Daily Papers

Huge language models (LMs) have ushered in a new era for AI, serving as a gateway to natural-language-based knowledge tasks. Although an essential element of modern AI, LMs are also inherently limited in a number of ways. We discuss these limitations and how they can be avoided by adopting a systems approach. Conceptualizing the challenge as one that involves knowledge and reasoning in addition to linguistic processing, we define a flexible architecture with multiple neural models, complemented by discrete knowledge and reasoning modules. We describe this neuro-symbolic architecture, dubbed the Modular Reasoning, Knowledge and Language (MRKL, pronounced "miracle") system, some of the technical challenges in implementing it, and Jurassic-X, AI21 Labs' MRKL system implementation.

Neuro-symbolic artificial intelligence (NSAI) represents a transformative approach in artificial intelligence (AI) by combining deep learning's ability to handle large-scale and unstructured data with the structured reasoning of symbolic methods. By leveraging their complementary strengths, NSAI enhances generalization, reasoning, and scalability while addressing key challenges such as transparency and data efficiency. This paper systematically studies diverse NSAI architectures, highlighting their unique approaches to integrating neural and symbolic components. It examines the alignment of contemporary AI techniques such as retrieval-augmented generation, graph neural networks, reinforcement learning, and multi-agent systems with NSAI paradigms. This study then evaluates these architectures against comprehensive set of criteria, including generalization, reasoning capabilities, transferability, and interpretability, therefore providing a comparative analysis of their respective strengths and limitations. Notably, the Neuro > Symbolic < Neuro model consistently outperforms its counterparts across all evaluation metrics. This result aligns with state-of-the-art research that highlight the efficacy of such architectures in harnessing advanced technologies like multi-agent systems.

As AI agents become increasingly autonomous, widely deployed in consequential contexts, and efficacious in bringing about real-world impacts, ensuring that their decisions are not only instrumentally effective but also normatively aligned has become critical. We introduce a neuro-symbolic reason-based containment architecture, Governor for Reason-Aligned ContainmEnt (GRACE), that decouples normative reasoning from instrumental decision-making and can contain AI agents of virtually any design. GRACE restructures decision-making into three modules: a Moral Module (MM) that determines permissible macro actions via deontic logic-based reasoning; a Decision-Making Module (DMM) that encapsulates the target agent while selecting instrumentally optimal primitive actions in accordance with derived macro actions; and a Guard that monitors and enforces moral compliance. The MM uses a reason-based formalism providing a semantic foundation for deontic logic, enabling interpretability, contestability, and justifiability. Its symbolic representation enriches the DMM's informational context and supports formal verification and statistical guarantees of alignment enforced by the Guard. We demonstrate GRACE on an example of a LLM therapy assistant, showing how it enables stakeholders to understand, contest, and refine agent behavior.

Personal Artificial Intelligence is currently hindered by the fragmentation of user data across isolated silos. While Retrieval-Augmented Generation offers a partial remedy, its reliance on unstructured vector similarity fails to capture the latent semantic topology and temporal dependencies essential for holistic sensemaking. We introduce EpisTwin, a neuro-symbolic framework that grounds generative reasoning in a verifiable, user-centric Personal Knowledge Graph. EpisTwin leverages Multimodal Language Models to lift heterogeneous, cross-application data into semantic triples. At inference, EpisTwin enables complex reasoning over the personal semantic graph via an agentic coordinator that combines Graph Retrieval-Augmented Generation with Online Deep Visual Refinement, dynamically re-grounding symbolic entities in their raw visual context. We also introduce PersonalQA-71-100, a synthetic benchmark designed to simulate a realistic user's digital footprint and evaluate EpisTwin performance. Our framework demonstrates robust results across a suite of state-of-the-art judge models, offering a promising direction for trustworthy Personal AI.

We present AXIOM, a trust-first neuro-symbolic execution architecture for natural-language mathematical reasoning. In AXIOM, the language model functions strictly as a canonicalizer: it rewrites informal problem text into a narrow schema consumed by a deterministic Computer-Algebra-System (CAS) pipeline, which derives and verifies the answer or abstains as a first-class output. Routing follows a 1:1:1 alignment between problem-shape regex, schema-specific prompt, and closed-form CAS handler, with 3,100+ such routes shipped and zero LOST_CORRECT regressions across 250+ consecutive ship commits. We report empirical results on 4 MATH categories with a cumulative correctness of 94.36% (2,592/2,747) at 100.00% trust on parseable (zero confident-wrong answers across the full 2,747-record benchmark), all four domains above the per-domain 70/90/70 floor with per-domain trust at 100.0%, and median latency of 1 ms on rule-only handlers (88% of records on the lm-eval arithmetic 20,000-record benchmark). The architecture has served ~30,000 production queries through a public deployment. The contribution we emphasize is not a final accuracy figure but the forward dynamic the architecture establishes: every logged abstain in production is a candidate correct after one ship cycle, since new tasks compose without regressing the registry. The operational discipline behind this property -- math-template bucketing, LOST_CORRECT scan as regression oracle, parseable-first onboarding, and abstain as first-class output -- constitutes a transferable framework for trustworthy neuro-symbolic systems beyond mathematics.

Vision-Language-Action (VLA) models have recently been proposed as a pathway toward generalist robotic policies capable of interpreting natural language and visual inputs to generate manipulation actions. However, their effectiveness and efficiency on structured, long-horizon manipulation tasks remain unclear. In this work, we present a head-to-head empirical comparison between a fine-tuned open-weight VLA model π0 and a neuro-symbolic architecture that combines PDDL-based symbolic planning with learned low-level control. We evaluate both approaches on structured variants of the Towers of Hanoi manipulation task in simulation while measuring both task performance and energy consumption during training and execution. On the 3-block task, the neuro-symbolic model achieves 95% success compared to 34% for the best-performing VLA. The neuro-symbolic model also generalizes to an unseen 4-block variant (78% success), whereas both VLAs fail to complete the task. During training, VLA fine-tuning consumes nearly two orders of magnitude more energy than the neuro-symbolic approach. These results highlight important trade-offs between end-to-end foundation-model approaches and structured reasoning architectures for long-horizon robotic manipulation, emphasizing the role of explicit symbolic structure in improving reliability, data efficiency, and energy efficiency. Code and models are available at https://price-is-not-right.github.io

Modern business environments demand continuous reconfiguration of cross-functional processes, yet most enterprise systems remain organized around siloed departments, rigid workflows, and hard-coded automation. Meanwhile, large language models (LLMs) demonstrate strong capabilities in interpreting natural language and synthesizing unstructured information, but they lack deterministic, auditable execution of complex business logic. We introduce Autonomous Business System (AUTOBUS), a system that integrates LLM-based AI agents, predicate-logic programming, and business-semantics-centric enterprise data into a unified neuro-symbolic architecture for executing end-to-end business initiatives. AUTOBUS models a business initiative as a network of interrelated tasks with explicit pre- and post-conditions, required data, evaluation rules, and API-level actions. Enterprise data is organized as a knowledge graph, whose entities, relationships, and constraints are translated into logic facts and foundational rules that ground reasoning and ensure semantic consistency. Core AI agents synthesize task instructions, enterprise semantics, and available tools into task-specific logic programs, which are executed by a logic engine that enforces constraints, coordinates auxiliary tools, and produces deterministic outcomes. Humans specify task instructions, define and maintain business semantics and policies, curate tools, and supervise high-impact or ambiguous decisions, ensuring accountability and adaptability. We detail the AUTOBUS architecture, the structure of AI-generated logic programs, and the human-AI collaboration model and present a case study that demonstrates accelerated time to market in a data-rich organization. A reference implementation of the case study is available at https://github.com/cecilpang/autobus-paper.

Modern artificial intelligence excels at statistical interpolation within seen manifolds but fundamentally fails at the exact reasoning required for theoretical physics and mathematics. We identify the "Float Wall" -- a catastrophic collapse of neural extrapolation at scales beyond 10^{16} -- caused by standard floating-point representation and linguistic tokenization (BPE). To resolve this, we introduce the Active Discoverer Framework, a digit-native neuro-symbolic architecture designed for invariant discovery. At its core is NumberNet, a Siamese Arithmetic Transformer that utilizes least-significant-bit (LSB) sequence encoding to achieve 0% precision loss and cosmic-scale extrapolation up to 10^{50}. To enforce physical grounding, we implement a Hamiltonian-based energy descent and Symmetry Grouping layer, ensuring the model respects Noether's theorem natively. The primary innovation is the Symbolic LaTeX Bottleneck: an active discovery loop where the model is forced to hypothesize unknown physical variables through an autoregressive LaTeX decoder. By reconciling numeric "hallucinations" with structurally valid mathematical expressions, the framework ensures that any discovered physics is parsimonious and human-interpretable. We evaluate this system against a 30-billion scale benchmark and the Universal Physics Pantheon, featuring 50 "Chaos Mode" systemic perturbations. Our results demonstrate that while traditional GBDT and LLM-based architectures collapse at cosmic scales, the Active Discoverer autonomously deduces universal constants such as the Gravitational Constant (G) with high fidelity. This framework establishes a path toward zero-hallucination artificial intelligence and truly autonomous scientific research agents.

The memory of contemporary Large Language Models is bound by a physical paradox: as they learn, they fill up. The linear accumulation (O(N)) of Key-Value states treats context as a warehouse of static artifacts, eventually forcing a destructive choice between amnesia and latency. We challenge this discrete orthodoxy, proposing that long-term memory is not the storage of items, but the persistence of a trajectory. We introduce Phonetic Trajectory Memory (PTM), a neuro-symbolic architecture that encodes language not as a sequence of tensors, but as a continuous path on an ergodic manifold governed by irrational rotation matrices. By decoupling the navigation (an invariant O(1) geometric signal) from the reconstruction (a probabilistic generative act), PTM achieves a compression magnitude of greater than 3,000x relative to dense caches. We demonstrate that retrieval becomes a process of resonance: the phonetic trace stabilizes the model against hallucination via "Signal Consensus" mechanism, securing up to approximately 92% factual accuracy. While this aggressive abstraction alters generative texture, it unlocks immediate access latency (approximately 34ms) independent of depth. Our results suggest that infinite context does not require infinite silicon; it requires treating memory not as data to be stored, but as a reconstructive process acting on a conserved, undying physical signal.

Large Language Models (LLMs) have demonstrated remarkable proficiency in natural language understanding, yet they struggle with strict multi-step reasoning, frequently suffering from hallucinations and inconsistency. Existing solutions like Chain-of-Thought (CoT) lack rigorous verification mechanisms, while standard Retrieval-Augmented Generation (RAG) often misses the complex, structural dependencies inherent in logical tasks. To bridge this gap, we propose a Neuro-Symbolic architecture that integrates a Logical Knowledge Graph (LKG) with dynamic solver routing. Specifically, we introduce an ontology-based LKG that treats logical rules and constraints as first-class topological nodes, enabling explicit modeling of dependencies extracted from text. We further design a Logic Router to dynamically dispatch tasks to the optimal symbolic engine, which is supported by a topology-aware hybrid retrieval mechanism. Experimental results on logical reasoning benchmarks demonstrate that our framework significantly outperforms state-of-the-art prompting and RAG baselines, delivering higher accuracy and verifiable reasoning paths.

We propose a fully spectral, neuro\-symbolic reasoning architecture that leverages Graph Signal Processing (GSP) as the primary computational backbone for integrating symbolic logic and neural inference. Unlike conventional reasoning models that treat spectral graph methods as peripheral components, our approach formulates the entire reasoning pipeline in the graph spectral domain. Logical entities and relationships are encoded as graph signals, processed via learnable spectral filters that control multi-scale information propagation, and mapped into symbolic predicates for rule-based inference. We present a complete mathematical framework for spectral reasoning, including graph Fourier transforms, band-selective attention, and spectral rule grounding. Experiments on benchmark reasoning datasets (ProofWriter, EntailmentBank, bAbI, CLUTRR, and ARC-Challenge) demonstrate improvements in logical consistency, interpretability, and computational efficiency over state\-of\-the\-art neuro\-symbolic models. Our results suggest that GSP provides a mathematically grounded and computationally efficient substrate for robust and interpretable reasoning systems.

In many reasoning problems, the premises are not observed as discrete symbols, but must be inferred from high-dimensional inputs. Further, the predicate vocabulary, argument structure, and trusted evidence are supplied by a Knowledge Graph (KG), or rule definitions. Classical neuro-symbolic pipelines have a discrete interface between perception and deduction. We present a neuro-soft-symbolic architecture for differentiable deductive reasoning over latent perceptual facts and knowledge-provided predicates. SoftReason removes the gradient gap by representing the deductive state as a local soft interpretation tensor over candidate constants and predicates. Perception proposes probabilistic base facts, KG triples enter as high-confidence soft evidence, and every query anchor, predicate choice, and closure update remains differentiable. Our core innovation is a learned differentiable lift of the immediate-consequence operator. It uses predicate-definition embeddings and latent composition channels to form soft body-predicate mixtures, aggregate over all possible witnesses, propose query-conditioned head facts, and update the interpretation through a monotone probabilistic OR. We instantiate the framework on Knowledge-aware Visual Question Answering (KVQA), and demonstrates how SoftReason supports end-to-end perceptual grounding, KG evidence injection, and differentiable deductive closure in one trainable architecture.

Long-horizon embodied task requires agents to act under partial observability while preserving both scene belief and execution progress. Flat histories or implicit policy states may contain past observations, but they do not provide an explicit interface for deciding which world facts support the currently active goal. We introduce Mimir, a neuro-symbolic memory that separates world memory from task memory and dynamically grounds them before each action. World memory maintains object locations, object states, and perceptual evidence, while task memory maintains an ordered goal agenda, progress state, hand state, failures, and execution constraints. A grounding module binds the active goal to recalled world candidates, fills missing source locations, and attaches evidence before planning and embodiment-specific execution. Across tested backbones, Mimir consistently improves on different EB-ALFRED and EB-Habitat tasks, with maximum gains of 42.5% and average gains of 23.0%, respectively. Compared with the best results among prior agent and memory systems evaluated under the same backbone, Mimir improves the overall average success rate by 8.5%. Finally, on the EB-Habitat Long-horizon subset, Mimir achieves 86.0% success rate, substantially outperforming current closed-source models. Our code will be released soon.

GCC and LLVM underpin much of modern software infrastructure, relying on distinct Intermediate Representations (IRs) to drive optimizations and code generation. However, the semantic and structural differences between these IRs create significant barriers for cross-toolchain interaction, limiting the reuse of compiler frontends, backends, and optimization pipelines across programming languages and compilation ecosystems. Traditional rule-based translators have attempted to bridge this gap, but their complexity and maintenance cost have hindered practical adoption. In this context, Large Language Models (LLMs) appear to be an emerging technology that offers a data-driven alternative, capable of learning complex mappings between heterogeneous compiler IRs directly from sufficiently representative examples. To explore this approach, this paper presents IRIS-14B, a 14-billion-parameter transformer model fine-tuned to translate GIMPLE (as emitted by GCC) to LLVM IR (as emitted by LLVM). The model is trained on paired IRs extracted from C sources and evaluated on the GIMPLE-to-LLVM IR transformation applied to IRs derived from real-world C code and competitive programming problems. To the best of our knowledge, IRIS-14B is the first model trained explicitly for IR-to-IR translation. It outperforms the accuracy of widely used models, including the largest state-of-the-art open models available today, ranging from 13 to 1,000 billion parameters, by up to 44 percentage points. The proposed transformation supports the integration of LLMs as complementary components within hybrid neuro-symbolic compiler architectures, where models such as IRIS-14B act as interoperability layers enabling cross-toolchain workflows without modifying existing compiler passes, while traditional compiler infrastructure continues to perform deterministic compilation and optimization.

