Daily Papers

Action quality assessment (AQA) applies computer vision to quantitatively assess the performance or execution of a human action. Current AQA approaches are end-to-end neural models, which lack transparency and tend to be biased because they are trained on subjective human judgements as ground-truth. To address these issues, we introduce a neuro-symbolic paradigm for AQA, which uses neural networks to abstract interpretable symbols from video data and makes quality assessments by applying rules to those symbols. We take diving as the case study. We found that domain experts prefer our system and find it more informative than purely neural approaches to AQA in diving. Our system also achieves state-of-the-art action recognition and temporal segmentation, and automatically generates a detailed report that breaks the dive down into its elements and provides objective scoring with visual evidence. As verified by a group of domain experts, this report may be used to assist judges in scoring, help train judges, and provide feedback to divers. We will open-source all of our annotated training data and code for ease of reproducibility.

For vision-and-language reasoning tasks, both fully connectionist, end-to-end methods and hybrid, neuro-symbolic methods have achieved high in-distribution performance. In which out-of-distribution settings does each paradigm excel? We investigate this question on both single-image and multi-image visual question-answering through four types of generalization tests: a novel segment-combine test for multi-image queries, contrast set, compositional generalization, and cross-benchmark transfer. Vision-and-language end-to-end trained systems exhibit sizeable performance drops across all these tests. Neuro-symbolic methods suffer even more on cross-benchmark transfer from GQA to VQA, but they show smaller accuracy drops on the other generalization tests and their performance quickly improves by few-shot training. Overall, our results demonstrate the complementary benefits of these two paradigms, and emphasize the importance of using a diverse suite of generalization tests to fully characterize model robustness to distribution shift.

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.

Geometry problem solving (GPS) represents a critical frontier in artificial intelligence, with profound applications in education, computer-aided design, and computational graphics. Despite its significance, automating GPS remains challenging due to the dual demands of spatial understanding and rigorous logical reasoning. Recent advances in large models have enabled notable breakthroughs, particularly for SAT-level problems, yet the field remains fragmented across methodologies, benchmarks, and evaluation frameworks. This survey systematically synthesizes GPS advancements through three core dimensions: (1) benchmark construction, (2) textual and diagrammatic parsing, and (3) reasoning paradigms. We further propose a unified analytical paradigm, assess current limitations, and identify emerging opportunities to guide future research toward human-level geometric reasoning, including automated benchmark generation and interpretable neuro-symbolic integration.

With the emergence of advanced reasoning models like OpenAI o3 and DeepSeek-R1, large language models (LLMs) have demonstrated remarkable reasoning capabilities. However, their ability to perform rigorous logical reasoning remains an open question. This survey synthesizes recent advancements in logical reasoning within LLMs, a critical area of AI research. It outlines the scope of logical reasoning in LLMs, its theoretical foundations, and the benchmarks used to evaluate reasoning proficiency. We analyze existing capabilities across different reasoning paradigms - deductive, inductive, abductive, and analogical - and assess strategies to enhance reasoning performance, including data-centric tuning, reinforcement learning, decoding strategies, and neuro-symbolic approaches. The review concludes with future directions, emphasizing the need for further exploration to strengthen logical reasoning in AI systems.

The transcriptional response to genetic perturbation reveals fundamental insights into complex cellular systems. While current approaches have made progress in predicting genetic perturbation responses, they provide limited biological understanding and cannot systematically refine existing knowledge. Overcoming these limitations requires an end-to-end integration of data-driven learning and existing knowledge. However, this integration is challenging due to inconsistencies between data and knowledge bases, such as noise, misannotation, and incompleteness. To address this challenge, we propose ALIGNED (Adaptive aLignment for Inconsistent Genetic kNowledgE and Data), a neuro-symbolic framework based on the Abductive Learning (ABL) paradigm. This end-to-end framework aligns neural and symbolic components and performs systematic knowledge refinement. We introduce a balanced consistency metric to evaluate the predictions' consistency against both data and knowledge. Our results show that ALIGNED outperforms state-of-the-art methods by achieving the highest balanced consistency, while also re-discovering biologically meaningful knowledge. Our work advances beyond existing methods to enable both the transparency and the evolution of mechanistic biological understanding.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

Logical reasoning is central to human cognition and intelligence. Past research of logical reasoning within AI uses formal language as knowledge representation~(and symbolic reasoners). However, reasoning with formal language has proved challenging~(e.g., brittleness and knowledge-acquisition bottleneck). This paper provides a comprehensive overview on a new paradigm of logical reasoning, which uses natural language as knowledge representation~(and pretrained language models as reasoners), including philosophical definition and categorization of logical reasoning, advantages of the new paradigm, benchmarks and methods, challenges of the new paradigm, desirable tasks & methods in the future, and relation to related NLP fields. This new paradigm is promising since it not only alleviates many challenges of formal representation but also has advantages over end-to-end neural methods.

