free" recurrent network due to the ability to capture recurrent patterns without using recurrent connections. Our recurrent module mainly comprises an enhanced dilated FSMN block by using gated convolutional units (GCU) and dense connections. In addition, a bottleneck layer and an output layer are also added for controlling information flow. The recurrent module relies on linear projections and convolutions for seamless, parallel processing of the entire sequence. The integrated MossFormer2 hybrid model demonstrates remarkable enhancements over MossFormer and surpasses other state-of-the-art methods in WSJ0-2/3mix, Libri2Mix, and WHAM!/WHAMR! benchmarks.

Transformers are the current architecture of choice for NLP, but their attention layers do not scale well to long contexts. Recent works propose to replace attention with linear recurrent layers -- this is the case for state space models, which enjoy efficient training and inference. However, it remains unclear whether these models are competitive with transformers in machine translation (MT). In this paper, we provide a rigorous and comprehensive experimental comparison between transformers and linear recurrent models for MT. Concretely, we experiment with RetNet, Mamba, and hybrid versions of Mamba which incorporate attention mechanisms. Our findings demonstrate that Mamba is highly competitive with transformers on sentence and paragraph-level datasets, where in the latter both models benefit from shifting the training distribution towards longer sequences. Further analysis show that integrating attention into Mamba improves translation quality, robustness to sequence length extrapolation, and the ability to recall named entities.

Memory Mosaics are networks of associative memories working in concert to achieve a prediction task of interest. Like transformers, memory mosaics possess compositional capabilities and in-context learning capabilities. Unlike transformers, memory mosaics achieve these capabilities in comparatively transparent ways. We demonstrate these capabilities on toy examples and we also show that memory mosaics perform as well or better than transformers on medium-scale language modeling tasks.

We introduce GoldFinch, a hybrid Linear Attention/Transformer sequence model that uses a new technique to efficiently generate a highly compressed and reusable KV-Cache in linear time and space with respect to sequence length. GoldFinch stacks our new GOLD transformer on top of an enhanced version of the Finch (RWKV-6) architecture. We train up to 1.5B parameter class models of the Finch, Llama, and GoldFinch architectures, and find dramatically improved modeling performance relative to both Finch and Llama. Our cache size savings increase linearly with model layer count, ranging from 756-2550 times smaller than the traditional transformer cache for common sizes, enabling inference of extremely large context lengths even on limited hardware. Although autoregressive generation has O(n) time complexity per token because of attention, pre-fill computation of the entire initial cache state for a submitted context costs only O(1) time per token due to the use of a recurrent neural network (RNN) to generate this cache. We release our trained weights and training code under the Apache 2.0 license for community use.

This paper introduces a novel approach to enhance the capabilities of Large Language Models (LLMs) in processing and understanding extensive text sequences, a critical aspect in applications requiring deep comprehension and synthesis of large volumes of information. Recognizing the inherent challenges in extending the context window for LLMs, primarily built on Transformer architecture, we propose a new model architecture, referred to as Zebra. This architecture efficiently manages the quadratic time and memory complexity issues associated with full attention in the Transformer by employing grouped local-global attention layers. Our model, akin to a zebra's alternating stripes, balances local and global attention layers, significantly reducing computational requirements and memory consumption. Comprehensive experiments, including pretraining from scratch, continuation of long context adaptation training, and long instruction tuning, are conducted to evaluate the Zebra's performance. The results show that Zebra achieves comparable or superior performance on both short and long sequence benchmarks, while also enhancing training and inference efficiency.

Recurrent Neural Networks (RNNs) have long been the dominant architecture in sequence-to-sequence learning. RNNs, however, are inherently sequential models that do not allow parallelization of their computations. Transformers are emerging as a natural alternative to standard RNNs, replacing recurrent computations with a multi-head attention mechanism. In this paper, we propose the SepFormer, a novel RNN-free Transformer-based neural network for speech separation. The SepFormer learns short and long-term dependencies with a multi-scale approach that employs transformers. The proposed model achieves state-of-the-art (SOTA) performance on the standard WSJ0-2/3mix datasets. It reaches an SI-SNRi of 22.3 dB on WSJ0-2mix and an SI-SNRi of 19.5 dB on WSJ0-3mix. The SepFormer inherits the parallelization advantages of Transformers and achieves a competitive performance even when downsampling the encoded representation by a factor of 8. It is thus significantly faster and it is less memory-demanding than the latest speech separation systems with comparable performance.

While transformers have shown remarkable success in natural language processing, their attention mechanism's large memory requirements have limited their ability to handle longer contexts. Prior approaches, such as recurrent memory or retrieval-based augmentation, have either compromised the random-access flexibility of attention (i.e., the capability to select any token in the entire context) or relied on separate mechanisms for relevant context retrieval, which may not be compatible with the model's attention. In this paper, we present a novel approach that allows access to the complete context while retaining random-access flexibility, closely resembling running attention on the entire context. Our method uses a landmark token to represent each block of the input and trains the attention to use it for selecting relevant blocks, enabling retrieval of blocks directly through the attention mechanism instead of by relying on a separate mechanism. Our approach seamlessly integrates with specialized data structures and the system's memory hierarchy, enabling processing of arbitrarily long context lengths. We demonstrate that our method can obtain comparable performance with Transformer-XL while significantly reducing the number of retrieved tokens in each step. Finally, we show that fine-tuning LLaMA 7B with our method successfully extends its context length capacity up to 32k tokens, allowing for inference at the context lengths of GPT-4.

We propose Axial Transformers, a self-attention-based autoregressive model for images and other data organized as high dimensional tensors. Existing autoregressive models either suffer from excessively large computational resource requirements for high dimensional data, or make compromises in terms of distribution expressiveness or ease of implementation in order to decrease resource requirements. Our architecture, by contrast, maintains both full expressiveness over joint distributions over data and ease of implementation with standard deep learning frameworks, while requiring reasonable memory and computation and achieving state-of-the-art results on standard generative modeling benchmarks. Our models are based on axial attention, a simple generalization of self-attention that naturally aligns with the multiple dimensions of the tensors in both the encoding and the decoding settings. Notably the proposed structure of the layers allows for the vast majority of the context to be computed in parallel during decoding without introducing any independence assumptions. This semi-parallel structure goes a long way to making decoding from even a very large Axial Transformer broadly applicable. We demonstrate state-of-the-art results for the Axial Transformer on the ImageNet-32 and ImageNet-64 image benchmarks as well as on the BAIR Robotic Pushing video benchmark. We open source the implementation of Axial Transformers.

Recent advancements in sequence modeling have led to the emergence of Structured State Space Models (SSMs) as an efficient alternative to Recurrent Neural Networks (RNNs) and Transformers, addressing challenges in long-range dependency modeling and computational efficiency. While RNNs suffer from vanishing gradients and sequential inefficiencies, and Transformers face quadratic complexity, SSMs leverage structured recurrence and state-space representations to achieve superior long-sequence processing with linear or near-linear complexity. This survey provides a comprehensive review of SSMs, tracing their evolution from the foundational S4 model to its successors like Mamba, Simplified Structured State Space Sequence Model (S5), and Jamba, highlighting their improvements in computational efficiency, memory optimization, and inference speed. By comparing SSMs with traditional sequence models across domains such as natural language processing (NLP), speech recognition, vision, and time-series forecasting, we demonstrate their advantages in handling long-range dependencies while reducing computational overhead. Despite their potential, challenges remain in areas such as training optimization, hybrid modeling, and interpretability. This survey serves as a structured guide for researchers and practitioners, detailing the advancements, trade-offs, and future directions of SSM-based architectures in AI and deep learning.