The Korean criminal justice system utilizes summary proceedings (guyaksik) to expedite high-volume minor infractions, such as simple driving under the influence (DUI), unlicensed driving, and minor traffic casualties. Although this mechanism improves judicial throughput, processing these cases creates a substantial administrative burden for prosecutors, driving the need for automated systems that can precisely translate unstructured legal text into deterministic statutory outcomes. While recent Large Language Models (LLMs) excel at semantic extraction, their probabilistic nature inherently limits their reliability in Legal Judgment Prediction tasks. Specifically, when confronted with the arithmetic constraints of legal statutes, LLMs can produce hallucinations. Given that legal accountability permits virtually no tolerance for stochastic errors, purely neural architectures remain limited in their direct judicial applications. To address these limitations, we propose a Neuro-Symbolic framework that bridges unstructured legal facts with formal verification. Our architecture restricts the LLM exclusively to semantic extraction, while offloading statutory fine calculations to a Satisfiability Modulo Theories solver. This division of labor reduces hallucination risks during computation. Furthermore, we incorporate a Human-in-the-Loop verification scheme to preserve professional legal oversight. We formalize the 2026 Sentencing Guidelines for Traffic Offenses within this pipeline, demonstrating a deterministic approach to supporting summary indictments.

Semantic code search is the task of retrieving a code snippet given a textual description of its functionality. Recent work has been focused on using similarity metrics between neural embeddings of text and code. However, current language models are known to struggle with longer, compositional text, and multi-step reasoning. To overcome this limitation, we propose supplementing the query sentence with a layout of its semantic structure. The semantic layout is used to break down the final reasoning decision into a series of lower-level decisions. We use a Neural Module Network architecture to implement this idea. We compare our model - NS3 (Neuro-Symbolic Semantic Search) - to a number of baselines, including state-of-the-art semantic code retrieval methods, and evaluate on two datasets - CodeSearchNet and Code Search and Question Answering. We demonstrate that our approach results in more precise code retrieval, and we study the effectiveness of our modular design when handling compositional queries.

Large Language Models (LLMs) are fundamentally constrained by the quadratic computational cost of self-attention and the "Lost in the Middle" phenomenon, where reasoning capabilities degrade as context windows expand. Existing solutions, primarily "Flat RAG" architectures relying on vector databases, treat memory as an unstructured bag of embeddings, failing to capture the hierarchical and temporal structure of long-horizon interactions. This paper presents Aeon, a Neuro-Symbolic Cognitive Operating System that redefines memory as a managed OS resource. Aeon structures memory into a Memory Palace (a spatial index implemented via Atlas, a SIMD-accelerated Page-Clustered Vector Index) and a Trace (a neuro-symbolic episodic graph). This architecture introduces three advances: (1) Symmetric INT8 Scalar Quantization, achieving 3.1x spatial compression and 5.6x math acceleration via NEON SDOT intrinsics; (2) a decoupled Write-Ahead Log (WAL) ensuring crash-recoverability with statistically negligible overhead (<1%); and (3) a Sidecar Blob Arena eliminating the prior 440-character text ceiling via an append-only mmap-backed blob file with generational garbage collection. The Semantic Lookaside Buffer (SLB) exploits conversational locality to achieve sub-5us retrieval latencies, with INT8 vectors dequantized to FP32 on cache insertion to preserve L1-resident lookup performance. Benchmarks on Apple M4 Max demonstrate that the combined architecture achieves 4.70ns INT8 dot product latency, 3.09us tree traversal at 100K nodes (3.4x over FP32), and P99 read latency of 750ns under hostile 16-thread contention via epoch-based reclamation.

Modern neural networks rely on generic activation functions (ReLU, GELU, SiLU) that ignore the mathematical structure inherent in scientific data. We propose Neuro-Symbolic Activation Discovery, a framework that uses Genetic Programming to extract interpretable mathematical formulas from data and inject them as custom activation functions. Our key contribution is the discovery of a Geometric Transfer phenomenon: activation functions learned from particle physics data successfully generalize to ecological classification, outperforming standard activations (ReLU, GELU, SiLU) in both accuracy and parameter efficiency. On the Forest Cover dataset, our Hybrid Transfer model achieves 82.4% accuracy with only 5,825 parameters, compared to 83.4% accuracy requiring 31,801 parameters for a conventional heavy network -- a 5.5x parameter reduction with only 1% accuracy loss. We introduce a Parameter Efficiency Score (E_{param} = AUC / log_{10}(Params)) and demonstrate that lightweight hybrid architectures consistently achieve 18-21% higher efficiency than over-parameterized baselines. Crucially, we establish boundary conditions: while Physics to Ecology transfer succeeds (both involve continuous Euclidean measurements), Physics to Text transfer fails (discrete word frequencies require different mathematical structures). Our work opens pathways toward domain-specific activation libraries for efficient scientific machine learning.

Flexible robotic automation requires systems that interpret operator intent, verify physical feasibility, and recover from execution failures across both the planning and execution stages. This paper proposes an agentic neuro-symbolic framework for human-in-the-loop industrial robotics, in which LLMs are used for tasks that require language understanding or contextual reasoning, while all verification, sequencing, and execution remain deterministic. The framework adapts the Planner-Generator-Evaluator (PGE) harness pattern from software engineering into a Specifier-Designer-Inspector (SDI) architecture for industrial robotics, combined with LangGraph-based dynamic routing for failure recovery. A two-tier recovery mechanism addresses structure-level replanning through context-aware orchestration and execution-level geometric failures through deterministic recovery skills. A Unity3D digital twin supports human inspection, modification, and re-verification prior to physical execution. Evaluated on natural-language commands across multiple difficulty levels against ten baselines, the proposed method achieves the highest task success. Ablation results confirm that structured command expansion, symbolic verification, selective LLM routing, and recovery skills are each individually necessary.

This paper proposes a neuro-symbolic framework for G-code generation that seeks to integrate the neural generative capabilities of the GLLM method (Abdelaal et al., 2025) with formal verification via a Separation Logic (SL) prover. To establish a reliable physical baseline, the framework extracts deterministic boundary representations from 3D CAD models (STEP files) using the OpenCASCADE framework. This extracted geometric data supports a two-component architecture: the LLM serves as an initial code generator, while the SL Prover, utilizing a Spatial Heap model, evaluates the output. By conceptualizing physical collisions as logical Spatial Data Races -- violations of the separating conjunction in SL -- our framework translates proof failures into structured mathematical feedback. These failures are condensed into bounding boxes that serve as directives for the LLM's iterative self-correction. Ultimately, this work aims to develop a self-correcting system that reduces the need for human supervision, leading to safer and verified autonomous manufacturing.

As LLM-based agents increasingly operate in high-stakes domains with real-world consequences, ensuring their behavioral safety becomes paramount. The dominant oversight paradigm, LLM-as-a-Judge, faces a fundamental dilemma: how can probabilistic systems reliably supervise other probabilistic systems without inheriting their failure modes? We argue that formal verification offers a principled escape from this dilemma, yet its adoption has been hindered by a critical bottleneck: the translation from natural language requirements to formal specifications. This paper bridges this gap by proposing , a neuro-symbolic framework that employs a bidirectional Formal-of-Thought architecture: LLMs serve as specification compilers that top-down decompose high-level human intent into atomic, verifiable constraints, then bottom-up prove compliance using Dafny specifications and Z3 Satisfiability modulo theories solving, which produces mathematical guarantees rather than probabilistic scores. We validate across three benchmarks spanning behavioral safety, multi-domain constraint adherence, and agentic upward deception detection. Experiments on 7 agent models demonstrate that achieves an average improvement of 16.6% over LLM-as-a-Judge baselines, enables weak-to-strong generalization where a 7B judge achieves over 90% accuracy detecting deception from 72B agents, and provides near-linear safety improvement through iterative refinement.

Navigating unseen, large-scale environments based on complex and abstract human instructions remains a formidable challenge for autonomous mobile robots. Addressing this requires robots to infer implicit semantics and efficiently explore large-scale task spaces. However, existing methods, ranging from end-to-end learning to foundation model-based modular architectures, often lack the capability to decompose complex tasks or employ efficient exploration strategies, leading to robot aimless wandering or target recognition failures. To address these limitations, we propose VL-Nav, a neuro-symbolic (NeSy) vision-language navigation system. The proposed system intertwines neural reasoning with symbolic guidance through two core components: (1) a NeSy task planner that leverages a symbolic 3D scene graph and image memory system to enhance the vision language models' (VLMs) neural reasoning capabilities for task decomposition and replanning; and (2) a NeSy exploration system that couples neural semantic cues with the symbolic heuristic function to efficiently gather the task-related information while minimizing unnecessary repeat travel during exploration. Validated on the DARPA TIAMAT Challenge navigation tasks, our system achieved an 83.4% success rate (SR) in indoor environments and 75% in outdoor scenarios. VL-Nav achieved an 86.3% SR in real-world experiments, including a challenging 483-meter run. Finally, we validate the system with complex instructions in a 3D multi-floor scenario.

Vision-Language-Action (VLA) models commonly generate robot actions token by token through Large Language Model (LLM) decoders, causing inference latency to grow with action sequence length and limiting closed-loop control frequency. We present Goal-Conditioned Vision-Predictor-Action (VPA), which replaces autoregressive decoders with a lightweight latent control loop. A shared vision encoder and a frozen text encoder embed observations, goal images, and instructions; a neuro-symbolic selector chooses a discrete skill; a Joint-Embedding Predictive Architecture (JEPA) predictor forecasts the next latent state; and a flow-matching solver generates an entire action chunk in a few integration steps, so that sequential network evaluations per decision step do not depend on the action horizon. We analyze inference complexity, regularization against representation collapse, and conditions under which latent sub-goal thresholding limits error accumulation across task phases. As an initial proof of concept, we evaluated VPA on the LIBERO-10 suite. The trainable model has under 20M parameters (checkpoint under 75 MB, excluding a frozen 63.4M-parameter CLIP text encoder); a decision step of a single-camera reference configuration takes 10-14 ms on an Apple M4; and trained only on LIBERO-10 demonstrations in under three hours on a single GPU, a two-camera policy succeeded in 40.0% of 200 evaluation episodes. These preliminary results from a single training run suggest the approach is workable. Code and weights are available at https://github.com/ylee-sling/Vision-Predictor-Action and https://huggingface.co/ylee-sling/vpa-libero10, and archived at https://doi.org/10.5281/zenodo.22960920.

This paper explores the integration of two AI subdisciplines employed in the development of artificial agents that exhibit intelligent behavior: Large Language Models (LLMs) and Cognitive Architectures (CAs). We present three integration approaches, each grounded in theoretical models and supported by preliminary empirical evidence. The modular approach, which introduces four models with varying degrees of integration, makes use of chain-of-thought prompting, and draws inspiration from augmented LLMs, the Common Model of Cognition, and the simulation theory of cognition. The agency approach, motivated by the Society of Mind theory and the LIDA cognitive architecture, proposes the formation of agent collections that interact at micro and macro cognitive levels, driven by either LLMs or symbolic components. The neuro-symbolic approach, which takes inspiration from the CLARION cognitive architecture, proposes a model where bottom-up learning extracts symbolic representations from an LLM layer and top-down guidance utilizes symbolic representations to direct prompt engineering in the LLM layer. These approaches aim to harness the strengths of both LLMs and CAs, while mitigating their weaknesses, thereby advancing the development of more robust AI systems. We discuss the tradeoffs and challenges associated with each approach.

Large language models (LLMs) hold broad knowledge in one set of weights, but lack interpretability and trustworthy reasoning, especially in high-stakes use cases. A neuro-symbolic model, with its interpretable architecture and System 2 reasoning capacity, is a promising alternative if built at the scale of LLMs; however, its symbolic backbone is usually constructed with human effort, so existing neuro-symbolic models are bottlenecked by the scope of the symbol component and usually domain-specific. A data-driven method could instead build a larger symbolic system by aligning and merging existing ones. We target its first, foundational step: matching units across these heterogeneous systems. Our method, SAE-IDF, encodes a symbol in its native context into a sparse code with a sparse autoencoder (SAE), re-weights each dimension by its rarity and matches across systems. On 12 tasks across 6 kinds of symbolic system, SAE-IDF outperforms the same LLM's dense baseline on all tasks with Gemma-2-9B and all but one with Llama-3.1-8B, by up to 45 points, consistently across SAE layers and configurations. SAE-IDF is also interpretable: every dimension of the sparse code has a human-readable meaning, so each match decomposes into named concepts (features). Our work paves the way to a universal symbolic backbone.

This paper reviews the state-of-the-art of language models architectures and strategies for "complex" question-answering (QA, CQA, CPS) with a focus on hybridization. Large Language Models (LLM) are good at leveraging public data on standard problems but once you want to tackle more specific complex questions or problems (e.g. How does the concept of personal freedom vary between different cultures ? What is the best mix of power generation methods to reduce climate change ?) you may need specific architecture, knowledge, skills, methods, sensitive data protection, explainability, human approval and versatile feedback... Recent projects like ChatGPT and GALACTICA have allowed non-specialists to grasp the great potential as well as the equally strong limitations of LLM in complex QA. In this paper, we start by reviewing required skills and evaluation techniques. We integrate findings from the robust community edited research papers BIG, BLOOM and HELM which open source, benchmark and analyze limits and challenges of LLM in terms of tasks complexity and strict evaluation on accuracy (e.g. fairness, robustness, toxicity, ...) as a baseline. We discuss some challenges associated with complex QA, including domain adaptation, decomposition and efficient multi-step QA, long form and non-factoid QA, safety and multi-sensitivity data protection, multimodal search, hallucinations, explainability and truthfulness, temporal reasoning. We analyze current solutions and promising research trends, using elements such as: hybrid LLM architectural patterns, training and prompting strategies, active human reinforcement learning supervised with AI, neuro-symbolic and structured knowledge grounding, program synthesis, iterated decomposition and others.

The neural Hawkes process (Mei & Eisner, 2017) is a generative model of irregularly spaced sequences of discrete events. To handle complex domains with many event types, Mei et al. (2020a) further consider a setting in which each event in the sequence updates a deductive database of facts (via domain-specific pattern-matching rules); future events are then conditioned on the database contents. They show how to convert such a symbolic system into a neuro-symbolic continuous-time generative model, in which each database fact and the possible event has a time-varying embedding that is derived from its symbolic provenance. In this paper, we modify both models, replacing their recurrent LSTM-based architectures with flatter attention-based architectures (Vaswani et al., 2017), which are simpler and more parallelizable. This does not appear to hurt our accuracy, which is comparable to or better than that of the original models as well as (where applicable) previous attention-based methods (Zuo et al., 2020; Zhang et al., 2020a).