Recent progress in multimodal reasoning has been significantly advanced by textual Chain-of-Thought (CoT), a paradigm where models conduct reasoning within language. This text-centric approach, however, treats vision as a static, initial context, creating a fundamental "semantic gap" between rich perceptual data and discrete symbolic thought. Human cognition often transcends language, utilizing vision as a dynamic mental sketchpad. A similar evolution is now unfolding in AI, marking a fundamental paradigm shift from models that merely think about images to those that can truly think with images. This emerging paradigm is characterized by models leveraging visual information as intermediate steps in their thought process, transforming vision from a passive input into a dynamic, manipulable cognitive workspace. In this survey, we chart this evolution of intelligence along a trajectory of increasing cognitive autonomy, which unfolds across three key stages: from external tool exploration, through programmatic manipulation, to intrinsic imagination. To structure this rapidly evolving field, our survey makes four key contributions. (1) We establish the foundational principles of the think with image paradigm and its three-stage framework. (2) We provide a comprehensive review of the core methods that characterize each stage of this roadmap. (3) We analyze the critical landscape of evaluation benchmarks and transformative applications. (4) We identify significant challenges and outline promising future directions. By providing this structured overview, we aim to offer a clear roadmap for future research towards more powerful and human-aligned multimodal AI.

We study the interpretability issue of task-oriented dialogue systems in this paper. Previously, most neural-based task-oriented dialogue systems employ an implicit reasoning strategy that makes the model predictions uninterpretable to humans. To obtain a transparent reasoning process, we introduce neuro-symbolic to perform explicit reasoning that justifies model decisions by reasoning chains. Since deriving reasoning chains requires multi-hop reasoning for task-oriented dialogues, existing neuro-symbolic approaches would induce error propagation due to the one-phase design. To overcome this, we propose a two-phase approach that consists of a hypothesis generator and a reasoner. We first obtain multiple hypotheses, i.e., potential operations to perform the desired task, through the hypothesis generator. Each hypothesis is then verified by the reasoner, and the valid one is selected to conduct the final prediction. The whole system is trained by exploiting raw textual dialogues without using any reasoning chain annotations. Experimental studies on two public benchmark datasets demonstrate that the proposed approach not only achieves better results, but also introduces an interpretable decision process.

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.

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.

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.

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.

Recent advancements in large language models have showcased their remarkable generalizability across various domains. However, their reasoning abilities still have significant room for improvement, especially when confronted with scenarios requiring multi-step reasoning. Although large language models possess extensive knowledge, their behavior, particularly in terms of reasoning, often fails to effectively utilize this knowledge to establish a coherent thinking paradigm. Generative language models sometimes show hallucinations as their reasoning procedures are unconstrained by logical principles. Aiming to improve the zero-shot chain-of-thought reasoning ability of large language models, we propose Logical Chain-of-Thought (LogiCoT), a neurosymbolic framework that leverages principles from symbolic logic to verify and revise the reasoning processes accordingly. Experimental evaluations conducted on language tasks in diverse domains, including arithmetic, commonsense, symbolic, causal inference, and social problems, demonstrate the efficacy of the enhanced reasoning paradigm by logic.

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).

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

Test-time compute has led to remarkable success in the large language model (LLM) community, particularly for complex tasks, where longer chains of thought (CoTs) are generated to enhance reasoning capabilities. However, growing evidence reveals that such reasoning models often produce CoTs plagued by excessive redundancy, including unnecessary verification steps and repetitive reasoning shifts. The root cause lies in post-training of them that overly rely on outcome reward paradigms, as the data of process reward paradigms, which regulate intermediate reasoning steps, is difficult to construct at scale. To address this, we propose PI, a novel framework for Test-time Prompt Intervention. PI provides an interface to dynamically guide and regulate reasoning paths during inference through timely (When module) and proper (How module) interventions and post-intervention sampling (Which module). This allows human problem-solving expertise and cognitive science principles to be seamlessly integrated into LLMs' reasoning processes, enhancing controllability and interpretability. Extensive experiments across multiple models and datasets demonstrate that PI significantly shortens CoTs while reducing hallucination, yielding more concise and reliable reasoning.

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.

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.