Modern sequence models (e.g., Transformers, linear RNNs, etc.) emerged as dominant backbones of recent deep learning frameworks, mainly due to their efficiency, representational power, and/or ability to capture long-range dependencies. Adopting these sequence models for graph-structured data has recently gained popularity as the alternative to Message Passing Neural Networks (MPNNs). There is, however, a lack of a common foundation about what constitutes a good graph sequence model, and a mathematical description of the benefits and deficiencies in adopting different sequence models for learning on graphs. To this end, we first present Graph Sequence Model (GSM), a unifying framework for adopting sequence models for graphs, consisting of three main steps: (1) Tokenization, which translates the graph into a set of sequences; (2) Local Encoding, which encodes local neighborhoods around each node; and (3) Global Encoding, which employs a scalable sequence model to capture long-range dependencies within the sequences. This framework allows us to understand, evaluate, and compare the power of different sequence model backbones in graph tasks. Our theoretical evaluations of the representation power of Transformers and modern recurrent models through the lens of global and local graph tasks show that there are both negative and positive sides for both types of models. Building on this observation, we present GSM++, a fast hybrid model that uses the Hierarchical Affinity Clustering (HAC) algorithm to tokenize the graph into hierarchical sequences, and then employs a hybrid architecture of Transformer to encode these sequences. Our theoretical and experimental results support the design of GSM++, showing that GSM++ outperforms baselines in most benchmark evaluations.

Working memory (WM), a fundamental cognitive process facilitating the temporary storage, integration, manipulation, and retrieval of information, plays a vital role in reasoning and decision-making tasks. Robust benchmark datasets that capture the multifaceted nature of WM are crucial for the effective development and evaluation of AI WM models. Here, we introduce a comprehensive Working Memory (WorM) benchmark dataset for this purpose. WorM comprises 10 tasks and a total of 1 million trials, assessing 4 functionalities, 3 domains, and 11 behavioral and neural characteristics of WM. We jointly trained and tested state-of-the-art recurrent neural networks and transformers on all these tasks. We also include human behavioral benchmarks as an upper bound for comparison. Our results suggest that AI models replicate some characteristics of WM in the brain, most notably primacy and recency effects, and neural clusters and correlates specialized for different domains and functionalities of WM. In the experiments, we also reveal some limitations in existing models to approximate human behavior. This dataset serves as a valuable resource for communities in cognitive psychology, neuroscience, and AI, offering a standardized framework to compare and enhance WM models, investigate WM's neural underpinnings, and develop WM models with human-like capabilities. Our source code and data are available at https://github.com/ZhangLab-DeepNeuroCogLab/WorM.

The fixed-size context of Transformer makes GPT models incapable of generating arbitrarily long text. In this paper, we introduce RecurrentGPT, a language-based simulacrum of the recurrence mechanism in RNNs. RecurrentGPT is built upon a large language model (LLM) such as ChatGPT and uses natural language to simulate the Long Short-Term Memory mechanism in an LSTM. At each timestep, RecurrentGPT generates a paragraph of text and updates its language-based long-short term memory stored on the hard drive and the prompt, respectively. This recurrence mechanism enables RecurrentGPT to generate texts of arbitrary length without forgetting. Since human users can easily observe and edit the natural language memories, RecurrentGPT is interpretable and enables interactive generation of long text. RecurrentGPT is an initial step towards next-generation computer-assisted writing systems beyond local editing suggestions. In addition to producing AI-generated content (AIGC), we also demonstrate the possibility of using RecurrentGPT as an interactive fiction that directly interacts with consumers. We call this usage of generative models by ``AI As Contents'' (AIAC), which we believe is the next form of conventional AIGC. We further demonstrate the possibility of using RecurrentGPT to create personalized interactive fiction that directly interacts with readers instead of interacting with writers. More broadly, RecurrentGPT demonstrates the utility of borrowing ideas from popular model designs in cognitive science and deep learning for prompting LLMs. Our code is available at https://github.com/aiwaves-cn/RecurrentGPT and an online demo is available at https://www.aiwaves.org/recurrentgpt.

What is the computational model behind a Transformer? Where recurrent neural networks have direct parallels in finite state machines, allowing clear discussion and thought around architecture variants or trained models, Transformers have no such familiar parallel. In this paper we aim to change that, proposing a computational model for the transformer-encoder in the form of a programming language. We map the basic components of a transformer-encoder -- attention and feed-forward computation -- into simple primitives, around which we form a programming language: the Restricted Access Sequence Processing Language (RASP). We show how RASP can be used to program solutions to tasks that could conceivably be learned by a Transformer, and how a Transformer can be trained to mimic a RASP solution. In particular, we provide RASP programs for histograms, sorting, and Dyck-languages. We further use our model to relate their difficulty in terms of the number of required layers and attention heads: analyzing a RASP program implies a maximum number of heads and layers necessary to encode a task in a transformer. Finally, we see how insights gained from our abstraction might be used to explain phenomena seen in recent works.

Linear Recurrent Neural Networks (linear RNNs) have emerged as competitive alternatives to Transformers for sequence modeling, offering efficient training and linear-time inference. However, existing architectures face a fundamental trade-off between expressivity and efficiency, dictated by the structure of their state-transition matrices. Diagonal matrices, used in models such as Mamba, GLA, or mLSTM, yield fast runtime but have limited expressivity. To address this, recent architectures such as DeltaNet and RWKV-7 adopted a diagonal plus rank-1 structure, which allows simultaneous token and channel mixing, improving associative recall and, as recently shown, state-tracking when allowing negative eigenvalues in the state-transition matrices. Building on the interpretation of DeltaNet's recurrence as performing one step of online gradient descent per token on an associative recall loss, we introduce DeltaProduct, which instead takes multiple (n_h) steps per token. This naturally leads to diagonal plus rank-n_h state-transition matrices, formed as products of n_h generalized Householder transformations, providing a tunable mechanism to balance expressivity and efficiency. We provide a detailed theoretical characterization of the state-tracking capability of DeltaProduct in finite precision, showing how it improves by increasing n_h. Our extensive experiments demonstrate that DeltaProduct outperforms DeltaNet in both state-tracking and language modeling, while also showing significantly improved length extrapolation capabilities.

Transformers with linear attention allow for efficient parallel training but can simultaneously be formulated as an RNN with 2D (matrix-valued) hidden states, thus enjoying linear (with respect to output length) inference complexity. Recent works such as RetNet (Sun et al., 2023) and TransNormerLLM (Qin et al., 2023a) observe that adding a global decay term to the additive RNN update rule greatly improves performance, sometimes outperforming standard Transformers with softmax attention when trained at scale. In this work we show that adding a data-dependent gating mechanism further improves performance. We derive a parallel form of this gated linear attention layer that enables efficient training. However, a straightforward, numerically stable implementation of this parallel form requires generalized matrix multiplications in log-space for numerical stability, and thus cannot take advantage of tensor cores on modern GPUs which are optimized for standard matrix multiplications. We develop a hardware-efficient version of the parallel form that can still make use of tensor cores through block-parallel computations over sequence chunks. Experiments on moderate-scale language modeling (340M-parameter models trained on 15B tokens, 1.3B-parameter models trained on 100B tokens) show that gated linear attention (GLA) Transformers perform competitively against a strong LLaMA-architecture Transformer baseline (Touvron et al., 2023) as well as Mamba (Gu & Dao, 2023), a recently introduced state-space model with a data-dependent state transition mechanism. For training speed, our Triton-based implementation performs comparably to CUDA-optimized FlashAttention-2 (Dao, 2023) under the regular 2048 training length setting, while outperforming FlashAttention-2 when training on longer sequences beyond 4096.