Developing models that can learn to reason is a notoriously challenging problem. We focus on reasoning in relational domains, where the use of Graph Neural Networks (GNNs) seems like a natural choice. However, previous work has shown that regular GNNs lack the ability to systematically generalize from training examples on test graphs requiring longer inference chains, which fundamentally limits their reasoning abilities. A common solution relies on neuro-symbolic methods that systematically reason by learning rules, but their scalability is often limited and they tend to make unrealistically strong assumptions, e.g.\ that the answer can always be inferred from a single relational path. We propose the Epistemic GNN (EpiGNN), a novel parameter-efficient and scalable GNN architecture with an epistemic inductive bias for systematic reasoning. Node embeddings in EpiGNNs are treated as epistemic states, and message passing is implemented accordingly. We show that EpiGNNs achieve state-of-the-art results on link prediction tasks that require systematic reasoning. Furthermore, for inductive knowledge graph completion, EpiGNNs rival the performance of state-of-the-art specialized approaches. Finally, we introduce two new benchmarks that go beyond standard relational reasoning by requiring the aggregation of information from multiple paths. Here, existing neuro-symbolic approaches fail, yet EpiGNNs learn to reason accurately. Code and datasets are available at https://github.com/erg0dic/gnn-sg.

Visual reasoning is critical for a wide range of computer vision tasks that go beyond surface-level object detection and classification. Despite notable advances in relational, symbolic, temporal, causal, and commonsense reasoning, existing surveys often address these directions in isolation, lacking a unified analysis and comparison across reasoning types, methodologies, and evaluation protocols. This survey aims to address this gap by categorizing visual reasoning into five major types (relational, symbolic, temporal, causal, and commonsense) and systematically examining their implementation through architectures such as graph-based models, memory networks, attention mechanisms, and neuro-symbolic systems. We review evaluation protocols designed to assess functional correctness, structural consistency, and causal validity, and critically analyze their limitations in terms of generalizability, reproducibility, and explanatory power. Beyond evaluation, we identify key open challenges in visual reasoning, including scalability to complex scenes, deeper integration of symbolic and neural paradigms, the lack of comprehensive benchmark datasets, and reasoning under weak supervision. Finally, we outline a forward-looking research agenda for next-generation vision systems, emphasizing that bridging perception and reasoning is essential for building transparent, trustworthy, and cross-domain adaptive AI systems, particularly in critical domains such as autonomous driving and medical diagnostics.

As the use of Large Language Models moves from chatbots into agentic systems, where outputs become actions with irreversible consequences on reality, the existing paradigm on AI Interpretability research, post-hoc interpretability, is structurally inadequate for safe and trustworthy model deployment: it explains behavior after the fact but cannot audit or intervene in an inference computation before it commits to an output. We therefore argue for a shift toward generative interpretability, an architectural property under which a model's inference pass natively exposes semantically meaningful checkpoints that are human-understandable and amenable to causal intervention. We show the merits of generative interpretability as comparison to other interpretability research paradigms, and propose Neuro-Symbolic Models as a concrete instantiation.

Large Language Models (LLMs) have succeeded remarkably in various natural language processing (NLP) tasks, yet their reasoning capabilities remain a fundamental challenge. While LLMs exhibit impressive fluency and factual recall, their ability to perform complex reasoning-spanning logical deduction, mathematical problem-solving, commonsense inference, and multi-step reasoning-often falls short of human expectations. This survey provides a comprehensive review of emerging techniques enhancing reasoning in LLMs. We categorize existing methods into key approaches, including prompting strategies (e.g., Chain-of-Thought reasoning, Self-Consistency, and Tree-of-Thought reasoning), architectural innovations (e.g., retrieval-augmented models, modular reasoning networks, and neuro-symbolic integration), and learning paradigms (e.g., fine-tuning with reasoning-specific datasets, reinforcement learning, and self-supervised reasoning objectives). Additionally, we explore evaluation frameworks used to assess reasoning in LLMs and highlight open challenges, such as hallucinations, robustness, and reasoning generalization across diverse tasks. By synthesizing recent advancements, this survey aims to provide insights into promising directions for future research and practical applications of reasoning-augmented LLMs.

Neuro-symbolic learning was proposed to address challenges with training neural networks for complex reasoning tasks with the added benefits of interpretability, reliability, and efficiency. Neuro-symbolic learning methods traditionally train neural models in conjunction with symbolic programs, but they face significant challenges that limit them to simplistic problems. On the other hand, purely-neural foundation models now reach state-of-the-art performance through prompting rather than training, but they are often unreliable and lack interpretability. Supplementing foundation models with symbolic programs, which we call neuro-symbolic prompting, provides a way to use these models for complex reasoning tasks. Doing so raises the question: What role does specialized model training as part of neuro-symbolic learning have in the age of foundation models? To explore this question, we highlight three pitfalls of traditional neuro-symbolic learning with respect to the compute, data, and programs leading to generalization problems. This position paper argues that foundation models enable generalizable neuro-symbolic solutions, offering a path towards achieving the original goals of neuro-symbolic learning without the downsides of training from scratch.

Modern systems in artificial intelligence (AI) somehow excel in domains for which they seem poorly suited. Intelligence has traditionally been modeled as operating over structured combinations of symbols, such as logical formulas. However, the strongest modern AI systems are based on neural networks, which instead represent information in continuous vectors. Vectors seem inadequate for capturing the structure of language, logic, and other cognitive domains, yet neural networks achieve impressive performance in these areas. How do they do it? In this work, we propose a potential answer: Despite appearances, perhaps the internal representations of neural networks implicitly realize symbolic structure. In support of this hypothesis, we show that the vector representations of a variety of neural networks can be closely approximated with symbolic structures: we can replace the network's entire representation-generating process with a closed-form equation instantiating a symbolic structure, and the network's behavior remains largely unchanged. This finding holds for both small-scale neural networks trained to manipulate lists as well as large language models (LLMs) operating in four domains that are central in symbolic traditions: arithmetic, logic, computer code, and language. Further, our symbolic approximation allows us to modify an LLM's behavior in targeted ways via precise interventions on its internal representations, showing that the LLM's behavior is reliant on the symbolic structures we have identified. This work provides a potential way to reconcile longstanding symbolic conceptions of intelligence with the vector-based nature of modern AI.

The integration of symbolic computing with neural networks has intrigued researchers since the first theorizations of Artificial intelligence (AI). The ability of Neuro-Symbolic (NeSy) methods to infer or exploit behavioral schema has been widely considered as one of the possible proxies for human-level intelligence. However, the limited semantic generalizability and the challenges in declining complex domains with pre-defined patterns and rules hinder their practical implementation in real-world scenarios. The unprecedented results achieved by connectionist systems since the last AI breakthrough in 2017 have raised questions about the competitiveness of NeSy solutions, with particular emphasis on the Natural Language Processing and Computer Vision fields. This survey examines task-specific advancements in the NeSy domain to explore how incorporating symbolic systems can enhance explainability and reasoning capabilities. Our findings are meant to serve as a resource for researchers exploring explainable NeSy methodologies for real-life tasks and applications. Reproducibility details and in-depth comments on each surveyed research work are made available at https://github.com/disi-unibo-nlp/task-oriented-neuro-symbolic.git.

Current advances in Artificial Intelligence (AI) and Machine Learning (ML) have achieved unprecedented impact across research communities and industry. Nevertheless, concerns about trust, safety, interpretability and accountability of AI were raised by influential thinkers. Many have identified the need for well-founded knowledge representation and reasoning to be integrated with deep learning and for sound explainability. Neural-symbolic computing has been an active area of research for many years seeking to bring together robust learning in neural networks with reasoning and explainability via symbolic representations for network models. In this paper, we relate recent and early research results in neurosymbolic AI with the objective of identifying the key ingredients of the next wave of AI systems. We focus on research that integrates in a principled way neural network-based learning with symbolic knowledge representation and logical reasoning. The insights provided by 20 years of neural-symbolic computing are shown to shed new light onto the increasingly prominent role of trust, safety, interpretability and accountability of AI. We also identify promising directions and challenges for the next decade of AI research from the perspective of neural-symbolic systems.

Humans interact with the environment using a combination of perception - transforming sensory inputs from their environment into symbols, and cognition - mapping symbols to knowledge about the environment for supporting abstraction, reasoning by analogy, and long-term planning. Human perception-inspired machine perception, in the context of AI, refers to large-scale pattern recognition from raw data using neural networks trained using self-supervised learning objectives such as next-word prediction or object recognition. On the other hand, machine cognition encompasses more complex computations, such as using knowledge of the environment to guide reasoning, analogy, and long-term planning. Humans can also control and explain their cognitive functions. This seems to require the retention of symbolic mappings from perception outputs to knowledge about their environment. For example, humans can follow and explain the guidelines and safety constraints driving their decision-making in safety-critical applications such as healthcare, criminal justice, and autonomous driving. This article introduces the rapidly emerging paradigm of Neurosymbolic AI combines neural networks and knowledge-guided symbolic approaches to create more capable and flexible AI systems. These systems have immense potential to advance both algorithm-level (e.g., abstraction, analogy, reasoning) and application-level (e.g., explainable and safety-constrained decision-making) capabilities of AI systems.

Diagrams matter. Unfortunately, the deep learning community has no standard method for diagramming architectures. The current combination of linear algebra notation and ad-hoc diagrams fails to offer the necessary precision to understand architectures in all their detail. However, this detail is critical for faithful implementation, mathematical analysis, further innovation, and ethical assurances. I present neural circuit diagrams, a graphical language tailored to the needs of communicating deep learning architectures. Neural circuit diagrams naturally keep track of the changing arrangement of data, precisely show how operations are broadcast over axes, and display the critical parallel behavior of linear operations. A lingering issue with existing diagramming methods is the inability to simultaneously express the detail of axes and the free arrangement of data, which neural circuit diagrams solve. Their compositional structure is analogous to code, creating a close correspondence between diagrams and implementation. In this work, I introduce neural circuit diagrams for an audience of machine learning researchers. After introducing neural circuit diagrams, I cover a host of architectures to show their utility and breed familiarity. This includes the transformer architecture, convolution (and its difficult-to-explain extensions), residual networks, the U-Net, and the vision transformer. I include a Jupyter notebook that provides evidence for the close correspondence between diagrams and code. Finally, I examine backpropagation using neural circuit diagrams. I show their utility in providing mathematical insight and analyzing algorithms' time and space complexities.

We propose NEURONA, a neuro-symbolic framework for fMRI decoding and concept grounding in neural activity. Leveraging image- and video-based fMRI question-answering datasets, NEURONA learns to decode interacting concepts from visual stimuli based on patterns of fMRI responses, integrating symbolic reasoning and compositional execution with fMRI grounding across brain regions. We demonstrate that incorporating structural priors (e.g., compositional predicate-argument dependencies between concepts) into the decoding process significantly improves both decoding accuracy over precise queries, and notably, generalization to unseen queries at test time. With NEURONA, we highlight neuro-symbolic frameworks as promising tools for understanding neural activity.

Parallel neurosymbolic architectures have been applied effectively in NLP by distilling knowledge from a logic theory into a deep model.However, prior art faces several limitations including supporting restricted forms of logic theories and relying on the assumption of independence between the logic and the deep network. We present Concordia, a framework overcoming the limitations of prior art. Concordia is agnostic both to the deep network and the logic theory offering support for a wide range of probabilistic theories. Our framework can support supervised training of both components and unsupervised training of the neural component. Concordia has been successfully applied to tasks beyond NLP and data classification, improving the accuracy of state-of-the-art on collective activity detection, entity linking and recommendation tasks.

Neurosymbolic (NeSy) frameworks combine neural representations and learning with symbolic representations and reasoning. Combining the reasoning capacities, explainability, and interpretability of symbolic processing with the flexibility and power of neural computing allows us to solve complex problems with more reliability while being data-efficient. However, this recently growing topic poses a challenge to developers with its learning curve, lack of user-friendly tools, libraries, and unifying frameworks. In this paper, we characterize the technical facets of existing NeSy frameworks, such as the symbolic representation language, integration with neural models, and the underlying algorithms. A majority of the NeSy research focuses on algorithms instead of providing generic frameworks for declarative problem specification to leverage problem solving. To highlight the key aspects of Neurosymbolic modeling, we showcase three generic NeSy frameworks - DeepProbLog, Scallop, and DomiKnowS. We identify the challenges within each facet that lay the foundation for identifying the expressivity of each framework in solving a variety of problems. Building on this foundation, we aim to spark transformative action and encourage the community to rethink this problem in novel ways.

With a view to bridging the gap between deep learning and symbolic AI, we present a novel end-to-end neural network architecture that learns to form propositional representations with an explicitly relational structure from raw pixel data. In order to evaluate and analyse the architecture, we introduce a family of simple visual relational reasoning tasks of varying complexity. We show that the proposed architecture, when pre-trained on a curriculum of such tasks, learns to generate reusable representations that better facilitate subsequent learning on previously unseen tasks when compared to a number of baseline architectures. The workings of a successfully trained model are visualised to shed some light on how the architecture functions.

What is it about human brains that allows us to reason symbolically whereas most other animals cannot? There is evidence that dynamic binding, the ability to combine neurons into groups on the fly, is necessary for symbolic thought, but there is also evidence that it is not sufficient. We propose that two kinds of hierarchical integration (integration of multiple role-bindings into multiplace predicates, and integration of multiple correspondences into structure mappings) are minimal requirements, on top of basic dynamic binding, to realize symbolic thought. We tested this hypothesis in a systematic collection of 17 simulations that explored the ability of cognitive architectures with and without the capacity for multi-place predicates and structure mapping to perform various kinds of tasks. The simulations were as generic as possible, in that no task could be performed based on any diagnostic features, depending instead on the capacity for multi-place predicates and structure mapping. The results are consistent with the hypothesis that, along with dynamic binding, multi-place predicates and structure mapping are minimal requirements for basic symbolic thought. These results inform our understanding of how human brains give rise to symbolic thought and speak to the differences between biological intelligence, which tends to generalize broadly from very few training examples, and modern approaches to machine learning, which typically require millions or billions of training examples. The results we report also have important implications for bio-inspired artificial intelligence.