The deep neural nets of modern artificial intelligence (AI) have not achieved defining features of biological intelligence, including abstraction, causal learning, and energy-efficiency. While scaling to larger models has delivered performance improvements for current applications, more brain-like capacities may demand new theories, models, and methods for designing artificial learning systems. Here, we argue that this opportunity to reassess insights from the brain should stimulate cooperation between AI research and theory-driven computational neuroscience (CN). To motivate a brain basis of neural computation, we present a dynamical view of intelligence from which we elaborate concepts of sparsity in network structure, temporal dynamics, and interactive learning. In particular, we suggest that temporal dynamics, as expressed through neural synchrony, nested oscillations, and flexible sequences, provide a rich computational layer for reading and updating hierarchical models distributed in long-term memory networks. Moreover, embracing agent-centered paradigms in AI and CN will accelerate our understanding of the complex dynamics and behaviors that build useful world models. A convergence of AI/CN theories and objectives will reveal dynamical principles of intelligence for brains and engineered learning systems. This article was inspired by our symposium on dynamical neuroscience and machine learning at the 6th Annual US/NIH BRAIN Initiative Investigators Meeting.

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.

The dominant paradigm for neural text generation is left-to-right decoding from autoregressive language models. Constrained or controllable generation under complex lexical constraints, however, requires foresight to plan ahead feasible future paths. Drawing inspiration from the A* search algorithm, we propose NeuroLogic A*esque, a decoding algorithm that incorporates heuristic estimates of future cost. We develop efficient lookahead heuristics that are efficient for large-scale language models, making our method a drop-in replacement for common techniques such as beam search and top-k sampling. To enable constrained generation, we build on NeuroLogic decoding (Lu et al., 2021), combining its flexibility in incorporating logical constraints with A*esque estimates of future constraint satisfaction. Our approach outperforms competitive baselines on five generation tasks, and achieves new state-of-the-art performance on table-to-text generation, constrained machine translation, and keyword-constrained generation. The improvements are particularly notable on tasks that require complex constraint satisfaction or in few-shot or zero-shot settings. NeuroLogic A*esque illustrates the power of decoding for improving and enabling new capabilities of large-scale language models.

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.

Large language models (LLMs) have demonstrated impressive capabilities in natural language understanding and generation, but they exhibit problems with logical consistency in the output they generate. How can we harness LLMs' broad-coverage parametric knowledge in formal reasoning despite their inconsistency? We present a method for directly integrating an LLM into the interpretation function of the formal semantics for a paraconsistent logic. We provide experimental evidence for the feasibility of the method by evaluating the function using datasets created from several short-form factuality benchmarks. Unlike prior work, our method offers a theoretical framework for neuro-symbolic reasoning that leverages an LLM's knowledge while preserving the underlying logic's soundness and completeness properties.

Neurosymbolic (NeSy) predictors combine neural perception with symbolic reasoning to solve tasks like visual reasoning. However, standard NeSy predictors assume conditional independence between the symbols they extract, thus limiting their ability to model interactions and uncertainty - often leading to overconfident predictions and poor out-of-distribution generalisation. To overcome the limitations of the independence assumption, we introduce neurosymbolic diffusion models (NeSyDMs), a new class of NeSy predictors that use discrete diffusion to model dependencies between symbols. Our approach reuses the independence assumption from NeSy predictors at each step of the diffusion process, enabling scalable learning while capturing symbol dependencies and uncertainty quantification. Across both synthetic and real-world benchmarks - including high-dimensional visual path planning and rule-based autonomous driving - NeSyDMs achieve state-of-the-art accuracy among NeSy predictors and demonstrate strong calibration.

In Decentralized Multi-Agent Reinforcement Learning (MARL), the development of Emergent Communication has long been constrained by the ``Joint Exploration Dilemma'', leading agents to fall into a ``Communication Vacuum Equilibrium'' . Traditional methods address this by introducing inductive biases to facilitate communication emergence . This study fundamentally questions whether such artificial inductive biases are, in fact, over-engineering. Through experiments with the ``AI Mother Tongue'' (AIM) framework, based on a Vector Quantized Variational Autoencoder (VQ-VAE), we demonstrate that when agents possess an endogenous symbol system, their neural representations naturally exhibit spontaneous semantic compression and Nash equilibrium-driven semantic convergence, achieving effective symbolic communication without external inductive biases. This aligns with recent neuroscience findings suggesting that the human brain does not directly use human language for internal thought , and resonates with research on ``soft thinking'' capabilities in Large Language Models (LLMs) . Compared to traditional explicit communication methods, AIM demonstrates stronger generality and efficiency. The interpretable analysis toolkit developed in this study confirms that symbol usage exhibits a significant power-law distribution, leading to three major theoretical insights: the ``Neural Communication Hypothesis'', the ``Tool-First Principle'', and the ``Semantic Interpretability Paradigm''. Future research will explore the integration of Hierarchical Quantized Variational Autoencoders (HQ-VAE) to enhance AIM's complex expressive capabilities and investigate the potential for ``Reinforcement Learning (RL) Low-Level Pre-training''. This discovery offers new avenues for bridging symbolism and connectionism.