Transformer achieves promising results on various tasks. However, self-attention suffers from quadratic memory requirements with respect to the sequence length. Existing work focuses on reducing time and space complexity from an algorithm perspective. In this work, we propose sequence parallelism, a memory-efficient parallelism method to help us break input sequence length limitation and train with longer sequences on GPUs efficiently. Our approach is compatible with most existing parallelisms (e.g. data parallelism, pipeline parallelism and tensor parallelism), which means our sequence parallelism makes 4D parallelism possible. More importantly, we no longer require a single device to hold the whole sequence. That is, with sparse attention, our sequence parallelism enables us to train transformer with infinite long sequence. Specifically, we split the input sequence into multiple chunks and feed each chunk into its corresponding device (i.e. GPU). To compute the attention output, we integrated ring-style communication with self-attention calculation and proposed Ring Self-Attention (RSA). Experiments show that sequence parallelism performs well when scaling with batch size and sequence length. Compared with tensor parallelism, our approach achieved 13.7times and 3.0times maximum batch size and sequence length respectively when scaling up to 64 NVIDIA P100 GPUs. With sparse attention, sequence can handle sequence with over 114K tokens, which is over 27times longer than existing sparse attention works holding the whole sequence on a single device.

Transformers have found extensive applications across various domains due to the powerful fitting capabilities. This success can be partially attributed to their inherent nonlinearity. Thus, in addition to the ReLU function employed in the original transformer architecture, researchers have explored alternative modules such as GeLU and SwishGLU to enhance nonlinearity and thereby augment representational capacity. In this paper, we propose a novel category of polynomial composition activations (PolyCom), designed to optimize the dynamics of transformers. Theoretically, we provide a comprehensive mathematical analysis of PolyCom, highlighting its enhanced expressivity and efficacy relative to other activation functions. Notably, we demonstrate that networks incorporating PolyCom achieve the optimal approximation rate, indicating that PolyCom networks require minimal parameters to approximate general smooth functions in Sobolev spaces. We conduct empirical experiments on the pre-training configurations of large language models (LLMs), including both dense and sparse architectures. By substituting conventional activation functions with PolyCom, we enable LLMs to capture higher-order interactions within the data, thus improving performance metrics in terms of accuracy and convergence rates. Extensive experimental results demonstrate the effectiveness of our method, showing substantial improvements over other activation functions. Code is available at https://github.com/BryceZhuo/PolyCom.

Recent years have seen a phenomenal rise in performance and applications of transformer neural networks. The family of transformer networks, including Bidirectional Encoder Representations from Transformer (BERT), Generative Pretrained Transformer (GPT) and Vision Transformer (ViT), have shown their effectiveness across Natural Language Processing (NLP) and Computer Vision (CV) domains. Transformer-based networks such as ChatGPT have impacted the lives of common men. However, the quest for high predictive performance has led to an exponential increase in transformers' memory and compute footprint. Researchers have proposed techniques to optimize transformer inference at all levels of abstraction. This paper presents a comprehensive survey of techniques for optimizing the inference phase of transformer networks. We survey techniques such as knowledge distillation, pruning, quantization, neural architecture search and lightweight network design at the algorithmic level. We further review hardware-level optimization techniques and the design of novel hardware accelerators for transformers. We summarize the quantitative results on the number of parameters/FLOPs and accuracy of several models/techniques to showcase the tradeoff exercised by them. We also outline future directions in this rapidly evolving field of research. We believe that this survey will educate both novice and seasoned researchers and also spark a plethora of research efforts in this field.

Transformers have recently been popular for learning and inference in the spatial-temporal domain. However, their performance relies on storing and applying attention to the feature tensor of each frame in video. Hence, their space and time complexity increase linearly as the length of video grows, which could be very costly for long videos. We propose a novel visual memory network architecture for the learning and inference problem in the spatial-temporal domain. We maintain a fixed set of memory slots in our memory network and propose an algorithm based on Gumbel-Softmax to learn an adaptive strategy to update this memory. Finally, this architecture is benchmarked on the video object segmentation (VOS) and video prediction problems. We demonstrate that our memory architecture achieves state-of-the-art results, outperforming transformer-based methods on VOS and other recent methods on video prediction while maintaining constant memory capacity independent of the sequence length.

Alternatives to recurrent neural networks, in particular, architectures based on attention or convolutions, have been gaining momentum for processing input sequences. In spite of their relevance, the computational properties of these alternatives have not yet been fully explored. We study the computational power of two of the most paradigmatic architectures exemplifying these mechanisms: the Transformer (Vaswani et al., 2017) and the Neural GPU (Kaiser & Sutskever, 2016). We show both models to be Turing complete exclusively based on their capacity to compute and access internal dense representations of the data. In particular, neither the Transformer nor the Neural GPU requires access to an external memory to become Turing complete. Our study also reveals some minimal sets of elements needed to obtain these completeness results.

While Transformers and other sequence-parallelizable neural network architectures seem like the current state of the art in sequence modeling, they specifically lack state-tracking capabilities. These are important for time-series tasks and logical reasoning. Traditional RNNs like LSTMs and GRUs, as well as modern variants like sLSTM do have these capabilities at the cost of strictly sequential processing. While this is often seen as a strong limitation, we show how fast these networks can get with our hardware-optimization FlashRNN in Triton and CUDA, optimizing kernels to the register level on modern GPUs. We extend traditional RNNs with a parallelization variant that processes multiple RNNs of smaller hidden state in parallel, similar to the head-wise processing in Transformers. To enable flexibility on different GPU variants, we introduce a new optimization framework for hardware-internal cache sizes, memory and compute handling. It models the hardware in a setting using polyhedral-like constraints, including the notion of divisibility. This speeds up the solution process in our ConstrINT library for general integer constraint satisfaction problems (integer CSPs). We show that our kernels can achieve 50x speed-ups over a vanilla PyTorch implementation and allow 40x larger hidden sizes compared to our Triton implementation. Our open-source kernels and the optimization library are released here to boost research in the direction of state-tracking enabled RNNs and sequence modeling: https://github.com/NX-AI/flashrnn

Linear RNN architectures, like Mamba, can be competitive with Transformer models in language modeling while having advantageous deployment characteristics. Given the focus on training large-scale Transformer models, we consider the challenge of converting these pretrained models for deployment. We demonstrate that it is feasible to distill large Transformers into linear RNNs by reusing the linear projection weights from attention layers with academic GPU resources. The resulting hybrid model, which incorporates a quarter of the attention layers, achieves performance comparable to the original Transformer in chat benchmarks and outperforms open-source hybrid Mamba models trained from scratch with trillions of tokens in both chat benchmarks and general benchmarks. Moreover, we introduce a hardware-aware speculative decoding algorithm that accelerates the inference speed of Mamba and hybrid models. Overall we show how, with limited computation resources, we can remove many of the original attention layers and generate from the resulting model more efficiently. Our top-performing model, distilled from Llama3-8B-Instruct, achieves a 29.61 length-controlled win rate on AlpacaEval 2 against GPT-4 and 7.35 on MT-Bench, surpassing the best instruction-tuned linear RNN model.