Despite the tremendous success, existing machine learning models still fall short of human-like systematic generalization -- learning compositional rules from limited data and applying them to unseen combinations in various domains. We propose Neural-Symbolic Recursive Machine (NSR) to tackle this deficiency. The core representation of NSR is a Grounded Symbol System (GSS) with combinatorial syntax and semantics, which entirely emerges from training data. Akin to the neuroscience studies suggesting separate brain systems for perceptual, syntactic, and semantic processing, NSR implements analogous separate modules of neural perception, syntactic parsing, and semantic reasoning, which are jointly learned by a deduction-abduction algorithm. We prove that NSR is expressive enough to model various sequence-to-sequence tasks. Superior systematic generalization is achieved via the inductive biases of equivariance and recursiveness embedded in NSR. In experiments, NSR achieves state-of-the-art performance in three benchmarks from different domains: SCAN for semantic parsing, PCFG for string manipulation, and HINT for arithmetic reasoning. Specifically, NSR achieves 100% generalization accuracy on SCAN and PCFG and outperforms state-of-the-art models on HINT by about 23%. Our NSR demonstrates stronger generalization than pure neural networks due to its symbolic representation and inductive biases. NSR also demonstrates better transferability than existing neural-symbolic approaches due to less domain-specific knowledge required.

This work introduces a new computational theory of mind grounded in set theory and hyperdimensional computing. Whereas traditional neural networks rely on continuous weights and matrix multiplication, this framework works with sparse binary data. It represents information as discrete sets, directly modeling biological neural population codes. I demonstrate that associative memory emerges naturally from network topologies featuring a combinatorially expanded hidden layer. Learning is driven by topological plasticity rather than scalar weight adjustments. This architecture unifies auto-associative and hetero-associative learning under a single core algorithm: information retrieval via subset pattern matching and exact nearest-neighbor search. Operating with constant-time complexity, these mechanisms bridge perceptual data (sparse distributed representations) and symbols (sparse holographic representations) without continuous bottlenecks. Mapping this framework to neuroanatomy, I propose that both the cerebellum and the neocortex implement variants of this algorithm, making subset pattern matching the fundamental engine of cognition. Because it relies on discrete logic rather than matrix arithmetic, this algorithm translates directly into in-memory hardware. This opens a new route toward synthetic intelligence with human-level energy efficiency.

We investigate a relatively under-explored class of hybrid neurosymbolic models that integrate symbolic learning with neural reasoning to construct data generators meeting formal correctness criteria. In Symbolic Neural Generators (SNGs), symbolic learners examine logical specifications of feasible data from a small set of instances -- sometimes just one. Each specification in turn constrains the conditional information supplied to a neural-based generator, which rejects any instance violating the symbolic specification. Like other neurosymbolic approaches, SNG exploits the complementary strengths of symbolic and neural methods. The outcome of an SNG is a pair (H, X), where H is a symbolic description of feasible instances constructed from data, and X a set of generated new instances that satisfy the description. We introduce a semantics for such systems, based on the construction of appropriate base and fibre partially-ordered sets combined into an overall partial order. We implement an SNG combining a restricted form of Inductive Logic Programming (ILP) with a large language model (LLM) and evaluate it on early-stage drug design. Our main interest is the description and the set of potential inhibitor molecules generated by the SNG. On benchmark problems -- where drug targets are well understood -- SNG performance is statistically comparable to state-of-the-art methods. On exploratory problems with poorly understood targets, generated molecules exhibit binding affinities on par with leading clinical candidates. Experts further find the symbolic specifications useful as preliminary filters, with several generated molecules identified as viable for synthesis and wet-lab testing.

Modern Vision-Language Models (VLMs) have achieved impressive performance in various tasks, yet they often struggle with compositional reasoning, the ability to decompose and recombine concepts to solve novel problems. While neuro-symbolic approaches offer a promising direction, they are typically constrained by crisp logical execution or predefined predicates, which limit flexibility. In this work, we introduce NePTune, a neuro-symbolic framework that overcomes these limitations through a hybrid execution model that integrates the perception capabilities of foundation vision models with the compositional expressiveness of symbolic reasoning. NePTune dynamically translates natural language queries into executable Python programs that blend imperative control flow with soft logic operators capable of reasoning over VLM-generated uncertainty. Operating in a training-free manner, NePTune, with a modular design, decouples perception from reasoning, yet its differentiable operations support fine-tuning. We evaluate NePTune on multiple visual reasoning benchmarks and various domains, utilizing adversarial tests, and demonstrate a significant improvement over strong base models, as well as its effective compositional generalization and adaptation capabilities in novel environments.

Background: The field of Artificial Intelligence has undergone cyclical periods of growth and decline, known as AI summers and winters. Currently, we are in the third AI summer, characterized by significant advancements and commercialization, particularly in the integration of Symbolic AI and Sub-Symbolic AI, leading to the emergence of Neuro-Symbolic AI. Methods: The review followed the PRISMA methodology, utilizing databases such as IEEE Explore, Google Scholar, arXiv, ACM, and SpringerLink. The inclusion criteria targeted peer-reviewed papers published between 2020 and 2024. Papers were screened for relevance to Neuro-Symbolic AI, with further inclusion based on the availability of associated codebases to ensure reproducibility. Results: From an initial pool of 1,428 papers, 167 met the inclusion criteria and were analyzed in detail. The majority of research efforts are concentrated in the areas of learning and inference (63%), logic and reasoning (35%), and knowledge representation (44%). Explainability and trustworthiness are less represented (28%), with Meta-Cognition being the least explored area (5%). The review identifies significant interdisciplinary opportunities, particularly in integrating explainability and trustworthiness with other research areas. Conclusion: Neuro-Symbolic AI research has seen rapid growth since 2020, with concentrated efforts in learning and inference. Significant gaps remain in explainability, trustworthiness, and Meta-Cognition. Addressing these gaps through interdisciplinary research will be crucial for advancing the field towards more intelligent, reliable, and context-aware AI systems.

Many recent studies have found evidence for emergent reasoning capabilities in large language models (LLMs), but debate persists concerning the robustness of these capabilities, and the extent to which they depend on structured reasoning mechanisms. To shed light on these issues, we study the internal mechanisms that support abstract reasoning in LLMs. We identify an emergent symbolic architecture that implements abstract reasoning via a series of three computations. In early layers, symbol abstraction heads convert input tokens to abstract variables based on the relations between those tokens. In intermediate layers, symbolic induction heads perform sequence induction over these abstract variables. Finally, in later layers, retrieval heads predict the next token by retrieving the value associated with the predicted abstract variable. These results point toward a resolution of the longstanding debate between symbolic and neural network approaches, suggesting that emergent reasoning in neural networks depends on the emergence of symbolic mechanisms.

This paper investigates robot manipulation based on human instruction with ambiguous requests. The intent is to compensate for imperfect natural language via visual observations. Early symbolic methods, based on manually defined symbols, built modular framework consist of semantic parsing and task planning for producing sequences of actions from natural language requests. Modern connectionist methods employ deep neural networks to automatically learn visual and linguistic features and map to a sequence of low-level actions, in an endto-end fashion. These two approaches are blended to create a hybrid, modular framework: it formulates instruction following as symbolic goal learning via deep neural networks followed by task planning via symbolic planners. Connectionist and symbolic modules are bridged with Planning Domain Definition Language. The vision-and-language learning network predicts its goal representation, which is sent to a planner for producing a task-completing action sequence. For improving the flexibility of natural language, we further incorporate implicit human intents with explicit human instructions. To learn generic features for vision and language, we propose to separately pretrain vision and language encoders on scene graph parsing and semantic textual similarity tasks. Benchmarking evaluates the impacts of different components of, or options for, the vision-and-language learning model and shows the effectiveness of pretraining strategies. Manipulation experiments conducted in the simulator AI2THOR show the robustness of the framework to novel scenarios.

Neural-symbolic learning, an intersection of neural networks and symbolic reasoning, aims to blend neural networks' learning capabilities with symbolic AI's interpretability and reasoning. This paper introduces an approach designed to improve the performance of neural models in learning reasoning tasks. It achieves this by integrating Answer Set Programming (ASP) solvers and domain-specific expertise, which is an approach that diverges from traditional complex neural-symbolic models. In this paper, a shallow artificial neural network (ANN) is specifically trained to solve Sudoku puzzles with minimal training data. The model has a unique loss function that integrates losses calculated using the ASP solver outputs, effectively enhancing its training efficiency. Most notably, the model shows a significant improvement in solving Sudoku puzzles using only 12 puzzles for training and testing without hyperparameter tuning. This advancement indicates that the model's enhanced reasoning capabilities have practical applications, extending well beyond Sudoku puzzles to potentially include a variety of other domains. The code can be found on GitHub: https://github.com/Fadi2200/ASPEN.

The human brain exhibits a striking degree of functional specialization, with distinct networks supporting language, formal reasoning, reasoning about other minds, and reasoning about the physical world. Is this modular organization a fundamental principle of how intelligent systems must be built, or an evolutionary accident specific to biological brains? Here, we test whether a similar organization emerges in Large Language Models--another class of intelligent systems created through a very different optimization process. Using circuit analyses across N=46 tasks spanning four cognitive domains (language, formal reasoning, social reasoning, physical reasoning), we find that LLMs develop a modular architecture that mirrors the human brain: tasks drawing on the same network in humans recruit overlapping neurons in LLMs, whereas tasks drawing on different networks recruit distinct neurons. The convergent emergence of modularity in brains and neural networks suggests that it may be a fundamental property of intelligent systems.

Large language models (LLMs) exhibit strong general-purpose reasoning capabilities, yet they frequently hallucinate when used as world models (WMs), where strict compliance with deterministic transition rules--particularly in corner cases--is essential. In contrast, Symbolic WMs provide logical consistency but lack semantic expressivity. To bridge this gap, we propose Neuro-Symbolic Synergy (NeSyS), a framework that integrates the probabilistic semantic priors of LLMs with executable symbolic rules to achieve both expressivity and robustness. NeSyS alternates training between the two models using trajectories inadequately explained by the other. Unlike rule-based prompting, the symbolic WM directly constrains the LLM by modifying its output probability distribution. The neural WM is fine-tuned only on trajectories not covered by symbolic rules, reducing training data by 50% without loss of accuracy. Extensive experiments on three distinct interactive environments, i.e., ScienceWorld, Webshop, and Plancraft, demonstrate NeSyS's consistent advantages over baselines in both WM prediction accuracy and data efficiency.

The field of artificial intelligence has seen explosive growth and exponential success. The last phase of development showcased deep learnings ability to solve a variety of difficult problems across a multitude of domains. Many of these networks met and exceeded human benchmarks by becoming experts in the domains in which they are trained. Though the successes of artificial intelligence have begun to overshadow its failures, there is still much that separates current artificial intelligence tools from becoming the exceptional general learners that humans are. In this paper, we identify the ten commandments upon which human intelligence is systematically and hierarchically built. We believe these commandments work collectively to serve as the essential ingredients that lead to the emergence of higher-order cognition and intelligence. This paper discusses a computational framework that could house these ten commandments and suggests new architectural modifications that could lead to the development of smarter, more explainable, and generalizable artificial systems inspired by a neuromorphic approach.

Over the last decades, deep neural networks based-models became the dominant paradigm in machine learning. Further, the use of artificial neural networks in symbolic learning has been seen as increasingly relevant recently. To study the capabilities of neural networks in the symbolic AI domain, researchers have explored the ability of deep neural networks to learn mathematical constructions, such as addition and multiplication, logic inference, such as theorem provers, and even the execution of computer programs. The latter is known to be too complex a task for neural networks. Therefore, the results were not always successful, and often required the introduction of biased elements in the learning process, in addition to restricting the scope of possible programs to be executed. In this work, we will analyze the ability of neural networks to learn how to execute programs as a whole. To do so, we propose a different approach. Instead of using an imperative programming language, with complex structures, we use the Lambda Calculus (λ-Calculus), a simple, but Turing-Complete mathematical formalism, which serves as the basis for modern functional programming languages and is at the heart of computability theory. We will introduce the use of integrated neural learning and lambda calculi formalization. Finally, we explore execution of a program in λ-Calculus is based on reductions, we will show that it is enough to learn how to perform these reductions so that we can execute any program. Keywords: Machine Learning, Lambda Calculus, Neurosymbolic AI, Neural Networks, Transformer Model, Sequence-to-Sequence Models, Computational Models

Harnessing the statistical power of neural networks to perform language understanding and symbolic reasoning is difficult, when it requires executing efficient discrete operations against a large knowledge-base. In this work, we introduce a Neural Symbolic Machine, which contains (a) a neural "programmer", i.e., a sequence-to-sequence model that maps language utterances to programs and utilizes a key-variable memory to handle compositionality (b) a symbolic "computer", i.e., a Lisp interpreter that performs program execution, and helps find good programs by pruning the search space. We apply REINFORCE to directly optimize the task reward of this structured prediction problem. To train with weak supervision and improve the stability of REINFORCE, we augment it with an iterative maximum-likelihood training process. NSM outperforms the state-of-the-art on the WebQuestionsSP dataset when trained from question-answer pairs only, without requiring any feature engineering or domain-specific knowledge.

Mathematical reasoning---a core ability within human intelligence---presents some unique challenges as a domain: we do not come to understand and solve mathematical problems primarily on the back of experience and evidence, but on the basis of inferring, learning, and exploiting laws, axioms, and symbol manipulation rules. In this paper, we present a new challenge for the evaluation (and eventually the design) of neural architectures and similar system, developing a task suite of mathematics problems involving sequential questions and answers in a free-form textual input/output format. The structured nature of the mathematics domain, covering arithmetic, algebra, probability and calculus, enables the construction of training and test splits designed to clearly illuminate the capabilities and failure-modes of different architectures, as well as evaluate their ability to compose and relate knowledge and learned processes. Having described the data generation process and its potential future expansions, we conduct a comprehensive analysis of models from two broad classes of the most powerful sequence-to-sequence architectures and find notable differences in their ability to resolve mathematical problems and generalize their knowledge.

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.

We present a framework where neural models develop an AI Mother Tongue, a native symbolic language that simultaneously supports intuitive reasoning, compositional symbol chains, and inherent interpretability. Unlike post-hoc explanation methods, our approach embeds reasoning directly into the model's representations: symbols capture meaningful semantic patterns, chains trace decision paths, and gated induction mechanisms guide selective focus, yielding transparent yet flexible reasoning. We introduce complementary training objectives to enhance symbol purity and decision sparsity, and employ a sequential specialization strategy to first build broad symbolic competence and then refine intuitive judgments. Experiments on AI tasks demonstrate competitive accuracy alongside verifiable reasoning traces, showing that AI Mother Tongue can serve as a unified mechanism for interpretability, intuition, and symbolic reasoning in neural models.

Dominant programming paradigms inherit an execution model optimised for a bygone era of a single human mind instructing a local machine, leaving contemporary systems burdened with historical path dependencies. When forced to host multi-dimensional, connectionist intelligence, this brittle assembly model fractures under the weight of a profound probabilistic-symbolic impedance mismatch. While contemporary Software 3.x frameworks attempt to patch the mismatch by encasing large language models (LLMs) in increasingly complicated external harnesses, this spiralling architectural complexity only compounds the carrying cost of static code assembly. To address the cause rather than the effects, this paper introduces Software 4.0 -- an autopoietic heterarchy of human intelligence, neural AI, and natively reflective symbolic substrate. Under this paradigm, software is transformed from an inert corpus to be parsed into a self-regulating metabolic network that natively verifies, modifies, and evolves its own structural integrity. We present Recognitive, the programming language and platform that materialises this architecture. By offloading the burden of structural verification to a deterministic substrate, it unlocks a superior inference-time scaling regime -- one where connectionist compute translates entirely into deep semantic exploration and hypothesis traversal rather than the ruinous computational and financial cost of simulating structural constraints probabilistically. Moving beyond the legacy 'Software Factory' mindset, we outline the theoretical foundations required to ground connectionist intent and arrive fully in the intelligence age. This is a foundational vision paper; empirical evaluation and formal specification of the type system and operational semantics are the subject of future work.