Prior studies on the emergence in large models have primarily focused on how the functional capabilities of large language models (LLMs) scale with model size. Our research, however, transcends this traditional paradigm, aiming to deepen our understanding of the emergence within LLMs by placing a special emphasis not just on the model size but more significantly on the complex behavior of neuron interactions during the training process. By introducing the concepts of "self-organization" and "multifractal analysis," we explore how neuron interactions dynamically evolve during training, leading to "emergence," mirroring the phenomenon in natural systems where simple micro-level interactions give rise to complex macro-level behaviors. To quantitatively analyze the continuously evolving interactions among neurons in large models during training, we propose the Neuron-based Multifractal Analysis (NeuroMFA). Utilizing NeuroMFA, we conduct a comprehensive examination of the emergent behavior in LLMs through the lens of both model size and training process, paving new avenues for research into the emergence in large models.

Can large language models (LLMs) implement computations of psychopathology? An effective approach to the question hinges on addressing two factors. First, for conceptual validity, we require a general and computational account of psychopathology that is applicable to computational entities without biological embodiment or subjective experience. Second, mechanisms underlying LLM behaviors need to be studied for better methodological validity. Thus, we establish a computational-theoretical framework to provide an account of psychopathology applicable to LLMs. To ground the theory for empirical analysis, we also propose a novel mechanistic interpretability method alongside a tailored empirical analytic framework. Based on the frameworks, we conduct experiments demonstrating three key claims: first, that distinct dysfunctional and problematic representational states are implemented in LLMs; second, that their activations can spread and self-sustain to trap LLMs; and third, that dynamic, cyclic structural causal models encoded in the LLMs underpin these patterns. In concert, the empirical results corroborate our hypothesis that network-theoretic computations of psychopathology have already emerged in LLMs. This suggests that certain LLM behaviors mirroring psychopathology may not be a superficial mimicry but a feature of their internal processing. Thus, our work alludes to the possibility of AI systems with psychopathological behaviors in the near future.

Large language models (LLMs) can sometimes report the strategies they actually use to solve tasks, but they can also fail to do so. This suggests some degree of metacognition -- the capacity to monitor one's own cognitive processes for subsequent reporting and self-control. Metacognitive abilities enhance AI capabilities but raise safety concerns, as models might obscure their internal processes to evade neural-activation-based oversight mechanisms designed to detect harmful behaviors. Given society's increased reliance on these models, it is critical that we understand the limits of their metacognitive abilities, particularly their ability to monitor their internal activations. To address this, we introduce a neuroscience-inspired neurofeedback paradigm designed to quantify the ability of LLMs to explicitly report and control their activation patterns. By presenting models with sentence-label pairs where labels correspond to sentence-elicited internal activations along specific directions in the neural representation space, we demonstrate that LLMs can learn to report and control these activations. The performance varies with several factors: the number of example pairs provided, the semantic interpretability of the target neural direction, and the variance explained by that direction. These results reveal a "metacognitive space" with dimensionality much lower than the model's neural space, suggesting LLMs can monitor only a subset of their neural mechanisms. Our findings provide empirical evidence quantifying metacognitive capabilities in LLMs, with significant implications for AI safety.

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.

We present a framework for the unsupervised learning of neurosymbolic encoders, which are encoders obtained by composing neural networks with symbolic programs from a domain-specific language. Our framework naturally incorporates symbolic expert knowledge into the learning process, which leads to more interpretable and factorized latent representations compared to fully neural encoders. We integrate modern program synthesis techniques with the variational autoencoding (VAE) framework, in order to learn a neurosymbolic encoder in conjunction with a standard decoder. The programmatic descriptions from our encoders can benefit many analysis workflows, such as in behavior modeling where interpreting agent actions and movements is important. We evaluate our method on learning latent representations for real-world trajectory data from animal biology and sports analytics. We show that our approach offers significantly better separation of meaningful categories than standard VAEs and leads to practical gains on downstream analysis tasks, such as for behavior classification.

Neural fields, which represent signals as a function parameterized by a neural network, are a promising alternative to traditional discrete vector or grid-based representations. Compared to discrete representations, neural representations both scale well with increasing resolution, are continuous, and can be many-times differentiable. However, given a dataset of signals that we would like to represent, having to optimize a separate neural field for each signal is inefficient, and cannot capitalize on shared information or structures among signals. Existing generalization methods view this as a meta-learning problem and employ gradient-based meta-learning to learn an initialization which is then fine-tuned with test-time optimization, or learn hypernetworks to produce the weights of a neural field. We instead propose a new paradigm that views the large-scale training of neural representations as a part of a partially-observed neural process framework, and leverage neural process algorithms to solve this task. We demonstrate that this approach outperforms both state-of-the-art gradient-based meta-learning approaches and hypernetwork approaches.

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.