Recurrent large language models that compete with Transformers in language modeling perplexity are emerging at a rapid rate (e.g., Mamba, RWKV). Excitingly, these architectures use a constant amount of memory during inference. However, due to the limited memory, recurrent LMs cannot recall and use all the information in long contexts leading to brittle in-context learning (ICL) quality. A key challenge for efficient LMs is selecting what information to store versus discard. In this work, we observe the order in which information is shown to the LM impacts the selection difficulty. To formalize this, we show that the hardness of information recall reduces to the hardness of a problem called set disjointness (SD), a quintessential problem in communication complexity that requires a streaming algorithm (e.g., recurrent model) to decide whether inputted sets are disjoint. We empirically and theoretically show that the recurrent memory required to solve SD changes with set order, i.e., whether the smaller set appears first in-context. Our analysis suggests, to mitigate the reliance on data order, we can put information in the right order in-context or process prompts non-causally. Towards that end, we propose: (1) JRT-Prompt, where context gets repeated multiple times in the prompt, effectively showing the model all data orders. This gives 11.0 pm 1.3 points of improvement, averaged across 16 recurrent LMs and the 6 ICL tasks, with 11.9times higher throughput than FlashAttention-2 for generation prefill (length 32k, batch size 16, NVidia H100). We then propose (2) JRT-RNN, which uses non-causal prefix-linear-attention to process prompts and provides 99% of Transformer quality at 360M params., 30B tokens and 96% at 1.3B params., 50B tokens on average across the tasks, with 19.2times higher throughput for prefill than FA2.

The most fundamental capability of modern AI methods such as Large Language Models (LLMs) is the ability to predict the next token in a long sequence of tokens, known as ``sequence modeling." Although the Transformers model is the current dominant approach to sequence modeling, its quadratic computational cost with respect to sequence length is a significant drawback. State-space models (SSMs) offer a promising alternative due to their linear decoding efficiency and high parallelizability during training. However, existing SSMs often rely on seemingly ad hoc linear recurrence designs. In this work, we explore SSM design through the lens of online learning, conceptualizing SSMs as meta-modules for specific online learning problems. This approach links SSM design to formulating precise online learning objectives, with state transition rules derived from optimizing these objectives. Based on this insight, we introduce a novel deep SSM architecture based on the implicit update for optimizing an online regression objective. Our experimental results show that our models outperform state-of-the-art SSMs, including the Mamba model, on standard sequence modeling benchmarks and language modeling tasks.

Deep learning, as a vital technique, has sparked a notable revolution in artificial intelligence. As the most representative architecture, Transformers have empowered numerous advanced models, especially the large language models that comprise billions of parameters, becoming a cornerstone in deep learning. Despite the impressive achievements, Transformers still face inherent limitations, particularly the time-consuming inference resulting from the quadratic computation complexity of attention calculation. Recently, a novel architecture named Mamba, drawing inspiration from classical state space models, has emerged as a promising alternative for building foundation models, delivering comparable modeling abilities to Transformers while preserving near-linear scalability concerning sequence length. This has sparked an increasing number of studies actively exploring Mamba's potential to achieve impressive performance across diverse domains. Given such rapid evolution, there is a critical need for a systematic review that consolidates existing Mamba-empowered models, offering a comprehensive understanding of this emerging model architecture. In this survey, we therefore conduct an in-depth investigation of recent Mamba-associated studies, covering from three main aspects: the advancements of Mamba-based models, the techniques of adapting Mamba to diverse data, and the applications where Mamba can excel. Specifically, we first recall the foundational knowledge of various representative deep learning models and the details of Mamba as preliminaries. Then, to showcase the significance of Mamba, we comprehensively review the related studies focusing on Mamba models' architecture design, data adaptability, and applications. Finally, we present an discussion of current limitations and explore various promising research directions to provide deeper insights for future investigations.

Transformer-based language models have recently been at the forefront of active research in text generation. However, these models' advances come at the price of prohibitive training costs, with parameter counts in the billions and compute requirements measured in petaflop/s-decades. In this paper, we investigate transformer-based architectures for improving model performance in a low-data regime by selectively replacing attention layers with feed-forward and quasi-recurrent neural network layers. We test these architectures on the standard Enwik8 and Wikitext-103 corpora. Our results show that our reduced architectures outperform existing models with a comparable number of parameters, and obtain comparable performance to larger models while significantly reducing the number of parameters.

The Transformer architecture, despite its widespread success, struggles with long-context scenarios due to quadratic computation and linear memory growth. While various linear attention variants mitigate these efficiency constraints by compressing context into fixed-size states, they often degrade performance in tasks such as in-context retrieval and reasoning. To address this limitation and achieve more effective context compression, we propose two key innovations. First, we introduce a row-sparse update formulation for linear attention by conceptualizing state updating as information classification. This enables sparse state updates via softmax-based top-k hard classification, thereby extending receptive fields and reducing inter-class interference. Second, we present Sparse State Expansion (SSE) within the sparse framework, which expands the contextual state into multiple partitions, effectively decoupling parameter size from state capacity while maintaining the sparse classification paradigm. Our design, supported by efficient parallelized implementations, yields effective classification and discriminative state representations. We extensively validate SSE in both pure linear and hybrid (SSE-H) architectures across language modeling, in-context retrieval, and mathematical reasoning benchmarks. SSE demonstrates strong retrieval performance and scales favorably with state size. Moreover, after reinforcement learning (RL) training, our 2B SSE-H model achieves state-of-the-art mathematical reasoning performance among small reasoning models, scoring 64.7 on AIME24 and 51.3 on AIME25, significantly outperforming similarly sized open-source Transformers. These results highlight SSE as a promising and efficient architecture for long-context modeling.

This review presents a comprehensive exploration of hybrid and ensemble deep learning models within Natural Language Processing (NLP), shedding light on their transformative potential across diverse tasks such as Sentiment Analysis, Named Entity Recognition, Machine Translation, Question Answering, Text Classification, Generation, Speech Recognition, Summarization, and Language Modeling. The paper systematically introduces each task, delineates key architectures from Recurrent Neural Networks (RNNs) to Transformer-based models like BERT, and evaluates their performance, challenges, and computational demands. The adaptability of ensemble techniques is emphasized, highlighting their capacity to enhance various NLP applications. Challenges in implementation, including computational overhead, overfitting, and model interpretation complexities, are addressed alongside the trade-off between interpretability and performance. Serving as a concise yet invaluable guide, this review synthesizes insights into tasks, architectures, and challenges, offering a holistic perspective for researchers and practitioners aiming to advance language-driven applications through ensemble deep learning in NLP.

The recent boom of linear forecasting models questions the ongoing passion for architectural modifications of Transformer-based forecasters. These forecasters leverage Transformers to model the global dependencies over temporal tokens of time series, with each token formed by multiple variates of the same timestamp. However, Transformers are challenged in forecasting series with larger lookback windows due to performance degradation and computation explosion. Besides, the embedding for each temporal token fuses multiple variates that represent potential delayed events and distinct physical measurements, which may fail in learning variate-centric representations and result in meaningless attention maps. In this work, we reflect on the competent duties of Transformer components and repurpose the Transformer architecture without any modification to the basic components. We propose iTransformer that simply applies the attention and feed-forward network on the inverted dimensions. Specifically, the time points of individual series are embedded into variate tokens which are utilized by the attention mechanism to capture multivariate correlations; meanwhile, the feed-forward network is applied for each variate token to learn nonlinear representations. The iTransformer model achieves state-of-the-art on challenging real-world datasets, which further empowers the Transformer family with promoted performance, generalization ability across different variates, and better utilization of arbitrary lookback windows, making it a nice alternative as the fundamental backbone of time series forecasting. Code is available at this repository: https://github.com/thuml/iTransformer.