In symbolic regression, the goal is to find an analytical expression that accurately fits experimental data with the minimal use of mathematical symbols such as operators, variables, and constants. However, the combinatorial space of possible expressions can make it challenging for traditional evolutionary algorithms to find the correct expression in a reasonable amount of time. To address this issue, Neural Symbolic Regression (NSR) algorithms have been developed that can quickly identify patterns in the data and generate analytical expressions. However, these methods, in their current form, lack the capability to incorporate user-defined prior knowledge, which is often required in natural sciences and engineering fields. To overcome this limitation, we propose a novel neural symbolic regression method, named Neural Symbolic Regression with Hypothesis (NSRwH) that enables the explicit incorporation of assumptions about the expected structure of the ground-truth expression into the prediction process. Our experiments demonstrate that the proposed conditioned deep learning model outperforms its unconditioned counterparts in terms of accuracy while also providing control over the predicted expression structure.

The development of artificial intelligence systems with advanced reasoning capabilities represents a persistent and long-standing research question. Traditionally, the primary strategy to address this challenge involved the adoption of symbolic approaches, where knowledge was explicitly represented by means of symbols and explicitly programmed rules. However, with the advent of machine learning, there has been a paradigm shift towards systems that can autonomously learn from data, requiring minimal human guidance. In light of this shift, in latest years, there has been increasing interest and efforts at endowing neural networks with the ability to reason, bridging the gap between data-driven learning and logical reasoning. Within this context, Neural Algorithmic Reasoning (NAR) stands out as a promising research field, aiming to integrate the structured and rule-based reasoning of algorithms with the adaptive learning capabilities of neural networks, typically by tasking neural models to mimic classical algorithms. In this dissertation, we provide theoretical and practical contributions to this area of research. We explore the connections between neural networks and tropical algebra, deriving powerful architectures that are aligned with algorithm execution. Furthermore, we discuss and show the ability of such neural reasoners to learn and manipulate complex algorithmic and combinatorial optimization concepts, such as the principle of strong duality. Finally, in our empirical efforts, we validate the real-world utility of NAR networks across different practical scenarios. This includes tasks as diverse as planning problems, large-scale edge classification tasks and the learning of polynomial-time approximate algorithms for NP-hard combinatorial problems. Through this exploration, we aim to showcase the potential integrating algorithmic reasoning in machine learning models.

Neural networks adapt very well to distributed and continuous representations, but struggle to generalize from small amounts of data. Symbolic systems commonly achieve data efficient generalization by exploiting modularity to benefit from local and discrete features of a representation. These features allow symbolic programs to be improved one module at a time and to experience combinatorial growth in the values they can successfully process. However, it is difficult to design a component that can be used to form symbolic abstractions and which is adequately overparametrized to learn arbitrary high-dimensional transformations. I present Graph-based Symbolically Synthesized Neural Networks (G-SSNNs), a class of neural modules that operate on representations modified with synthesized symbolic programs to include a fixed set of local and discrete features. I demonstrate that the choice of injected features within a G-SSNN module modulates the data efficiency and generalization of baseline neural models, creating predictable patterns of both heightened and curtailed generalization. By training G-SSNNs, we also derive information about desirable semantics of symbolic programs without manual engineering. This information is compact and amenable to abstraction, but can also be flexibly recontextualized for other high-dimensional settings. In future work, I will investigate data efficient generalization and the transferability of learned symbolic representations in more complex G-SSNN designs based on more complex classes of symbolic programs. Experimental code and data are available at https://github.com/shlomenu/symbolically_synthesized_networks .

Neural Architecture Search (NAS) algorithms automate the task of finding optimal deep learning architectures given an initial search space of possible operations. Developing these search spaces is usually a manual affair with pre-optimized search spaces being more efficient, rather than searching from scratch. In this paper we present a new framework called Neural Architecture Type System (NeuralArTS) that categorizes the infinite set of network operations in a structured type system. We further demonstrate how NeuralArTS can be applied to convolutional layers and propose several future directions.

Within the limited scope of this paper, we argue that artificial general intelligence cannot emerge from current neural network paradigms regardless of scale, nor is such an approach healthy for the field at present. Drawing on various notions, discussions, present-day developments and observations, current debates and critiques, experiments, and so on in between philosophy, including the Chinese Room Argument and Gödelian argument, neuroscientific ideas, computer science, the theoretical consideration of artificial intelligence, and learning theory, we address conceptually that neural networks are architecturally insufficient for genuine understanding. They operate as static function approximators of a limited encoding framework - a 'sophisticated sponge' exhibiting complex behaviours without structural richness that constitute intelligence. We critique the theoretical foundations the field relies on and created of recent times; for example, an interesting heuristic as neural scaling law (as an example, arXiv:2001.08361 ) made prominent in a wrong way of interpretation, The Universal Approximation Theorem addresses the wrong level of abstraction and, in parts, partially, the question of current architectures lacking dynamic restructuring capabilities. We propose a framework distinguishing existential facilities (computational substrate) from architectural organization (interpretive structures), and outline principles for what genuine machine intelligence would require, and furthermore, a conceptual method of structuralizing the richer framework on which the principle of neural network system takes hold.

Neural Module Networks, originally proposed for the task of visual question answering, are a class of neural network architectures that involve human-specified neural modules, each designed for a specific form of reasoning. In current formulations of such networks only the parameters of the neural modules and/or the order of their execution is learned. In this work, we further expand this approach and also learn the underlying internal structure of modules in terms of the ordering and combination of simple and elementary arithmetic operators. Our results show that one is indeed able to simultaneously learn both internal module structure and module sequencing without extra supervisory signals for module execution sequencing. With this approach, we report performance comparable to models using hand-designed modules.

Toward combining inductive reasoning with perception abilities, we develop techniques for neurosymbolic program synthesis where perceptual input is first parsed by neural nets into a low-dimensional interpretable representation, which is then processed by a synthesized program. We explore several techniques for relaxing the problem and jointly learning all modules end-to-end with gradient descent: multitask learning; amortized inference; overparameterization; and a differentiable strategy for penalizing lengthy programs. Collectedly this toolbox improves the stability of gradient-guided program search, and suggests ways of learning both how to perceive input as discrete abstractions, and how to symbolically process those abstractions as programs.

The symbolic architecture of non-ordinary consciousness remains largely unmapped in cognitive science and artificial intelligence. While conventional models prioritize rational coherence, altered states such as those induced by psychedelics reveal distinct symbolic regimes characterized by recursive metaphor, ego dissolution, and semantic destabilization. We present Glyph, a generative symbolic interface designed to simulate psilocybin-like symbolic cognition in large language models. Rather than modeling perception or mood, Glyph enacts symbolic transformation through recursive reentry, metaphoric modulation, and entropy-scaled destabilization -- a triadic operator formalized within a tensorial linguistic framework. Experimental comparison with baseline GPT-4o reveals that Glyph consistently generates high-entropy, metaphor-saturated, and ego-dissolving language across diverse symbolic prompt categories. These results validate the emergence of non-ordinary cognitive patterns and support a new paradigm for simulating altered consciousness through language. Glyph opens novel pathways for modeling symbolic cognition, exploring metaphor theory, and encoding knowledge in recursively altered semantic spaces.

What mathematical functions do neural network components learn? Symbolic distillation addresses this question by expressing neural network components with interpretable, closed-form mathematical expressions that expose the functional structure learned during training. We develop symbolic distillation as a systematic, architecture-agnostic methodology, and release our approach as the open-source SymTorch package - a PySR-powered library built natively for the PyTorch ecosystem. Applying this methodology across diverse architectures, we find that SymTorch is successful in the automated discovery of physical laws. Specifically, our approach (1) recovers pairwise interaction forces from graph neural networks trained on empirical n-body observations, (2) distills the exact closed-form PDE/ODE solutions of multiple physical systems, including the value of constants, from physics-informed neural networks trained on sparse data, and (3) uncovers the chaotic dynamics of the Lorenz system from high-dimensional data, ultimately outperforming the base neural network on downstream prediction tasks. We further demonstrate the utility of our framework for model interpretability by providing an optimized implementation of SLIME - a symbolic extension to the LIME explainability method. SLIME consistently outperforms LIME across predictive metrics across eight popular classification and regression benchmarks, while still providing an interpretable local symbolic model. Lastly, we investigate replacing transformer MLP layers with symbolic surrogates: replacing 1-7 layers with symbolic approximations yields 2-19\% throughput improvements and up to 18.7\% VRAM reduction, with the resulting hybrid models lying on the Pareto front of throughput versus perplexity among open-source LLMs of comparable scale.

The integration of knowledge extracted from diverse models, whether described by domain experts or generated by machine learning algorithms, has historically been challenged by the absence of a suitable framework for specifying and integrating structures, learning processes, data transformations, and data models or rules. In this work, we extend algebraic specification methods to address these challenges within such a framework. In our work, we tackle the challenging task of developing a comprehensive framework for defining and analyzing deep learning architectures. We believe that previous efforts have fallen short by failing to establish a clear connection between the constraints a model must adhere to and its actual implementation. Our methodology employs graphical structures that resemble Ehresmann's sketches, interpreted within a universe of fuzzy sets. This approach offers a unified theory that elegantly encompasses both deterministic and non-deterministic neural network designs. Furthermore, we highlight how this theory naturally incorporates fundamental concepts from computer science and automata theory. Our extended algebraic specification framework, grounded in graphical structures akin to Ehresmann's sketches, offers a promising solution for integrating knowledge across disparate models and domains. By bridging the gap between domain-specific expertise and machine-generated insights, we pave the way for more comprehensive, collaborative, and effective approaches to knowledge integration and modeling.

We present (Experience-Modulated Biologically-inspired Emergent Reasoning), a hybrid cognitive architecture that reorganises the relationship between large language models (LLMs) and memory: rather than augmenting an LLM with retrieval tools, we place the LLM as a replaceable reasoning engine within a persistent, biologically-grounded associative substrate. The architecture centres on a 220,000-neuron spiking neural network (SNN) with spike-timing-dependent plasticity (STDP), four-layer hierarchical organisation (sensory/concept/category/meta-pattern), inhibitory E/I balance, and reward-modulated learning. Text embeddings are encoded into the SNN via a novel z-score standardised top-k population code that is dimension-independent by construction, achieving 82.2\% discrimination retention across embedding dimensionalities. We show that STDP lateral propagation during idle operation can trigger and shape LLM actions without external prompting or scripted triggers: the SNN determines when to act and what associations to surface, while the LLM selects the action type and generates content. In one instance, the system autonomously initiated contact with a user after learned person-topic associations fired laterally during an 8-hour idle period. From a clean start with zero learned weights, the first SNN-triggered action occurred after only 7 conversational exchanges (14 messages).

There is a concerted effort to build domain-general artificial intelligence in the form of universal neural network models with sufficient computational flexibility to solve a wide variety of cognitive tasks but without requiring fine-tuning on individual problem spaces and domains. To do this, models need appropriate priors and inductive biases, such that trained models can generalise to out-of-distribution examples and new problem sets. Here we provide an overview of the hallmarks endowing biological neural networks with the functionality needed for flexible cognition, in order to establish which features might also be important to achieve similar functionality in artificial systems. We specifically discuss the role of system-level distribution of network communication and recurrence, in addition to the role of short-term topological changes for efficient local computation. As machine learning models become more complex, these principles may provide valuable directions in an otherwise vast space of possible architectures. In addition, testing these inductive biases within artificial systems may help us to understand the biological principles underlying domain-general cognition.

Artificial neural networks for motor control usually adopt generic architectures like fully connected MLPs. While general, these tabula rasa architectures rely on large amounts of experience to learn, are not easily transferable to new bodies, and have internal dynamics that are difficult to interpret. In nature, animals are born with highly structured connectivity in their nervous systems shaped by evolution; this innate circuitry acts synergistically with learning mechanisms to provide inductive biases that enable most animals to function well soon after birth and learn efficiently. Convolutional networks inspired by visual circuitry have encoded useful biases for vision. However, it is unknown the extent to which ANN architectures inspired by neural circuitry can yield useful biases for other AI domains. In this work, we ask what advantages biologically inspired ANN architecture can provide in the domain of motor control. Specifically, we translate C. elegans locomotion circuits into an ANN model controlling a simulated Swimmer agent. On a locomotion task, our architecture achieves good initial performance and asymptotic performance comparable with MLPs, while dramatically improving data efficiency and requiring orders of magnitude fewer parameters. Our architecture is interpretable and transfers to new body designs. An ablation analysis shows that constrained excitation/inhibition is crucial for learning, while weight initialization contributes to good initial performance. Our work demonstrates several advantages of biologically inspired ANN architecture and encourages future work in more complex embodied control.

Deep learning models struggle with systematic compositional generalization, a hallmark of human cognition. We propose Mirage, a neuro-inspired dual-process model that offers a processing account for this ability. It combines a fast, intuitive ``System~1'' (a meta-trained Transformer) with a deliberate, rule-based ``System~2'' (a Schema Engine), mirroring the brain's neocortical and hippocampal--prefrontal circuits. Trained to perform general, single-step decomposition on a stream of random grammars, Mirage achieves >99\% accuracy on all splits of the SCAN benchmark in a task-agnostic setting. Ablations confirm that the model's systematic behavior emerges from the architectural interplay of its two systems, particularly its use of explicit, prioritized schemas and iterative refinement. In line with recent progress on recursive/recurrent Transformer approaches, Mirage preserves an iterative neural update while externalizing declarative control into an interpretable schema module. Our work provides a concrete computational model for interpreting how compositional reasoning can arise from a modular cognitive architecture.

Test-time scaling has enabled Large Language Models (LLMs) to tackle complex reasoning, yet the limitations of current Chain-of-Thought (CoT) evaluation obscures whether performance gains stem from genuine reasoning or mere verbosity. To address this, (1) we propose a novel neuro-symbolic framework for the non-intrusive, comprehensive process-centric evaluation of reasoning. (2) Through this lens, we identify four distinct behavioral prototypes and diagnose the failure modes. (3) We examine the impact of inference mode, training strategy, and model scale. Our analysis reveals that extended token generation is not a prerequisite for deep reasoning. Furthermore, we reveal critical constraints: mixing long and short CoT data in training risks in premature saturation and collapse, while distillation into smaller models captures behavioral length but fails to replicate logical efficacy due to intrinsic capacity limits.