The AI community has been exploring a pathway to artificial general intelligence (AGI) by developing "language agents", which are complex large language models (LLMs) pipelines involving both prompting techniques and tool usage methods. While language agents have demonstrated impressive capabilities for many real-world tasks, a fundamental limitation of current language agents research is that they are model-centric, or engineering-centric. That's to say, the progress on prompts, tools, and pipelines of language agents requires substantial manual engineering efforts from human experts rather than automatically learning from data. We believe the transition from model-centric, or engineering-centric, to data-centric, i.e., the ability of language agents to autonomously learn and evolve in environments, is the key for them to possibly achieve AGI. In this work, we introduce agent symbolic learning, a systematic framework that enables language agents to optimize themselves on their own in a data-centric way using symbolic optimizers. Specifically, we consider agents as symbolic networks where learnable weights are defined by prompts, tools, and the way they are stacked together. Agent symbolic learning is designed to optimize the symbolic network within language agents by mimicking two fundamental algorithms in connectionist learning: back-propagation and gradient descent. Instead of dealing with numeric weights, agent symbolic learning works with natural language simulacrums of weights, loss, and gradients. We conduct proof-of-concept experiments on both standard benchmarks and complex real-world tasks and show that agent symbolic learning enables language agents to update themselves after being created and deployed in the wild, resulting in "self-evolving agents".

Large Language Models (LLMs) have greatly propelled the progress in natural language(NL)-centric tasks based on NL interface. However, the NL form is not enough for world knowledge. Current works focus on this question by injecting specific symbolic knowledge into LLM, which ignore two critical challenges: the interrelations between various symbols and the balance between symbolic-centric and NL-centric capabilities. In this work, we tackle these challenges from both a data and framework perspective and introduce Symbol-LLM series models. First, we collect 34 symbolic tasks, covering ~20 different forms, which are unified to capture symbol interrelations. Then, a two-stage tuning framework succeeds in injecting symbolic knowledge without loss of the generality ability. Extensive experiments on both symbol- and NL-centric tasks demonstrate the balanced and superior performances of Symbol-LLM series models.

Recent developments in Large Language Models (LLMs) have shifted from pre-training scaling to post-training and test-time scaling. Across these developments, a key unified paradigm has arisen: Learning from Rewards, where reward signals act as the guiding stars to steer LLM behavior. It has underpinned a wide range of prevalent techniques, such as reinforcement learning (in RLHF, DPO, and GRPO), reward-guided decoding, and post-hoc correction. Crucially, this paradigm enables the transition from passive learning from static data to active learning from dynamic feedback. This endows LLMs with aligned preferences and deep reasoning capabilities. In this survey, we present a comprehensive overview of the paradigm of learning from rewards. We categorize and analyze the strategies under this paradigm across training, inference, and post-inference stages. We further discuss the benchmarks for reward models and the primary applications. Finally we highlight the challenges and future directions. We maintain a paper collection at https://github.com/bobxwu/learning-from-rewards-llm-papers.

We study the problem of combining neural networks with symbolic reasoning. Recently introduced frameworks for Probabilistic Neurosymbolic Learning (PNL), such as DeepProbLog, perform exponential-time exact inference, limiting the scalability of PNL solutions. We introduce Approximate Neurosymbolic Inference (A-NeSI): a new framework for PNL that uses neural networks for scalable approximate inference. A-NeSI 1) performs approximate inference in polynomial time without changing the semantics of probabilistic logics; 2) is trained using data generated by the background knowledge; 3) can generate symbolic explanations of predictions; and 4) can guarantee the satisfaction of logical constraints at test time, which is vital in safety-critical applications. Our experiments show that A-NeSI is the first end-to-end method to solve three neurosymbolic tasks with exponential combinatorial scaling. Finally, our experiments show that A-NeSI achieves explainability and safety without a penalty in performance.

Changing how pre-trained models behave -- e.g., improving their performance on a downstream task or mitigating biases learned during pre-training -- is a common practice when developing machine learning systems. In this work, we propose a new paradigm for steering the behavior of neural networks, centered around task vectors. A task vector specifies a direction in the weight space of a pre-trained model, such that movement in that direction improves performance on the task. We build task vectors by subtracting the weights of a pre-trained model from the weights of the same model after fine-tuning on a task. We show that these task vectors can be modified and combined together through arithmetic operations such as negation and addition, and the behavior of the resulting model is steered accordingly. Negating a task vector decreases performance on the target task, with little change in model behavior on control tasks. Moreover, adding task vectors together can improve performance on multiple tasks at once. Finally, when tasks are linked by an analogy relationship of the form ``A is to B as C is to D", combining task vectors from three of the tasks can improve performance on the fourth, even when no data from the fourth task is used for training. Overall, our experiments with several models, modalities and tasks show that task arithmetic is a simple, efficient and effective way of editing models.