With the evolution of large language models, traditional Transformer models become computationally demanding for lengthy sequences due to the quadratic growth in computation with respect to the sequence length. Mamba, emerging as a groundbreaking architecture in the field of generative AI, demonstrates remarkable proficiency in handling elongated sequences with reduced computational and memory complexity. Nevertheless, the existing training framework of Mamba presents inefficiency with variable-length sequence inputs. Either single-sequence training results in low GPU utilization, or batched processing of variable-length sequences to a maximum length incurs considerable memory and computational overhead. To address this problem, we analyze the performance of bottleneck operators in Mamba under diverse tensor shapes and proposed PackMamba, a high-throughput Mamba that efficiently handles variable-length sequences. Diving deep into state-space models (SSMs), we modify the parallel operators to avoid passing information between individual sequences while maintaining high performance. Experimental results on an NVIDIA A100 GPU demonstrate throughput exceeding the baseline single-sequence processing scheme: 3.06x speedup on the 1.4B model and 2.62x on the 2.8B model.

Transformers are widely used as generic backbones in computer vision, despite initially introduced for natural language processing. Recently, the Long Short-Term Memory (LSTM) has been extended to a scalable and performant architecture - the xLSTM - which overcomes long-standing LSTM limitations via exponential gating and parallelizable matrix memory structure. In this report, we introduce Vision-LSTM (ViL), an adaption of the xLSTM building blocks to computer vision. ViL comprises a stack of xLSTM blocks where odd blocks process the sequence of patch tokens from top to bottom while even blocks go from bottom to top. Experiments show that ViL holds promise to be further deployed as new generic backbone for computer vision architectures.

Transformer-based models have achieved great success in various NLP, vision, and speech tasks. However, the core of Transformer, the self-attention mechanism, has a quadratic time and memory complexity with respect to the sequence length, which hinders applications of Transformer-based models to long sequences. Many approaches have been proposed to mitigate this problem, such as sparse attention mechanisms, low-rank matrix approximations and scalable kernels, and token mixing alternatives to self-attention. We propose a novel Pooling Network (PoNet) for token mixing in long sequences with linear complexity. We design multi-granularity pooling and pooling fusion to capture different levels of contextual information and combine their interactions with tokens. On the Long Range Arena benchmark, PoNet significantly outperforms Transformer and achieves competitive accuracy, while being only slightly slower than the fastest model, FNet, across all sequence lengths measured on GPUs. We also conduct systematic studies on the transfer learning capability of PoNet and observe that PoNet achieves 95.7% of the accuracy of BERT on the GLUE benchmark, outperforming FNet by 4.5% relative. Comprehensive ablation analysis demonstrates effectiveness of the designed multi-granularity pooling and pooling fusion for token mixing in long sequences and efficacy of the designed pre-training tasks for PoNet to learn transferable contextualized language representations.

Access to external knowledge is essential for many natural language processing tasks, such as question answering and dialogue. Existing methods often rely on a parametric model that stores knowledge in its parameters, or use a retrieval-augmented model that has access to an external knowledge source. Parametric and retrieval-augmented models have complementary strengths in terms of computational efficiency and predictive accuracy. To combine the strength of both approaches, we propose the Efficient Memory-Augmented Transformer (EMAT) -- it encodes external knowledge into a key-value memory and exploits the fast maximum inner product search for memory querying. We also introduce pre-training tasks that allow EMAT to encode informative key-value representations, and to learn an implicit strategy to integrate multiple memory slots into the transformer. Experiments on various knowledge-intensive tasks such as question answering and dialogue datasets show that, simply augmenting parametric models (T5-base) using our method produces more accurate results (e.g., 25.8 -> 44.3 EM on NQ) while retaining a high throughput (e.g., 1000 queries/s on NQ). Compared to retrieval-augmented models, EMAT runs substantially faster across the board and produces more accurate results on WoW and ELI5. Our code and datasets are available at https://github. com/uclnlp/EMAT.

Large Language Models (LLMs) have shown strong abilities in general language tasks, yet adapting them to specific domains remains a challenge. Current method like Domain Adaptive Pretraining (DAPT) requires costly full-parameter training and suffers from catastrophic forgetting. Meanwhile, Retrieval-Augmented Generation (RAG) introduces substantial inference latency due to expensive nearest-neighbor searches and longer context. This paper introduces Memory Decoder, a plug-and-play pretrained memory that enables efficient domain adaptation without changing the original model's parameters. Memory Decoder employs a small transformer decoder that learns to imitate the behavior of an external non-parametric retriever. Once trained, Memory Decoder can be seamlessly integrated with any pretrained language model that shares the same tokenizer, requiring no model-specific modifications. Experimental results demonstrate that Memory Decoder enables effective adaptation of various Qwen and Llama models to three distinct specialized domains: biomedicine, finance, and law, reducing perplexity by an average of 6.17 points. Overall, Memory Decoder introduces a novel paradigm centered on a specially pretrained memory component designed for domain-specific adaptation. This memory architecture can be integrated in a plug-and-play manner, consistently enhancing performance across multiple models within the target domain.

Recent advances in deep learning have mainly relied on Transformers due to their data dependency and ability to learn at scale. The attention module in these architectures, however, exhibits quadratic time and space in input size, limiting their scalability for long-sequence modeling. Despite recent attempts to design efficient and effective architecture backbone for multi-dimensional data, such as images and multivariate time series, existing models are either data independent, or fail to allow inter- and intra-dimension communication. Recently, State Space Models (SSMs), and more specifically Selective State Space Models, with efficient hardware-aware implementation, have shown promising potential for long sequence modeling. Motivated by the success of SSMs, we present MambaMixer, a new architecture with data-dependent weights that uses a dual selection mechanism across tokens and channels, called Selective Token and Channel Mixer. MambaMixer connects selective mixers using a weighted averaging mechanism, allowing layers to have direct access to early features. As a proof of concept, we design Vision MambaMixer (ViM2) and Time Series MambaMixer (TSM2) architectures based on the MambaMixer block and explore their performance in various vision and time series forecasting tasks. Our results underline the importance of selective mixing across both tokens and channels. In ImageNet classification, object detection, and semantic segmentation tasks, ViM2 achieves competitive performance with well-established vision models and outperforms SSM-based vision models. In time series forecasting, TSM2 achieves outstanding performance compared to state-of-the-art methods while demonstrating significantly improved computational cost. These results show that while Transformers, cross-channel attention, and MLPs are sufficient for good performance in time series forecasting, neither is necessary.

Transformer networks have lead to important progress in language modeling and machine translation. These models include two consecutive modules, a feed-forward layer and a self-attention layer. The latter allows the network to capture long term dependencies and are often regarded as the key ingredient in the success of Transformers. Building upon this intuition, we propose a new model that solely consists of attention layers. More precisely, we augment the self-attention layers with persistent memory vectors that play a similar role as the feed-forward layer. Thanks to these vectors, we can remove the feed-forward layer without degrading the performance of a transformer. Our evaluation shows the benefits brought by our model on standard character and word level language modeling benchmarks.

Transformer architecture has widespread applications, particularly in Natural Language Processing and computer vision. Recently Transformers have been employed in various aspects of time-series analysis. This tutorial provides an overview of the Transformer architecture, its applications, and a collection of examples from recent research papers in time-series analysis. We delve into an explanation of the core components of the Transformer, including the self-attention mechanism, positional encoding, multi-head, and encoder/decoder. Several enhancements to the initial, Transformer architecture are highlighted to tackle time-series tasks. The tutorial also provides best practices and techniques to overcome the challenge of effectively training Transformers for time-series analysis.