We present VISPROG, a neuro-symbolic approach to solving complex and compositional visual tasks given natural language instructions. VISPROG avoids the need for any task-specific training. Instead, it uses the in-context learning ability of large language models to generate python-like modular programs, which are then executed to get both the solution and a comprehensive and interpretable rationale. Each line of the generated program may invoke one of several off-the-shelf computer vision models, image processing routines, or python functions to produce intermediate outputs that may be consumed by subsequent parts of the program. We demonstrate the flexibility of VISPROG on 4 diverse tasks - compositional visual question answering, zero-shot reasoning on image pairs, factual knowledge object tagging, and language-guided image editing. We believe neuro-symbolic approaches like VISPROG are an exciting avenue to easily and effectively expand the scope of AI systems to serve the long tail of complex tasks that people may wish to perform.

In this article, we introduce a neuro-symbolic approach that combines a low-level perception task performed by a neural network with a high-level reasoning task performed by a possibilistic rule-based system. The goal is to be able to derive for each input instance the degree of possibility that it belongs to a target (meta-)concept. This (meta-)concept is connected to intermediate concepts by a possibilistic rule-based system. The probability of each intermediate concept for the input instance is inferred using a neural network. The connection between the low-level perception task and the high-level reasoning task lies in the transformation of neural network outputs modeled by probability distributions (through softmax activation) into possibility distributions. The use of intermediate concepts is valuable for the explanation purpose: using the rule-based system, the classification of an input instance as an element of the (meta-)concept can be justified by the fact that intermediate concepts have been recognized. From the technical side, our contribution consists of the design of efficient methods for defining the matrix relation and the equation system associated with a possibilistic rule-based system. The corresponding matrix and equation are key data structures used to perform inferences from a possibilistic rule-based system and to learn the values of the rule parameters in such a system according to a training data sample. Furthermore, leveraging recent results on the handling of inconsistent systems of fuzzy relational equations, an approach for learning rule parameters according to multiple training data samples is presented. Experiments carried out on the MNIST addition problems and the MNIST Sudoku puzzles problems highlight the effectiveness of our approach compared with state-of-the-art neuro-symbolic ones.

Neuro-symbolic systems aim to combine the expressive structure of symbolic logic with the flexibility of neural learning; yet, generative models typically lack mechanisms to enforce declarative constraints at generation time. We propose Logic-Guided Vector Fields (LGVF), a neuro-symbolic framework that injects symbolic knowledge, specified as differentiable relaxations of logical constraints, into flow matching generative models. LGVF couples two complementary mechanisms: (1) a training-time logic loss that penalizes constraint violations along continuous flow trajectories, with weights that emphasize correctness near the target distribution; and (2) an inference-time adjustment that steers sampling using constraint gradients, acting as a lightweight, logic-informed correction to the learned dynamics. We evaluate LGVF on three constrained generation case studies spanning linear, nonlinear, and multi-region feasibility constraints. Across all settings, LGVF reduces constraint violations by 59-82% compared to standard flow matching and achieves the lowest violation rates in each case. In the linear and ring settings, LGVF also improves distributional fidelity as measured by MMD, while in the multi-obstacle setting, we observe a satisfaction-fidelity trade-off, with improved feasibility but increased MMD. Beyond quantitative gains, LGVF yields constraint-aware vector fields exhibiting emergent obstacle-avoidance behavior, routing samples around forbidden regions without explicit path planning.

Automated neural network architecture design remains a significant challenge in computer vision. Task diversity and computational constraints require both effective architectures and efficient search methods. Large Language Models (LLMs) present a promising alternative to computationally intensive Neural Architecture Search (NAS), but their application to architecture generation in computer vision has not been systematically studied, particularly regarding prompt engineering and validation strategies. Building on the task-agnostic NNGPT/LEMUR framework, this work introduces and validates two key contributions for computer vision. First, we present Few-Shot Architecture Prompting (FSAP), the first systematic study of the number of supporting examples (n = 1, 2, 3, 4, 5, 6) for LLM-based architecture generation. We find that using n = 3 examples best balances architectural diversity and context focus for vision tasks. Second, we introduce Whitespace-Normalized Hash Validation, a lightweight deduplication method (less than 1 ms) that provides a 100x speedup over AST parsing and prevents redundant training of duplicate computer vision architectures. In large-scale experiments across seven computer vision benchmarks (MNIST, CIFAR-10, CIFAR-100, CelebA, ImageNette, SVHN, Places365), we generated 1,900 unique architectures. We also introduce a dataset-balanced evaluation methodology to address the challenge of comparing architectures across heterogeneous vision tasks. These contributions provide actionable guidelines for LLM-based architecture search in computer vision and establish rigorous evaluation practices, making automated design more accessible to researchers with limited computational resources.

Can machines truly think, reason and act in domains like humans? This enduring question continues to shape the pursuit of Artificial General Intelligence (AGI). Despite the growing capabilities of models such as GPT-4.5, DeepSeek, Claude 3.5 Sonnet, Phi-4, and Grok 3, which exhibit multimodal fluency and partial reasoning, these systems remain fundamentally limited by their reliance on token-level prediction and lack of grounded agency. This paper offers a cross-disciplinary synthesis of AGI development, spanning artificial intelligence, cognitive neuroscience, psychology, generative models, and agent-based systems. We analyze the architectural and cognitive foundations of general intelligence, highlighting the role of modular reasoning, persistent memory, and multi-agent coordination. In particular, we emphasize the rise of Agentic RAG frameworks that combine retrieval, planning, and dynamic tool use to enable more adaptive behavior. We discuss generalization strategies, including information compression, test-time adaptation, and training-free methods, as critical pathways toward flexible, domain-agnostic intelligence. Vision-Language Models (VLMs) are reexamined not just as perception modules but as evolving interfaces for embodied understanding and collaborative task completion. We also argue that true intelligence arises not from scale alone but from the integration of memory and reasoning: an orchestration of modular, interactive, and self-improving components where compression enables adaptive behavior. Drawing on advances in neurosymbolic systems, reinforcement learning, and cognitive scaffolding, we explore how recent architectures begin to bridge the gap between statistical learning and goal-directed cognition. Finally, we identify key scientific, technical, and ethical challenges on the path to AGI.

The informational synthesis of neural structures, processes, parameters and characteristics that allow a unified description and modeling as neural machines of natural and artificial neural systems is presented. The general informational parameters as the global quantitative measure of the neural systems computing potential as absolute and relative neural power were proposed. Neural information organizing and processing follows the way in which nature manages neural information by developing functions, functionalities and circuits related to different internal or peripheral components and also to the whole system through a non-deterministic memorization, fragmentation and aggregation of afferent and efferent information, deep neural information processing representing multiple alternations of fragmentation and aggregation stages. The relevant neural characteristics were integrated into a neural machine type model that incorporates unitary also peripheral or interface components as the central ones. The proposed approach allows overcoming the technical constraints in artificial computational implementations of neural information processes and also provides a more relevant description of natural ones.

Modern AI architectures used to solve visual reasoning tasks typically rely heavily on global connectivity and synchronization. As biological systems demonstrate, though, sophisticated computation can be performed in a more decentralized fashion. In this work, we test the reasoning capabilities of Neural Cellular Automata (NCAs), networks of recurrent cells that use strictly local connectivity and asynchronous updates. NCAs have been extensively studied in artificial life experiments, but it is unclear whether they can perform complex multi-step reasoning. We show that NCAs produce spatio-temporal dynamics capable of solving challenging visual reasoning tasks, including large mazes, Sudoku, and ARC-AGI-1. Furthermore, we provide evidence that NCAs generalize out-of-distribution when running with larger grids, longer rollouts, or parallel trials; and that the latter can be made more efficient via pruning of redundant trajectories. We find that these generalization capabilities depend on training with sample replay and stochastic perturbations, and that stochasticity remains beneficial at test time. Finally, we show that NCAs are robust reasoners capable of dynamically modulating compute to recover efficiently from damage, and that they can scale to solve reasoning in raw pixel space.

Visual reasoning, particularly spatial reasoning, is a challenging cognitive task that requires understanding object relationships and their interactions within complex environments, especially in robotics domain. Existing vision_language models (VLMs) excel at perception tasks but struggle with fine-grained spatial reasoning due to their implicit, correlation-driven reasoning and reliance solely on images. We propose a novel neuro_symbolic framework that integrates both panoramic-image and 3D point cloud information, combining neural perception with symbolic reasoning to explicitly model spatial and logical relationships. Our framework consists of a perception module for detecting entities and extracting attributes, and a reasoning module that constructs a structured scene graph to support precise, interpretable queries. Evaluated on the JRDB-Reasoning dataset, our approach demonstrates superior performance and reliability in crowded, human_built environments while maintaining a lightweight design suitable for robotics and embodied AI applications.

Compositionality is a pivotal property of symbolic reasoning. However, how well recent neural models capture compositionality remains underexplored in the symbolic reasoning tasks. This study empirically addresses this question by systematically examining recently published pre-trained seq2seq models with a carefully controlled dataset of multi-hop arithmetic symbolic reasoning. We introduce a skill tree on compositionality in arithmetic symbolic reasoning that defines the hierarchical levels of complexity along with three compositionality dimensions: systematicity, productivity, and substitutivity. Our experiments revealed that among the three types of composition, the models struggled most with systematicity, performing poorly even with relatively simple compositions. That difficulty was not resolved even after training the models with intermediate reasoning steps.

Lane topology extraction involves detecting lanes and traffic elements and determining their relationships, a key perception task for mapless autonomous driving. This task requires complex reasoning, such as determining whether it is possible to turn left into a specific lane. To address this challenge, we introduce neuro-symbolic methods powered by vision-language foundation models (VLMs). Existing approaches have notable limitations: (1) Dense visual prompting with VLMs can achieve strong performance but is costly in terms of both financial resources and carbon footprint, making it impractical for robotics applications. (2) Neuro-symbolic reasoning methods for 3D scene understanding fail to integrate visual inputs when synthesizing programs, making them ineffective in handling complex corner cases. To this end, we propose a fast-slow neuro-symbolic lane topology extraction algorithm, named Chameleon, which alternates between a fast system that directly reasons over detected instances using synthesized programs and a slow system that utilizes a VLM with a chain-of-thought design to handle corner cases. Chameleon leverages the strengths of both approaches, providing an affordable solution while maintaining high performance. We evaluate the method on the OpenLane-V2 dataset, showing consistent improvements across various baseline detectors. Our code, data, and models are publicly available at https://github.com/XR-Lee/neural-symbolic

Neural architecture search (NAS) finds high performing networks for a given task. Yet the results of NAS are fairly prosaic; they did not e.g. create a shift from convolutional structures to transformers. This is not least because the search spaces in NAS often aren't diverse enough to include such transformations a priori. Instead, for NAS to provide greater potential for fundamental design shifts, we need a novel expressive search space design which is built from more fundamental operations. To this end, we introduce einspace, a search space based on a parameterised probabilistic context-free grammar. Our space is versatile, supporting architectures of various sizes and complexities, while also containing diverse network operations which allow it to model convolutions, attention components and more. It contains many existing competitive architectures, and provides flexibility for discovering new ones. Using this search space, we perform experiments to find novel architectures as well as improvements on existing ones on the diverse Unseen NAS datasets. We show that competitive architectures can be obtained by searching from scratch, and we consistently find large improvements when initialising the search with strong baselines. We believe that this work is an important advancement towards a transformative NAS paradigm where search space expressivity and strategic search initialisation play key roles.

The structure of biological neural circuits-modular, hierarchical, and sparsely interconnected-reflects an efficient trade-off between wiring cost, functional specialization, and robustness. These principles offer valuable insights for artificial neural network (ANN) design, especially as networks grow in depth and scale. Sparsity, in particular, has been widely explored for reducing memory and computation, improving speed, and enhancing generalization. Motivated by systems neuroscience findings, we explore how patterns of functional connectivity in the mouse visual cortex-specifically, ensemble-to-ensemble communication, can inform ANN design. We introduce G2GNet, a novel architecture that imposes sparse, modular connectivity across feedforward layers. Despite having significantly fewer parameters than fully connected models, G2GNet achieves superior accuracy on standard vision benchmarks. To our knowledge, this is the first architecture to incorporate biologically observed functional connectivity patterns as a structural bias in ANN design. We complement this static bias with a dynamic sparse training (DST) mechanism that prunes and regrows edges during training. We also propose a Hebbian-inspired rewiring rule based on activation correlations, drawing on principles of biological plasticity. G2GNet achieves up to 75% sparsity while improving accuracy by up to 4.3% on benchmarks, including Fashion-MNIST, CIFAR-10, and CIFAR-100, outperforming dense baselines with far fewer computations.

Scaling robot learning to long-horizon tasks remains a formidable challenge. While end-to-end policies often lack the structural priors needed for effective long-term reasoning, traditional neuro-symbolic methods rely heavily on hand-crafted symbolic priors. To address the issue, we introduce ENAP (Emergent Neural Automaton Policy), a framework that allows a bi-level neuro-symbolic policy adaptively emerge from visuomotor demonstrations. Specifically, we first employ adaptive clustering and an extension of the L* algorithm to infer a Mealy state machine from visuomotor data, which serves as an interpretable high-level planner capturing latent task modes. Then, this discrete structure guides a low-level reactive residual network to learn precise continuous control via behavior cloning (BC). By explicitly modeling the task structure with discrete transitions and continuous residuals, ENAP achieves high sample efficiency and interpretability without requiring task-specific labels. Extensive experiments on complex manipulation and long-horizon tasks demonstrate that ENAP outperforms state-of-the-art (SoTA) end-to-end VLA policies by up to 27% in low-data regimes, while offering a structured representation of robotic intent (Fig. 1).

Recent years have seen an increasing amount of work on embodied AI agents that can perform tasks by following human language instructions. However, most of these agents are reactive, meaning that they simply learn and imitate behaviors encountered in the training data. These reactive agents are insufficient for long-horizon complex tasks. To address this limitation, we propose a neuro-symbolic deliberative agent that, while following language instructions, proactively applies reasoning and planning based on its neural and symbolic representations acquired from past experience (e.g., natural language and egocentric vision). We show that our deliberative agent achieves greater than 70% improvement over reactive baselines on the challenging TEACh benchmark. Moreover, the underlying reasoning and planning processes, together with our modular framework, offer impressive transparency and explainability to the behaviors of the agent. This enables an in-depth understanding of the agent's capabilities, which shed light on challenges and opportunities for future embodied agents for instruction following. The code is available at https://github.com/sled-group/DANLI.

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.

Designing machine learning architectures for processing neural networks in their raw weight matrix form is a newly introduced research direction. Unfortunately, the unique symmetry structure of deep weight spaces makes this design very challenging. If successful, such architectures would be capable of performing a wide range of intriguing tasks, from adapting a pre-trained network to a new domain to editing objects represented as functions (INRs or NeRFs). As a first step towards this goal, we present here a novel network architecture for learning in deep weight spaces. It takes as input a concatenation of weights and biases of a pre-trained MLP and processes it using a composition of layers that are equivariant to the natural permutation symmetry of the MLP's weights: Changing the order of neurons in intermediate layers of the MLP does not affect the function it represents. We provide a full characterization of all affine equivariant and invariant layers for these symmetries and show how these layers can be implemented using three basic operations: pooling, broadcasting, and fully connected layers applied to the input in an appropriate manner. We demonstrate the effectiveness of our architecture and its advantages over natural baselines in a variety of learning tasks.