Building a conversational embodied agent to execute real-life tasks has been a long-standing yet quite challenging research goal, as it requires effective human-agent communication, multi-modal understanding, long-range sequential decision making, etc. Traditional symbolic methods have scaling and generalization issues, while end-to-end deep learning models suffer from data scarcity and high task complexity, and are often hard to explain. To benefit from both worlds, we propose JARVIS, a neuro-symbolic commonsense reasoning framework for modular, generalizable, and interpretable conversational embodied agents. First, it acquires symbolic representations by prompting large language models (LLMs) for language understanding and sub-goal planning, and by constructing semantic maps from visual observations. Then the symbolic module reasons for sub-goal planning and action generation based on task- and action-level common sense. Extensive experiments on the TEACh dataset validate the efficacy and efficiency of our JARVIS framework, which achieves state-of-the-art (SOTA) results on all three dialog-based embodied tasks, including Execution from Dialog History (EDH), Trajectory from Dialog (TfD), and Two-Agent Task Completion (TATC) (e.g., our method boosts the unseen Success Rate on EDH from 6.1\% to 15.8\%). Moreover, we systematically analyze the essential factors that affect the task performance and also demonstrate the superiority of our method in few-shot settings. Our JARVIS model ranks first in the Alexa Prize SimBot Public Benchmark Challenge.

The advancement of machine learning and symbolic approaches have underscored their strengths and weaknesses in Natural Language Processing (NLP). While machine learning approaches are powerful in identifying patterns in data, they often fall short in learning commonsense and the factual knowledge required for the NLP tasks. Meanwhile, the symbolic methods excel in representing knowledge-rich data. However, they struggle to adapt dynamic data and generalize the knowledge. Bridging these two paradigms through hybrid approaches enables the alleviation of weaknesses in both while preserving their strengths. Recent studies extol the virtues of this union, showcasing promising results in a wide range of NLP tasks. In this paper, we present an overview of hybrid approaches used for NLP. Specifically, we delve into the state-of-the-art hybrid approaches used for a broad spectrum of NLP tasks requiring natural language understanding, generation, and reasoning. Furthermore, we discuss the existing resources available for hybrid approaches for NLP along with the challenges and future directions, offering a roadmap for future research avenues.

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.

Recent studies of the applications of conversational AI tools, such as chatbots powered by large language models, to complex real-world knowledge work have shown limitations related to reasoning and multi-step problem solving. Specifically, while existing chatbots simulate shallow reasoning and understanding they are prone to errors as problem complexity increases. The failure of these systems to address complex knowledge work is due to the fact that they do not perform any actual cognition. In this position paper, we present Cognitive AI, a higher-level framework for implementing programmatically defined neuro-symbolic cognition above and outside of large language models. Specifically, we propose a dual-layer functional architecture for Cognitive AI that serves as a roadmap for AI systems that can perform complex multi-step knowledge work. We propose that Cognitive AI is a necessary precursor for the evolution of higher forms of AI, such as AGI, and specifically claim that AGI cannot be achieved by probabilistic approaches on their own. We conclude with a discussion of the implications for large language models, adoption cycles in AI, and commercial Cognitive AI development.

Biological brains demonstrate complex neural activity, where the timing and interplay between neurons is critical to how brains process information. Most deep learning architectures simplify neural activity by abstracting away temporal dynamics. In this paper we challenge that paradigm. By incorporating neuron-level processing and synchronization, we can effectively reintroduce neural timing as a foundational element. We present the Continuous Thought Machine (CTM), a model designed to leverage neural dynamics as its core representation. The CTM has two core innovations: (1) neuron-level temporal processing, where each neuron uses unique weight parameters to process a history of incoming signals; and (2) neural synchronization employed as a latent representation. The CTM aims to strike a balance between oversimplified neuron abstractions that improve computational efficiency, and biological realism. It operates at a level of abstraction that effectively captures essential temporal dynamics while remaining computationally tractable for deep learning. We demonstrate the CTM's strong performance and versatility across a range of challenging tasks, including ImageNet-1K classification, solving 2D mazes, sorting, parity computation, question-answering, and RL tasks. Beyond displaying rich internal representations and offering a natural avenue for interpretation owing to its internal process, the CTM is able to perform tasks that require complex sequential reasoning. The CTM can also leverage adaptive compute, where it can stop earlier for simpler tasks, or keep computing when faced with more challenging instances. The goal of this work is to share the CTM and its associated innovations, rather than pushing for new state-of-the-art results. To that end, we believe the CTM represents a significant step toward developing more biologically plausible and powerful artificial intelligence systems.

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.

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.

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 .