The Receptance Weighted Key Value (RWKV) model offers a novel alternative to the Transformer architecture, merging the benefits of recurrent and attention-based systems. Unlike conventional Transformers, which depend heavily on self-attention, RWKV adeptly captures long-range dependencies with minimal computational demands. By utilizing a recurrent framework, RWKV addresses some computational inefficiencies found in Transformers, particularly in tasks with long sequences. RWKV has recently drawn considerable attention for its robust performance across multiple domains. Despite its growing popularity, no systematic review of the RWKV model exists. This paper seeks to fill this gap as the first comprehensive review of the RWKV architecture, its core principles, and its varied applications, such as natural language generation, natural language understanding, and computer vision. We assess how RWKV compares to traditional Transformer models, highlighting its capability to manage long sequences efficiently and lower computational costs. Furthermore, we explore the challenges RWKV encounters and propose potential directions for future research and advancement. We consistently maintain the related open-source materials at: https://github.com/MLGroupJLU/RWKV-Survey.

A central goal of sequence modeling is designing a single principled model that can address sequence data across a range of modalities and tasks, particularly on long-range dependencies. Although conventional models including RNNs, CNNs, and Transformers have specialized variants for capturing long dependencies, they still struggle to scale to very long sequences of 10000 or more steps. A promising recent approach proposed modeling sequences by simulating the fundamental state space model (SSM) \( x'(t) = Ax(t) + Bu(t), y(t) = Cx(t) + Du(t) \), and showed that for appropriate choices of the state matrix \( A \), this system could handle long-range dependencies mathematically and empirically. However, this method has prohibitive computation and memory requirements, rendering it infeasible as a general sequence modeling solution. We propose the Structured State Space sequence model (S4) based on a new parameterization for the SSM, and show that it can be computed much more efficiently than prior approaches while preserving their theoretical strengths. Our technique involves conditioning \( A \) with a low-rank correction, allowing it to be diagonalized stably and reducing the SSM to the well-studied computation of a Cauchy kernel. S4 achieves strong empirical results across a diverse range of established benchmarks, including (i) 91\% accuracy on sequential CIFAR-10 with no data augmentation or auxiliary losses, on par with a larger 2-D ResNet, (ii) substantially closing the gap to Transformers on image and language modeling tasks, while performing generation 60times faster (iii) SoTA on every task from the Long Range Arena benchmark, including solving the challenging Path-X task of length 16k that all prior work fails on, while being as efficient as all competitors.

State-of-the-art solutions in the areas of "Language Modelling & Generating Text", "Speech Recognition", "Generating Image Descriptions" or "Video Tagging" have been using Recurrent Neural Networks as the foundation for their approaches. Understanding the underlying concepts is therefore of tremendous importance if we want to keep up with recent or upcoming publications in those areas. In this work we give a short overview over some of the most important concepts in the realm of Recurrent Neural Networks which enables readers to easily understand the fundamentals such as but not limited to "Backpropagation through Time" or "Long Short-Term Memory Units" as well as some of the more recent advances like the "Attention Mechanism" or "Pointer Networks". We also give recommendations for further reading regarding more complex topics where it is necessary.

Recurrent neural networks (RNNs) have fast inference and scale efficiently on long sequences, but they are difficult to train and hard to scale. We propose Hawk, an RNN with gated linear recurrences, and Griffin, a hybrid model that mixes gated linear recurrences with local attention. Hawk exceeds the reported performance of Mamba on downstream tasks, while Griffin matches the performance of Llama-2 despite being trained on over 6 times fewer tokens. We also show that Griffin can extrapolate on sequences significantly longer than those seen during training. Our models match the hardware efficiency of Transformers during training, and during inference they have lower latency and significantly higher throughput. We scale Griffin up to 14B parameters, and explain how to shard our models for efficient distributed training.

Recent advances in efficient sequence modeling have led to attention-free layers, such as Mamba, RWKV, and various gated RNNs, all featuring sub-quadratic complexity in sequence length and excellent scaling properties, enabling the construction of a new type of foundation models. In this paper, we present a unified view of these models, formulating such layers as implicit causal self-attention layers. The formulation includes most of their sub-components and is not limited to a specific part of the architecture. The framework compares the underlying mechanisms on similar grounds for different layers and provides a direct means for applying explainability methods. Our experiments show that our attention matrices and attribution method outperform an alternative and a more limited formulation that was recently proposed for Mamba. For the other architectures for which our method is the first to provide such a view, our method is effective and competitive in the relevant metrics compared to the results obtained by state-of-the-art transformer explainability methods. Our code is publicly available.

Relative Positional Encoding (RPE), which encodes the relative distance between any pair of tokens, is one of the most successful modifications to the original Transformer. As far as we know, theoretical understanding of the RPE-based Transformers is largely unexplored. In this work, we mathematically analyze the power of RPE-based Transformers regarding whether the model is capable of approximating any continuous sequence-to-sequence functions. One may naturally assume the answer is in the affirmative -- RPE-based Transformers are universal function approximators. However, we present a negative result by showing there exist continuous sequence-to-sequence functions that RPE-based Transformers cannot approximate no matter how deep and wide the neural network is. One key reason lies in that most RPEs are placed in the softmax attention that always generates a right stochastic matrix. This restricts the network from capturing positional information in the RPEs and limits its capacity. To overcome the problem and make the model more powerful, we first present sufficient conditions for RPE-based Transformers to achieve universal function approximation. With the theoretical guidance, we develop a novel attention module, called Universal RPE-based (URPE) Attention, which satisfies the conditions. Therefore, the corresponding URPE-based Transformers become universal function approximators. Extensive experiments covering typical architectures and tasks demonstrate that our model is parameter-efficient and can achieve superior performance to strong baselines in a wide range of applications. The code will be made publicly available at https://github.com/lsj2408/URPE.

Transformers have become the go-to architecture for language and vision tasks, yet their theoretical properties, especially memorization capacity, remain elusive. This paper investigates the memorization abilities of multi-head attention mechanisms, examining how many example sequences they can memorize, as a function of the number of heads and sequence length. Motivated by experimental findings on vision transformers, we introduce novel assumptions about the linear independence of input data, distinct from the commonly used general-position assumption. Under these assumptions, we demonstrate that an attention layer with H heads, dimension d, and context size n < d, featuring Theta(Hd^2) parameters, can memorize Omega(Hn) examples. Our analysis sheds light on how different attention heads handle various example sequences, aided by the softmax operator's saturation property. We validate our findings through experiments on synthetic data.

Linear Transformers have gained attention as efficient alternatives to standard Transformers, but their performance in retrieval and long-context tasks has been limited. To address these limitations, recent work has explored two distinct mechanisms: gating for adaptive memory control and the delta update rule for precise memory modifications. We observe that these mechanisms are complementary: gating enables rapid memory erasure while the delta rule facilitates targeted updates. Building on this insight, we introduce the gated delta rule and develop a parallel training algorithm optimized for modern hardware. Our proposed architecture, Gated DeltaNet, consistently surpasses existing models like Mamba2 and DeltaNet across multiple benchmarks, including language modeling, common-sense reasoning, in-context retrieval, length extrapolation, and long-context understanding. We further enhance performance by developing hybrid architectures that combine Gated DeltaNet layers with sliding window attention or Mamba2 layers, achieving both improved training efficiency and superior task performance.