The article identified 42 cognitive architectures for creating general artificial intelligence (AGI) and proposed a set of interrelated functional blocks that an agent approaching AGI in its capabilities should possess. Since the required set of blocks is not found in any of the existing architectures, the article proposes a new cognitive architecture for intelligent systems approaching AGI in their capabilities. As one of the key solutions within the framework of the architecture, a universal method of knowledge representation is proposed, which allows combining various non-formalized, partially and fully formalized methods of knowledge representation in a single knowledge base, such as texts in natural languages, images, audio and video recordings, graphs, algorithms, databases, neural networks, knowledge graphs, ontologies, frames, essence-property-relation models, production systems, predicate calculus models, conceptual models, and others. To combine and structure various fragments of knowledge, archigraph models are used, constructed as a development of annotated metagraphs. As components, the cognitive architecture being developed includes machine consciousness, machine subconsciousness, blocks of interaction with the external environment, a goal management block, an emotional control system, a block of social interaction, a block of reflection, an ethics block and a worldview block, a learning block, a monitoring block, blocks of statement and solving problems, self-organization and meta learning block.

We propose the Neuro-Symbolic Concept Learner (NS-CL), a model that learns visual concepts, words, and semantic parsing of sentences without explicit supervision on any of them; instead, our model learns by simply looking at images and reading paired questions and answers. Our model builds an object-based scene representation and translates sentences into executable, symbolic programs. To bridge the learning of two modules, we use a neuro-symbolic reasoning module that executes these programs on the latent scene representation. Analogical to human concept learning, the perception module learns visual concepts based on the language description of the object being referred to. Meanwhile, the learned visual concepts facilitate learning new words and parsing new sentences. We use curriculum learning to guide the searching over the large compositional space of images and language. Extensive experiments demonstrate the accuracy and efficiency of our model on learning visual concepts, word representations, and semantic parsing of sentences. Further, our method allows easy generalization to new object attributes, compositions, language concepts, scenes and questions, and even new program domains. It also empowers applications including visual question answering and bidirectional image-text retrieval.

We present the COGnitive Neural GENerative system (CogNGen), a cognitive architecture that combines two neurobiologically-plausible, computational models: predictive processing and hyperdimensional/vector-symbolic models. We draw inspiration from architectures such as ACT-R and Spaun/Nengo. CogNGen is in broad agreement with these, providing a level of detail between ACT-R's high-level symbolic description of human cognition and Spaun's low-level neurobiological description, furthermore creating the groundwork for designing agents that learn continually from diverse tasks and model human performance at larger scales than what is possible with current systems. We test CogNGen on four maze-learning tasks, including those that test memory and planning, and find that CogNGen matches performance of deep reinforcement learning models and exceeds on a task designed to test memory.

Cortical neurons are complex, multi-timescale processors wired into recurrent circuits, shaped by long evolutionary pressure under stringent biological constraints. Mainstream machine learning, by contrast, predominantly builds models from extremely simple units, a default inherited from early neural-network theory. We treat this as a normative architectural question. How should one split a fixed parameter budget P between the number of units N, per-unit effective complexity k_e, and per-unit connectivity k_c? What controls the optimal allocation? This calls for a model in which per-unit complexity can be tuned independently of width and connectivity. Accordingly, we introduce the ELM Network, whose recurrent layer is built from Expressive Leaky Memory (ELM) neurons, chosen to mirror functional components of cortical neurons. The architecture allows for individually adjusting N, k_e, and k_c and trains stably across orders of magnitude in scale. We evaluate the model on two qualitatively different sequence benchmarks: the neuromorphic SHD-Adding task and Enwik8 character-level language modeling. Performance improves monotonically along each of the three axes individually. Under a fixed budget, a clear non-trivial optimum emerges in their tradeoff, and larger budgets favor both more and more complex neurons. A closed-form information-theoretic model captures these tradeoffs and attributes the diminishing returns at two ends to: per-neuron signal-to-noise saturation and across-neuron redundancy. A hyperparameter sweep spanning three orders of magnitude in trainable parameters traces a near-Pareto-frontier scaling law consistent with the framework. This suggests that the simple-unit default in ML is not obviously optimal once this tradeoff surface is probed, and offers a normative lens on cortex's reliance on complex spatio-temporal integrators.

With the increasing number of new neural architecture designs and substantial existing neural architectures, it becomes difficult for the researchers to situate their contributions compared with existing neural architectures or establish the connections between their designs and other relevant ones. To discover similar neural architectures in an efficient and automatic manner, we define a new problem Neural Architecture Retrieval which retrieves a set of existing neural architectures which have similar designs to the query neural architecture. Existing graph pre-training strategies cannot address the computational graph in neural architectures due to the graph size and motifs. To fulfill this potential, we propose to divide the graph into motifs which are used to rebuild the macro graph to tackle these issues, and introduce multi-level contrastive learning to achieve accurate graph representation learning. Extensive evaluations on both human-designed and synthesized neural architectures demonstrate the superiority of our algorithm. Such a dataset which contains 12k real-world network architectures, as well as their embedding, is built for neural architecture retrieval.

Humans leverage compositionality to efficiently learn new concepts, understanding how familiar parts can combine together to form novel objects. In contrast, popular computer vision models struggle to make the same types of inferences, requiring more data and generalizing less flexibly than people do. Here, we study these distinctively human abilities across a range of different types of visual composition, examining how people classify and generate ``alien figures'' with rich relational structure. We also develop a Bayesian program induction model which searches for the best programs for generating the candidate visual figures, utilizing a large program space containing different compositional mechanisms and abstractions. In few shot classification tasks, we find that people and the program induction model can make a range of meaningful compositional generalizations, with the model providing a strong account of the experimental data as well as interpretable parameters that reveal human assumptions about the factors invariant to category membership (here, to rotation and changing part attachment). In few shot generation tasks, both people and the models are able to construct compelling novel examples, with people behaving in additional structured ways beyond the model capabilities, e.g. making choices that complete a set or reconfiguring existing parts in highly novel ways. To capture these additional behavioral patterns, we develop an alternative model based on neuro-symbolic program induction: this model also composes new concepts from existing parts yet, distinctively, it utilizes neural network modules to successfully capture residual statistical structure. Together, our behavioral and computational findings show how people and models can produce a rich variety of compositional behavior when classifying and generating visual objects.

The notion of equality (identity) is simple and ubiquitous, making it a key case study for broader questions about the representations supporting abstract relational reasoning. Previous work suggested that neural networks were not suitable models of human relational reasoning because they could not represent mathematically identity, the most basic form of equality. We revisit this question. In our experiments, we assess out-of-sample generalization of equality using both arbitrary representations and representations that have been pretrained on separate tasks to imbue them with structure. We find neural networks are able to learn (1) basic equality (mathematical identity), (2) sequential equality problems (learning ABA-patterned sequences) with only positive training instances, and (3) a complex, hierarchical equality problem with only basic equality training instances ("zero-shot'" generalization). In the two latter cases, our models perform tasks proposed in previous work to demarcate human-unique symbolic abilities. These results suggest that essential aspects of symbolic reasoning can emerge from data-driven, non-symbolic learning processes.

Transformer architectures have revolutionized artificial intelligence (AI) through their attention mechanisms, yet the computational principles underlying their success remain opaque. We present a novel theoretical framework that reinterprets the core computation of attention as Pavlovian conditioning. Our model finds a direct mathematical analogue in linear attention, which simplifies the analysis of the underlying associative process. We demonstrate that attention's queries, keys, and values can be mapped to the three elements of classical conditioning: test stimuli that probe associations, conditional stimuli (CS) that serve as retrieval cues, and unconditional stimuli (US) that contain response information. Through this lens, we suggest that each attention operation constructs a transient associative memory via a Hebbian rule, where CS-US pairs form dynamic associations that test stimuli can later retrieve. Our framework yields several theoretical insights grounded in this linearized model: (1) a capacity theorem showing that attention heads can store O(d_k) associations before interference degrades retrieval; (2) an error propagation analysis revealing fundamental architectural trade-offs of balancing model depth, width, and head redundancy to maintain reliability; and (3) an understanding of how biologically plausible learning rules could enhance transformer architectures. By establishing this deep connection, we suggest that the success of modern AI may stem not from architectural novelty alone, but from implementing computational principles that biology optimized over millions of years of evolution.

We propose the Neural Logic Machine (NLM), a neural-symbolic architecture for both inductive learning and logic reasoning. NLMs exploit the power of both neural networks---as function approximators, and logic programming---as a symbolic processor for objects with properties, relations, logic connectives, and quantifiers. After being trained on small-scale tasks (such as sorting short arrays), NLMs can recover lifted rules, and generalize to large-scale tasks (such as sorting longer arrays). In our experiments, NLMs achieve perfect generalization in a number of tasks, from relational reasoning tasks on the family tree and general graphs, to decision making tasks including sorting arrays, finding shortest paths, and playing the blocks world. Most of these tasks are hard to accomplish for neural networks or inductive logic programming alone.

Major advancements in the capabilities of computer vision models have been primarily fueled by rapid expansion of datasets, model parameters, and computational budgets, leading to ever-increasing demands on computational infrastructure. However, as these models are deployed in increasingly diverse and resource-constrained environments, there is a pressing need for architectures that can deliver high performance while requiring fewer computational resources. This dissertation focuses on architectural principles through which models can achieve increased performance while reducing their computational demands. We discuss strides towards this goal through three directions. First, we focus on data ingress and egress, investigating how information may be passed into and retrieved from our core neural processing units. This ensures that our models make the most of available data, allowing smaller architectures to become more performant. Second, we investigate modifications to the core neural architecture, applied to restricted attention in vision transformers. This section explores how removing uniform context windows in restricted attention increases the expressivity of the underlying neural architecture. Third, we explore the natural structures of Normalizing Flows and how we can leverage these properties to better distill model knowledge. These contributions demonstrate that careful design of neural architectures can increase the efficiency of machine learning algorithms, allowing them to become smaller, faster, and cheaper.

The rapid evolution of artificial intelligence (AI) has shifted from static, data-driven models to dynamic systems capable of perceiving and interacting with real-world environments. Despite advancements in pattern recognition and symbolic reasoning, current AI systems, such as large language models, remain disembodied, unable to physically engage with the world. This limitation has driven the rise of embodied AI, where autonomous agents, such as humanoid robots, must navigate and manipulate unstructured environments with human-like adaptability. At the core of this challenge lies the concept of Neural Brain, a central intelligence system designed to drive embodied agents with human-like adaptability. A Neural Brain must seamlessly integrate multimodal sensing and perception with cognitive capabilities. Achieving this also requires an adaptive memory system and energy-efficient hardware-software co-design, enabling real-time action in dynamic environments. This paper introduces a unified framework for the Neural Brain of embodied agents, addressing two fundamental challenges: (1) defining the core components of Neural Brain and (2) bridging the gap between static AI models and the dynamic adaptability required for real-world deployment. To this end, we propose a biologically inspired architecture that integrates multimodal active sensing, perception-cognition-action function, neuroplasticity-based memory storage and updating, and neuromorphic hardware/software optimization. Furthermore, we also review the latest research on embodied agents across these four aspects and analyze the gap between current AI systems and human intelligence. By synthesizing insights from neuroscience, we outline a roadmap towards the development of generalizable, autonomous agents capable of human-level intelligence in real-world scenarios.

The synergy between symbolic knowledge, often represented by Knowledge Graphs (KGs), and the generative capabilities of neural networks is central to advancing neurosymbolic AI. A primary bottleneck in realizing this potential is the difficulty of automating KG construction, which faces challenges related to output reliability, consistency, and verifiability. These issues can manifest as structural inconsistencies within the generated graphs, such as the formation of disconnected isolated islands of data or the inaccurate conflation of abstract classes with specific instances. To address these challenges, we propose HyDRA, a Hybrid-Driven Reasoning Architecture designed for verifiable KG automation. Given a domain or an initial set of documents, HyDRA first constructs an ontology via a panel of collaborative neurosymbolic agents. These agents collaboratively agree on a set of competency questions (CQs) that define the scope and requirements the ontology must be able to answer. Given these CQs, we build an ontology graph that subsequently guides the automated extraction of triplets for KG generation from arbitrary documents. Inspired by design-by-contracts (DbC) principles, our method leverages verifiable contracts as the primary control mechanism to steer the generative process of Large Language Models (LLMs). To verify the output of our approach, we extend beyond standard benchmarks and propose an evaluation framework that assesses the functional correctness of the resulting KG by leveraging symbolic verifications as described by the neurosymbolic AI framework, SymbolicAI. This work contributes a hybrid-driven architecture for improving the reliability of automated KG construction and the exploration of evaluation methods for measuring the functional integrity of its output. The code is publicly available.

Mental rotation -- the ability to compare objects seen from different viewpoints -- is a fundamental example of mental simulation and spatial world modelling in humans. Here we propose a mechanistic model of human mental rotation, leveraging advances in deep, equivariant, and neuro-symbolic learning. Our model consists of three stacked components: (1) an equivariant neural encoder, taking images as input and producing 3D spatial representations of objects, (2) a neuro-symbolic object encoder, deriving symbolic descriptions of objects from these spatial representations, and (3) a neural decision agent, comparing these symbolic descriptions to prescribe rotation simulations in 3D latent space via a recurrent pathway. Our model design is guided by the abundant experimental literature on mental rotation, which we complemented with experiments in VR where participants could at times manipulate the objects to compare, providing us with additional insights into the cognitive process of mental rotation. Our model captures well the performance, response times and behavior of participants in our and others' experiments. The necessity of each model component is shown through systematic ablations. Our work adds to a recent collection of deep neural models of human spatial reasoning, further demonstrating the potency of integrating deep, equivariant, and symbolic representations to model the human mind.

The latest Deep Learning (DL) models for detection and classification have achieved an unprecedented performance over classical machine learning algorithms. However, DL models are black-box methods hard to debug, interpret, and certify. DL alone cannot provide explanations that can be validated by a non technical audience. In contrast, symbolic AI systems that convert concepts into rules or symbols -- such as knowledge graphs -- are easier to explain. However, they present lower generalisation and scaling capabilities. A very important challenge is to fuse DL representations with expert knowledge. One way to address this challenge, as well as the performance-explainability trade-off is by leveraging the best of both streams without obviating domain expert knowledge. We tackle such problem by considering the symbolic knowledge is expressed in form of a domain expert knowledge graph. We present the eXplainable Neural-symbolic learning (X-NeSyL) methodology, designed to learn both symbolic and deep representations, together with an explainability metric to assess the level of alignment of machine and human expert explanations. The ultimate objective is to fuse DL representations with expert domain knowledge during the learning process to serve as a sound basis for explainability. X-NeSyL methodology involves the concrete use of two notions of explanation at inference and training time respectively: 1) EXPLANet: Expert-aligned eXplainable Part-based cLAssifier NETwork Architecture, a compositional CNN that makes use of symbolic representations, and 2) SHAP-Backprop, an explainable AI-informed training procedure that guides the DL process to align with such symbolic representations in form of knowledge graphs. We showcase X-NeSyL methodology using MonuMAI dataset for monument facade image classification, and demonstrate that our approach improves explainability and performance.