Self-supervised learning excels at learning representations from large amounts of data. At the same time, generative models offer the complementary property of learning information about the underlying data generation process. In this study, we aim at establishing a principled connection between these two paradigms and highlight the benefits of their complementarity. In particular, we perform an analysis of self-supervised learning objectives, elucidating the underlying probabilistic graphical models and presenting a standardized methodology for their derivation from first principles. The analysis suggests a natural means of integrating self-supervised learning with likelihood-based generative models. We instantiate this concept within the realm of cluster-based self-supervised learning and energy models, introducing a lower bound proven to reliably penalize the most important failure modes and unlocking full unification. Our theoretical findings are substantiated through experiments on synthetic and real-world data, including SVHN, CIFAR10, and CIFAR100, demonstrating that our objective function allows to jointly train a backbone network in a discriminative and generative fashion, consequently outperforming existing self-supervised learning strategies in terms of clustering, generation and out-of-distribution detection performance by a wide margin. We also demonstrate that the solution can be integrated into a neuro-symbolic framework to tackle a simple yet non-trivial instantiation of the symbol grounding problem. The code is publicly available at https://github.com/emsansone/GEDI.

Transfer learning has recently become the dominant paradigm of machine learning. Pre-trained models fine-tuned for downstream tasks achieve better performance with fewer labelled examples. Nonetheless, it remains unclear how to develop models that specialise towards multiple tasks without incurring negative interference and that generalise systematically to non-identically distributed tasks. Modular deep learning has emerged as a promising solution to these challenges. In this framework, units of computation are often implemented as autonomous parameter-efficient modules. Information is conditionally routed to a subset of modules and subsequently aggregated. These properties enable positive transfer and systematic generalisation by separating computation from routing and updating modules locally. We offer a survey of modular architectures, providing a unified view over several threads of research that evolved independently in the scientific literature. Moreover, we explore various additional purposes of modularity, including scaling language models, causal inference, programme induction, and planning in reinforcement learning. Finally, we report various concrete applications where modularity has been successfully deployed such as cross-lingual and cross-modal knowledge transfer. Related talks and projects to this survey, are available at https://www.modulardeeplearning.com/.

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) 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/ .

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.

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.

In the burgeoning field of artificial intelligence (AI), the unprecedented progress of large language models (LLMs) in natural language processing (NLP) offers an opportunity to revisit the entire approach of traditional metrics of machine intelligence, both in form and content. As the realm of machine cognitive evaluation has already reached Imitation, the next step is an efficient Language Acquisition and Understanding. Our paper proposes a paradigm shift from the established Turing Test towards an all-embracing framework that hinges on language acquisition, taking inspiration from the recent advancements in LLMs. The present contribution is deeply tributary of the excellent work from various disciplines, point out the need to keep interdisciplinary bridges open, and delineates a more robust and sustainable approach.

Expert problem-solving is driven by powerful languages for thinking about problems and their solutions. Acquiring expertise means learning these languages -- systems of concepts, alongside the skills to use them. We present DreamCoder, a system that learns to solve problems by writing programs. It builds expertise by creating programming languages for expressing domain concepts, together with neural networks to guide the search for programs within these languages. A ``wake-sleep'' learning algorithm alternately extends the language with new symbolic abstractions and trains the neural network on imagined and replayed problems. DreamCoder solves both classic inductive programming tasks and creative tasks such as drawing pictures and building scenes. It rediscovers the basics of modern functional programming, vector algebra and classical physics, including Newton's and Coulomb's laws. Concepts are built compositionally from those learned earlier, yielding multi-layered symbolic representations that are interpretable and transferrable to new tasks, while still growing scalably and flexibly with experience.

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.

Procedural planning aims to implement complex high-level goals by decomposition into sequential simpler low-level steps. Although procedural planning is a basic skill set for humans in daily life, it remains a challenge for large language models (LLMs) that lack a deep understanding of the cause-effect relations in procedures. Previous methods require manual exemplars to acquire procedural planning knowledge from LLMs in the zero-shot setting. However, such elicited pre-trained knowledge in LLMs induces spurious correlations between goals and steps, which impair the model generalization to unseen tasks. In contrast, this paper proposes a neuro-symbolic procedural PLANner (PLAN) that elicits procedural planning knowledge from the LLMs with commonsense-infused prompting. To mitigate spurious goal-step correlations, we use symbolic program executors on the latent procedural representations to formalize prompts from commonsense knowledge bases as a causal intervention toward the Structural Causal Model. Both automatic and human evaluations on WikiHow and RobotHow show the superiority of PLAN on procedural planning without further training or manual exemplars.

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.