Natural Language Generation (NLG) models are prone to generating repetitive utterances. In this work, we study the repetition problem for encoder-decoder models, using both recurrent neural network (RNN) and transformer architectures. To this end, we consider the chit-chat task, where the problem is more prominent than in other tasks that need encoder-decoder architectures. We first study the influence of model architectures. By using pre-attention and highway connections for RNNs, we manage to achieve lower repetition rates. However, this method does not generalize to other models such as transformers. We hypothesize that the deeper reason is that in the training corpora, there are hard tokens that are more difficult for a generative model to learn than others and, once learning has finished, hard tokens are still under-learned, so that repetitive generations are more likely to happen. Based on this hypothesis, we propose token loss dynamic reweighting (TLDR) that applies differentiable weights to individual token losses. By using higher weights for hard tokens and lower weights for easy tokens, NLG models are able to learn individual tokens at different paces. Experiments on chit-chat benchmark datasets show that TLDR is more effective in repetition reduction for both RNN and transformer architectures than baselines using different weighting functions.

Vector Symbolic Architectures (VSAs) have emerged as a novel framework for enabling interpretable machine learning algorithms equipped with the ability to reason and explain their decision processes. The basic idea is to represent discrete information through high dimensional random vectors. Complex data structures can be built up with operations over vectors such as the "binding" operation involving element-wise vector multiplication, which associates data together. The reverse task of decomposing the associated elements is a combinatorially hard task, with an exponentially large search space. The main algorithm for performing this search is the resonator network, inspired by Hopfield network-based memory search operations. In this work, we introduce a new variant of the resonator network, based on self-attention based update rules in the iterative search problem. This update rule, based on the Hopfield network with log-sum-exp energy function and norm-bounded states, is shown to substantially improve the performance and rate of convergence. As a result, our algorithm enables a larger capacity for associative memory, enabling applications in many tasks like perception based pattern recognition, scene decomposition, and object reasoning. We substantiate our algorithm with a thorough evaluation and comparisons to baselines.

Selective state-space models (SSMs) like Mamba overcome some of the shortcomings of Transformers, such as quadratic computational complexity with sequence length and large inference-time memory requirements from the key-value cache. Moreover, recent studies have shown that SSMs can match or exceed the language modeling capabilities of Transformers, making them an attractive alternative. In a controlled setting (e.g., same data), however, studies so far have only presented small scale experiments comparing SSMs to Transformers. To understand the strengths and weaknesses of these architectures at larger scales, we present a direct comparison between 8B-parameter Mamba, Mamba-2, and Transformer models trained on the same datasets of up to 3.5T tokens. We also compare these models to a hybrid architecture consisting of 43% Mamba-2, 7% attention, and 50% MLP layers (Mamba-2-Hybrid). Using a diverse set of tasks, we answer the question of whether Mamba models can match Transformers at larger training budgets. Our results show that while pure SSMs match or exceed Transformers on many tasks, they lag behind Transformers on tasks which require strong copying or in-context learning abilities (e.g., 5-shot MMLU, Phonebook) or long-context reasoning. In contrast, we find that the 8B Mamba-2-Hybrid exceeds the 8B Transformer on all 12 standard tasks we evaluated (+2.65 points on average) and is predicted to be up to 8x faster when generating tokens at inference time. To validate long-context capabilities, we provide additional experiments evaluating variants of the Mamba-2-Hybrid and Transformer extended to support 16K, 32K, and 128K sequences. On an additional 23 long-context tasks, the hybrid model continues to closely match or exceed the Transformer on average. To enable further study, we release the checkpoints as well as the code used to train our models as part of NVIDIA's Megatron-LM project.

Existing analyses of the expressive capacity of Transformer models have required excessively deep layers for data memorization, leading to a discrepancy with the Transformers actually used in practice. This is primarily due to the interpretation of the softmax function as an approximation of the hardmax function. By clarifying the connection between the softmax function and the Boltzmann operator, we prove that a single layer of self-attention with low-rank weight matrices possesses the capability to perfectly capture the context of an entire input sequence. As a consequence, we show that one-layer and single-head Transformers have a memorization capacity for finite samples, and that Transformers consisting of one self-attention layer with two feed-forward neural networks are universal approximators for continuous permutation equivariant functions on a compact domain.

Neural networks are powerful and flexible models that work well for many difficult learning tasks in image, speech and natural language understanding. Despite their success, neural networks are still hard to design. In this paper, we use a recurrent network to generate the model descriptions of neural networks and train this RNN with reinforcement learning to maximize the expected accuracy of the generated architectures on a validation set. On the CIFAR-10 dataset, our method, starting from scratch, can design a novel network architecture that rivals the best human-invented architecture in terms of test set accuracy. Our CIFAR-10 model achieves a test error rate of 3.65, which is 0.09 percent better and 1.05x faster than the previous state-of-the-art model that used a similar architectural scheme. On the Penn Treebank dataset, our model can compose a novel recurrent cell that outperforms the widely-used LSTM cell, and other state-of-the-art baselines. Our cell achieves a test set perplexity of 62.4 on the Penn Treebank, which is 3.6 perplexity better than the previous state-of-the-art model. The cell can also be transferred to the character language modeling task on PTB and achieves a state-of-the-art perplexity of 1.214.

Transformers have a potential of learning longer-term dependency, but are limited by a fixed-length context in the setting of language modeling. We propose a novel neural architecture Transformer-XL that enables learning dependency beyond a fixed length without disrupting temporal coherence. It consists of a segment-level recurrence mechanism and a novel positional encoding scheme. Our method not only enables capturing longer-term dependency, but also resolves the context fragmentation problem. As a result, Transformer-XL learns dependency that is 80% longer than RNNs and 450% longer than vanilla Transformers, achieves better performance on both short and long sequences, and is up to 1,800+ times faster than vanilla Transformers during evaluation. Notably, we improve the state-of-the-art results of bpc/perplexity to 0.99 on enwiki8, 1.08 on text8, 18.3 on WikiText-103, 21.8 on One Billion Word, and 54.5 on Penn Treebank (without finetuning). When trained only on WikiText-103, Transformer-XL manages to generate reasonably coherent, novel text articles with thousands of tokens. Our code, pretrained models, and hyperparameters are available in both Tensorflow and PyTorch.

This report presents PixelBytes, an approach for unified multimodal representation learning. Drawing inspiration from sequence models like Image Transformers, PixelCNN, and Mamba-Bytes, we explore integrating text, audio, action-state, and pixelated images (sprites) into a cohesive representation. We conducted experiments on a PixelBytes Pokemon dataset and an Optimal-Control dataset. Our investigation covered various model architectures, including Recurrent Neural Networks (RNNs), State Space Models (SSMs), and Attention-based models, with a focus on bidirectional processing and our PxBy embedding technique. We evaluated models based on data reduction strategies and autoregressive learning, specifically examining Long Short-Term Memory (LSTM) networks in predictive and autoregressive modes. Our results indicate that autoregressive models perform better than predictive models in this context. Additionally, we found that diffusion models can be applied to control problems and parallelized generation. PixelBytes aims to contribute to the development of foundation models for multimodal data processing and generation. The project's code, models, and datasets are available online.