We present a neuro-symbolic (NeSy) workflow combining a symbolic-based learning technique with a large language model (LLM) agent to generate synthetic data for code comment classification in the C programming language. We also show how generating controlled synthetic data using this workflow fixes some of the notable weaknesses of LLM-based generation and increases the performance of classical machine learning models on the code comment classification task. Our best model, a Neural Network, achieves a Macro-F1 score of 91.412% with an increase of 1.033% after data augmentation.

One of the primary driving forces contributing to the superior performance of Large Language Models (LLMs) is the extensive availability of human-annotated natural language data, which is used for alignment fine-tuning. This inspired researchers to investigate self-training methods to mitigate the extensive reliance on human annotations. However, the current success of self-training has been primarily observed in natural language scenarios, rather than in the increasingly important neural-symbolic scenarios. To this end, we propose an environment-guided neural-symbolic self-training framework named ENVISIONS. It aims to overcome two main challenges: (1) the scarcity of symbolic data, and (2) the limited proficiency of LLMs in processing symbolic language. Extensive evaluations conducted on three distinct domains demonstrate the effectiveness of our approach. Additionally, we have conducted a comprehensive analysis to uncover the factors contributing to ENVISIONS's success, thereby offering valuable insights for future research in this area. Code will be available at https://github.com/xufangzhi/ENVISIONS.

Compositional generalization is crucial for artificial intelligence agents to solve complex vision-language reasoning tasks. Neuro-symbolic approaches have demonstrated promise in capturing compositional structures, but they face critical challenges: (a) reliance on predefined predicates for symbolic representations that limit adaptability, (b) difficulty in extracting predicates from raw data, and (c) using non-differentiable operations for combining primitive concepts. To address these issues, we propose NeSyCoCo, a neuro-symbolic framework that leverages large language models (LLMs) to generate symbolic representations and map them to differentiable neural computations. NeSyCoCo introduces three innovations: (a) augmenting natural language inputs with dependency structures to enhance the alignment with symbolic representations, (b) employing distributed word representations to link diverse, linguistically motivated logical predicates to neural modules, and (c) using the soft composition of normalized predicate scores to align symbolic and differentiable reasoning. Our framework achieves state-of-the-art results on the ReaSCAN and CLEVR-CoGenT compositional generalization benchmarks and demonstrates robust performance with novel concepts in the CLEVR-SYN benchmark.

Large Language Models (LLMs) display striking surface fluency yet systematically fail at tasks requiring symbolic reasoning, arithmetic accuracy, and logical consistency. This paper offers a structural diagnosis of such failures, revealing a persistent gap between comprehension and competence. Through controlled experiments and architectural analysis, we demonstrate that LLMs often articulate correct principles without reliably applying them--a failure rooted not in knowledge access, but in computational execution. We term this phenomenon the computational split-brain syndrome, where instruction and action pathways are geometrically and functionally dissociated. This core limitation recurs across domains, from mathematical operations to relational inferences, and explains why model behavior remains brittle even under idealized prompting. We argue that LLMs function as powerful pattern completion engines, but lack the architectural scaffolding for principled, compositional reasoning. Our findings delineate the boundary of current LLM capabilities and motivate future models with metacognitive control, principle lifting, and structurally grounded execution. This diagnosis also clarifies why mechanistic interpretability findings may reflect training-specific pattern coordination rather than universal computational principles, and why the geometric separation between instruction and execution pathways suggests limitations in neural introspection and mechanistic analysis.

Recent works have shown that Large Language Models (LLMs) could empower traditional neuro-symbolic models via programming capabilities to translate language into module descriptions, thus achieving strong visual reasoning results while maintaining the model's transparency and efficiency. However, these models usually exhaustively generate the entire code snippet given each new instance of a task, which is extremely ineffective. We propose generative neuro-symbolic visual reasoning by growing and reusing modules. Specifically, our model consists of three unique stages, module initialization, module generation, and module execution. First, given a vision-language task, we adopt LLMs to examine whether we could reuse and grow over established modules to handle this new task. If not, we initialize a new module needed by the task and specify the inputs and outputs of this new module. After that, the new module is created by querying LLMs to generate corresponding code snippets that match the requirements. In order to get a better sense of the new module's ability, we treat few-shot training examples as test cases to see if our new module could pass these cases. If yes, the new module is added to the module library for future reuse. Finally, we evaluate the performance of our model on the testing set by executing the parsed programs with the newly made visual modules to get the results. We find the proposed model possesses several advantages. First, it performs competitively on standard tasks like visual question answering and referring expression comprehension; Second, the modules learned from one task can be seamlessly transferred to new tasks; Last but not least, it is able to adapt to new visual reasoning tasks by observing a few training examples and reusing modules.

Neural networks have a reputation for being better at solving statistical or approximate problems than at performing calculations or working with symbolic data. In this paper, we show that they can be surprisingly good at more elaborated tasks in mathematics, such as symbolic integration and solving differential equations. We propose a syntax for representing mathematical problems, and methods for generating large datasets that can be used to train sequence-to-sequence models. We achieve results that outperform commercial Computer Algebra Systems such as Matlab or Mathematica.

Large language models (LLMs) with memory are computationally universal. However, mainstream LLMs are not taking full advantage of memory, and the designs are heavily influenced by biological brains. Due to their approximate nature and proneness to the accumulation of errors, conventional neural memory mechanisms cannot support LLMs to simulate complex reasoning. In this paper, we seek inspiration from modern computer architectures to augment LLMs with symbolic memory for complex multi-hop reasoning. Such a symbolic memory framework is instantiated as an LLM and a set of SQL databases, where the LLM generates SQL instructions to manipulate the SQL databases. We validate the effectiveness of the proposed memory framework on a synthetic dataset requiring complex reasoning. The project website is available at https://chatdatabase.github.io/ .

The multi-modal nature of many vision problems calls for neural network architectures that can perform multiple tasks concurrently. Typically, such architectures have been handcrafted in the literature. However, given the size and complexity of the problem, this manual architecture exploration likely exceeds human design abilities. In this paper, we propose a principled approach, rooted in differentiable neural architecture search, to automatically define branching (tree-like) structures in the encoding stage of a multi-task neural network. To allow flexibility within resource-constrained environments, we introduce a proxyless, resource-aware loss that dynamically controls the model size. Evaluations across a variety of dense prediction tasks show that our approach consistently finds high-performing branching structures within limited resource budgets.

Neural networks for image recognition have evolved through extensive manual design from simple chain-like models to structures with multiple wiring paths. The success of ResNets and DenseNets is due in large part to their innovative wiring plans. Now, neural architecture search (NAS) studies are exploring the joint optimization of wiring and operation types, however, the space of possible wirings is constrained and still driven by manual design despite being searched. In this paper, we explore a more diverse set of connectivity patterns through the lens of randomly wired neural networks. To do this, we first define the concept of a stochastic network generator that encapsulates the entire network generation process. Encapsulation provides a unified view of NAS and randomly wired networks. Then, we use three classical random graph models to generate randomly wired graphs for networks. The results are surprising: several variants of these random generators yield network instances that have competitive accuracy on the ImageNet benchmark. These results suggest that new efforts focusing on designing better network generators may lead to new breakthroughs by exploring less constrained search spaces with more room for novel design.

Understanding how complex cognitive functions are organized within artificial systems is central to interpreting large language models (LLMs) and relating them to biological cognition. Yet although LLMs exhibit broad cognitive-like behaviours, it remains unclear whether their internal representations form reproducible functional systems that explain behaviour, failure and links to human cognition. Here we present NeuroCogMap, a cognitive neuroscience-inspired framework that organizes internal features of LLMs into functional parcels and links them to interpretable functions, cognitive capabilities and a cognitive hierarchy. These parcels form a stable and semantically coherent organization that is partly conserved across models and functionally linked to model outputs. Within this organization, major LLM failures, including hallucination, bias, refusal failure and sycophancy, correspond to distinct disruptions in representational and behavioural-control systems, yielding internal signatures for mechanism-guided detection and targeted intervention. Beyond model behaviour, NeuroCogMap improves prediction of human cortical responses during naturalistic language comprehension, with the strongest correspondence in higher-order association cortex. At the cognitive level, its internal signatures expose latent strategies that guide refinements of classical models of human decision-making. Together, these findings establish NeuroCogMap as a system-level framework for mapping functional organization in artificial systems and for relating this organization to human cortical function and cognitive behaviour.

Ablation studies have been widely used in the field of neuroscience to tackle complex biological systems such as the extensively studied Drosophila central nervous system, the vertebrate brain and more interestingly and most delicately, the human brain. In the past, these kinds of studies were utilized to uncover structure and organization in the brain, i.e. a mapping of features inherent to external stimuli onto different areas of the neocortex. considering the growth in size and complexity of state-of-the-art artificial neural networks (ANNs) and the corresponding growth in complexity of the tasks that are tackled by these networks, the question arises whether ablation studies may be used to investigate these networks for a similar organization of their inner representations. In this paper, we address this question and performed two ablation studies in two fundamentally different ANNs to investigate their inner representations of two well-known benchmark datasets from the computer vision domain. We found that features distinct to the local and global structure of the data are selectively represented in specific parts of the network. Furthermore, some of these representations are redundant, awarding the network a certain robustness to structural damages. We further determined the importance of specific parts of the network for the classification task solely based on the weight structure of single units. Finally, we examined the ability of damaged networks to recover from the consequences of ablations by means of recovery training. We argue that ablations studies are a feasible method to investigate knowledge representations in ANNs and are especially helpful to examine a networks robustness to structural damages, a feature of ANNs that will become increasingly important for future safety-critical applications.

In the past decade, advances in deep learning have resulted in breakthroughs in a variety of areas, including computer vision, natural language understanding, speech recognition, and reinforcement learning. Specialized, high-performing neural architectures are crucial to the success of deep learning in these areas. Neural architecture search (NAS), the process of automating the design of neural architectures for a given task, is an inevitable next step in automating machine learning and has already outpaced the best human-designed architectures on many tasks. In the past few years, research in NAS has been progressing rapidly, with over 1000 papers released since 2020 (Deng and Lindauer, 2021). In this survey, we provide an organized and comprehensive guide to neural architecture search. We give a taxonomy of search spaces, algorithms, and speedup techniques, and we discuss resources such as benchmarks, best practices, other surveys, and open-source libraries.

Neural Architecture Search (NAS) aims to automatically discover high-performing deep neural network (DNN) architectures. However, conventional algorithm-driven NAS relies on carefully hand-crafted search spaces to ensure executability, which restricts open-ended exploration. Recent coding-based agentic approaches using large language models (LLMs) reduce manual design, but current LLMs struggle to reliably generate complex, valid architectures, and their proposals are often biased toward a narrow set of patterns observed in their training data. To bridge reliable algorithmic search with powerful LLM assistance, we propose LLMasTool, a hierarchical tree-based NAS framework for stable and open-ended model evolution. Our method automatically extracts reusable modules from arbitrary source code and represents full architectures as hierarchical trees, enabling evolution through reliable tree transformations rather than code generation. At each evolution step, coarse-level planning is governed by a diversity-guided algorithm that leverages Bayesian modeling to improve exploration efficiency, while the LLM resolves the remaining degrees of freedom to ensure a meaningful evolutionary trajectory and an executable generated architecture. With this formulation, instead of fully agentic LLM approaches, our method explores diverse directions beyond the inherent biases in the LLM. Our method improves over existing NAS methods by 0.69, 1.83, and 2.68 points on CIFAR-10, CIFAR-100, and ImageNet16-120, demonstrating its effectiveness.

While transformers achieve strong performance, their internal decision-making processes remain opaque. We investigate whether architectural constraints can enforce interpretability by design through architectural stream independence: maintaining a token stream (carrying symbolic structure) and contextual semantics in separated streams that remain independently observable throughout processing, with integration delayed until output. We validate this principle through the Late Fusion Architecture (LFA), which demonstrates interpretable symbolic heads through all the final layers, while standard transformers show dissolution by the third of six layers; we quantify this effect by introducing the Token-Position Dependence Score (PDS), with PDS_{max} = 0.276 and 0.058, respectively. Crucially, intervention experiments demonstrate functional modularity: suppressing LFA's recency heads causes minimal semantic damage (Cohen's d = -0.158) versus catastrophic entanglement in baselines (d = -0.672). LFA demonstrates that architectural constraints improve underlying learning mechanisms, averaging 42% stability versus 19% and 11% for baseline comparisons, with extremes from 50% on LFA's best pairs (6 of 12 heads position-invariant) down to 0% complete collapse in over-constrained cases. By preventing premature entanglement, architectural independence steers models toward semantic understanding over positional heuristics, establishing interpretability as an architectural design criterion enforceable through structural constraints rather than post-hoc analysis.

A hallmark of intelligence is the ability to autonomously learn new flexible, cognitive behaviors - that is, behaviors where the appropriate action depends not just on immediate stimuli (as in simple reflexive stimulus-response associations), but on contextual information that must be adequately acquired, stored and processed. While many meta-learning algorithms can design agents that autonomously learn new tasks, cognitive tasks adds another level of learning and memory to typical ``learning-to-learn'' problems. Here we evolve neural networks, endowed with plastic connections and neuromodulation, over a sizable set of simple cognitive tasks adapted from a computational neuroscience framework. The resulting evolved networks can automatically modify their own connectivity to acquire a novel simple cognitive task, never seen during evolution, from stimuli and rewards alone, through the spontaneous operation of their evolved neural organization and plasticity system. Our results emphasize the importance of carefully considering the multiple learning loops involved in the emergence of intelligent behavior.

Most of the Neural Cellular Automata (NCAs) defined in the literature have a common theme: they are based on regular grids with a Moore neighborhood (one-hop neighbour). They do not take into account long-range connections and more complex topologies as we can find in the brain. In this paper, we introduce BraiNCA, a brain-inspired NCA with an attention layer, long-range connections and complex topology. BraiNCAs shows better results in terms of robustness and speed of learning on the two tasks compared to Vanilla NCAs establishing that incorporating attention-based message selection together with explicit long-range edges can yield more sample-efficient and damage-tolerant self-organization than purely local, grid-based update rules. These results support the hypothesis that, for tasks requiring distributed coordination over extended spatial and temporal scales, the choice of interaction topology and the ability to dynamically route information will impact the robustness and speed of learning of an NCA. More broadly, BraiNCA provides brain-inspired NCA formulation that preserves the decentralized local update principle while better reflecting non-local connectivity patterns, making it a promising substrate for studying collective computation under biologically-realistic network structure and evolving cognitive substrates.