World models are a fundamental component in model-based reinforcement learning (MBRL). To perform temporally extended and consistent simulations of the future in partially observable environments, world models need to possess long-term memory. However, state-of-the-art MBRL agents, such as Dreamer, predominantly employ recurrent neural networks (RNNs) as their world model backbone, which have limited memory capacity. In this paper, we seek to explore alternative world model backbones for improving long-term memory. In particular, we investigate the effectiveness of Transformers and Structured State Space Sequence (S4) models, motivated by their remarkable ability to capture long-range dependencies in low-dimensional sequences and their complementary strengths. We propose S4WM, the first world model compatible with parallelizable SSMs including S4 and its variants. By incorporating latent variable modeling, S4WM can efficiently generate high-dimensional image sequences through latent imagination. Furthermore, we extensively compare RNN-, Transformer-, and S4-based world models across four sets of environments, which we have tailored to assess crucial memory capabilities of world models, including long-term imagination, context-dependent recall, reward prediction, and memory-based reasoning. Our findings demonstrate that S4WM outperforms Transformer-based world models in terms of long-term memory, while exhibiting greater efficiency during training and imagination. These results pave the way for the development of stronger MBRL agents.

Multi-agent reinforcement learning (MARL) demonstrates significant progress in solving cooperative and competitive multi-agent problems in various environments. One of the principal challenges in MARL is the need for explicit prediction of the agents' behavior to achieve cooperation. To resolve this issue, we propose the Shared Recurrent Memory Transformer (SRMT) which extends memory transformers to multi-agent settings by pooling and globally broadcasting individual working memories, enabling agents to exchange information implicitly and coordinate their actions. We evaluate SRMT on the Partially Observable Multi-Agent Pathfinding problem in a toy Bottleneck navigation task that requires agents to pass through a narrow corridor and on a POGEMA benchmark set of tasks. In the Bottleneck task, SRMT consistently outperforms a variety of reinforcement learning baselines, especially under sparse rewards, and generalizes effectively to longer corridors than those seen during training. On POGEMA maps, including Mazes, Random, and MovingAI, SRMT is competitive with recent MARL, hybrid, and planning-based algorithms. These results suggest that incorporating shared recurrent memory into the transformer-based architectures can enhance coordination in decentralized multi-agent systems. The source code for training and evaluation is available on GitHub: https://github.com/Aloriosa/srmt.

Compositional relational reasoning (CRR) is a hallmark of human intelligence, but we lack a clear understanding of whether and how existing transformer large language models (LLMs) can solve CRR tasks. To enable systematic exploration of the CRR capability of LLMs, we first propose a new synthetic benchmark called Generalized Associative Recall (GAR) by integrating and generalizing the essence of several tasks in mechanistic interpretability (MI) study in a unified framework. Evaluation shows that GAR is challenging enough for existing LLMs, revealing their fundamental deficiency in CRR. Meanwhile, it is easy enough for systematic MI study. Then, to understand how LLMs solve GAR tasks, we use attribution patching to discover the core circuits reused by Vicuna-33B across different tasks and a set of vital attention heads. Intervention experiments show that the correct functioning of these heads significantly impacts task performance. Especially, we identify two classes of heads whose activations represent the abstract notion of true and false in GAR tasks respectively. They play a fundamental role in CRR across various models and tasks. The dataset and code are available at https://github.com/Caiyun-AI/GAR.

We present a novel non attention based architecture for large language models (LLMs) that efficiently handles very long context windows, on the order of hundreds of thousands to potentially millions of tokens. Unlike traditional Transformer designs, which suffer from quadratic memory and computation overload due to the nature of the self attention mechanism, our model avoids token to token attention entirely. Instead, it combines the following complementary components: State Space blocks (inspired by S4) that learn continuous time convolution kernels and scale near linearly with sequence length, Multi Resolution Convolution layers that capture local context at different dilation levels, a lightweight Recurrent Supervisor to maintain a global hidden state across sequential chunks, and Retrieval Augmented External Memory that stores and retrieves high-level chunk embeddings without reintroducing quadratic operations.

Recent work demonstrated Transformers' ability to efficiently copy strings of exponential sizes, distinguishing them from other architectures. We present the Causal Relation Network (CausalRN), an all-MLP sequence modeling architecture that can match Transformers on the copying task. Extending Relation Networks (RNs), we implemented key innovations to support autoregressive sequence modeling while maintaining computational feasibility. We discovered that exponentially-activated RNs are reducible to linear time complexity, and pre-activation normalization induces an infinitely growing memory pool, similar to a KV cache. In ablation study, we found both exponential activation and pre-activation normalization are indispensable for Transformer-level copying. Our findings provide new insights into what actually constitutes strong in-context retrieval.

Transformers evaluated in a single, fixed-depth pass are provably limited in expressive power to the constant-depth circuit class TC0. Running a Transformer autoregressively removes that ceiling -- first in next-token prediction and, more recently, in chain-of-thought reasoning. Both regimes rely on feedback loops that decode internal states into tokens only to re-encode them in subsequent steps. While this "thinking aloud" mirrors human reasoning, biological brains iterate without externalising intermediate states as language. To boost the expressive power of encoder Transformers without resorting to token-level autoregression, we introduce the SELF-Transformer: an encoder layer that iteratively refines its own attention weights to a fixed point. Instead of producing -- in one pass -- the alignment matrix that remixes the input sequence, the SELF-Transformer iteratively updates that matrix internally, scaling test-time computation with input difficulty. This adaptivity yields up to 20\% accuracy gains on encoder-style benchmarks without increasing parameter count, demonstrating that input-adaptive alignment at test time offers substantial benefits for only a modest extra compute budget. Self-Transformers thus recover much of the expressive power of iterative reasoning while preserving the simplicity of pure encoder architectures.

Many real-world applications require the prediction of long sequence time-series, such as electricity consumption planning. Long sequence time-series forecasting (LSTF) demands a high prediction capacity of the model, which is the ability to capture precise long-range dependency coupling between output and input efficiently. Recent studies have shown the potential of Transformer to increase the prediction capacity. However, there are several severe issues with Transformer that prevent it from being directly applicable to LSTF, including quadratic time complexity, high memory usage, and inherent limitation of the encoder-decoder architecture. To address these issues, we design an efficient transformer-based model for LSTF, named Informer, with three distinctive characteristics: (i) a ProbSparse self-attention mechanism, which achieves O(L log L) in time complexity and memory usage, and has comparable performance on sequences' dependency alignment. (ii) the self-attention distilling highlights dominating attention by halving cascading layer input, and efficiently handles extreme long input sequences. (iii) the generative style decoder, while conceptually simple, predicts the long time-series sequences at one forward operation rather than a step-by-step way, which drastically improves the inference speed of long-sequence predictions. Extensive experiments on four large-scale datasets demonstrate that Informer significantly outperforms existing methods and provides a new solution to the LSTF problem.

Autoregressive Transformers adopted in Large Language Models (LLMs) are hard to scale to long sequences. Despite several works trying to reduce their computational cost, most of LLMs still adopt attention layers between all pairs of tokens in the sequence, thus incurring a quadratic cost. In this study, we present a novel approach that dynamically prunes contextual information while preserving the model's expressiveness, resulting in reduced memory and computational requirements during inference. Our method employs a learnable mechanism that determines which uninformative tokens can be dropped from the context at any point across the generation process. By doing so, our approach not only addresses performance concerns but also enhances interpretability, providing valuable insight into the model's decision-making process. Our technique can be applied to existing pre-trained models through a straightforward fine-tuning process, and the pruning strength can be specified by a sparsity parameter. Notably, our empirical findings demonstrate that we can effectively prune up to 80\% of the context without significant performance degradation on downstream tasks, offering a valuable tool for mitigating inference costs. Our reference implementation achieves up to 2times increase in inference throughput and even greater memory savings.