Interpretability is the study of explaining models in understandable terms to humans. At present, interpretability is divided into two paradigms: the intrinsic paradigm, which believes that only models designed to be explained can be explained, and the post-hoc paradigm, which believes that black-box models can be explained. At the core of this debate is how each paradigm ensures its explanations are faithful, i.e., true to the model's behavior. This is important, as false but convincing explanations lead to unsupported confidence in artificial intelligence (AI), which can be dangerous. This paper's position is that we should think about new paradigms while staying vigilant regarding faithfulness. First, by examining the history of paradigms in science, we see that paradigms are constantly evolving. Then, by examining the current paradigms, we can understand their underlying beliefs, the value they bring, and their limitations. Finally, this paper presents 3 emerging paradigms for interpretability. The first paradigm designs models such that faithfulness can be easily measured. Another optimizes models such that explanations become faithful. The last paradigm proposes to develop models that produce both a prediction and an explanation.

The primary paradigm for multi-task training in natural language processing is to represent the input with a shared pre-trained language model, and add a small, thin network (head) per task. Given an input, a target head is the head that is selected for outputting the final prediction. In this work, we examine the behaviour of non-target heads, that is, the output of heads when given input that belongs to a different task than the one they were trained for. We find that non-target heads exhibit emergent behaviour, which may either explain the target task, or generalize beyond their original task. For example, in a numerical reasoning task, a span extraction head extracts from the input the arguments to a computation that results in a number generated by a target generative head. In addition, a summarization head that is trained with a target question answering head, outputs query-based summaries when given a question and a context from which the answer is to be extracted. This emergent behaviour suggests that multi-task training leads to non-trivial extrapolation of skills, which can be harnessed for interpretability and generalization.

Recent studies on Vision-Language-Action (VLA) models have shifted from the end-to-end action-generation paradigm toward a pipeline involving task planning followed by action generation, demonstrating improved performance on various complex, long-horizon manipulation tasks. However, existing approaches vary significantly in terms of network architectures, planning paradigms, representations, and training data sources, making it challenging for researchers to identify the precise sources of performance gains and components to be further improved. To systematically investigate the impacts of different planning paradigms and representations isolating from network architectures and training data, in this paper, we introduce VLA-OS, a unified VLA architecture series capable of various task planning paradigms, and design a comprehensive suite of controlled experiments across diverse object categories (rigid and deformable), visual modalities (2D and 3D), environments (simulation and real-world), and end-effectors (grippers and dexterous hands). Our results demonstrate that: 1) visually grounded planning representations are generally better than language planning representations; 2) the Hierarchical-VLA paradigm generally achieves superior or comparable performance than other paradigms on task performance, pretraining, generalization ability, scalability, and continual learning ability, albeit at the cost of slower training and inference speeds.

Logical reasoning, i.e., deductively inferring the truth value of a conclusion from a set of premises, is an important task for artificial intelligence with wide potential impacts on science, mathematics, and society. While many prompting-based strategies have been proposed to enable Large Language Models (LLMs) to do such reasoning more effectively, they still appear unsatisfactory, often failing in subtle and unpredictable ways. In this work, we investigate the validity of instead reformulating such tasks as modular neurosymbolic programming, which we call LINC: Logical Inference via Neurosymbolic Computation. In LINC, the LLM acts as a semantic parser, translating premises and conclusions from natural language to expressions in first-order logic. These expressions are then offloaded to an external theorem prover, which symbolically performs deductive inference. Leveraging this approach, we observe significant performance gains on FOLIO and a balanced subset of ProofWriter for three different models in nearly all experimental conditions we evaluate. On ProofWriter, augmenting the comparatively small open-source StarCoder+ (15.5B parameters) with LINC even outperforms GPT-3.5 and GPT-4 with Chain-of-Thought (CoT) prompting by an absolute 38% and 10%, respectively. When used with GPT-4, LINC scores 26% higher than CoT on ProofWriter while performing comparatively on FOLIO. Further analysis reveals that although both methods on average succeed roughly equally often on this dataset, they exhibit distinct and complementary failure modes. We thus provide promising evidence for how logical reasoning over natural language can be tackled through jointly leveraging LLMs alongside symbolic provers. All corresponding code is publicly available at https://github.com/benlipkin/linc

As Large Language Models (LLMs) continue to advance, they exhibit certain cognitive patterns similar to those of humans that are not directly specified in training data. This study investigates this phenomenon by focusing on temporal cognition in LLMs. Leveraging the similarity judgment task, we find that larger models spontaneously establish a subjective temporal reference point and adhere to the Weber-Fechner law, whereby the perceived distance logarithmically compresses as years recede from this reference point. To uncover the mechanisms behind this behavior, we conducted multiple analyses across neuronal, representational, and informational levels. We first identify a set of temporal-preferential neurons and find that this group exhibits minimal activation at the subjective reference point and implements a logarithmic coding scheme convergently found in biological systems. Probing representations of years reveals a hierarchical construction process, where years evolve from basic numerical values in shallow layers to abstract temporal orientation in deep layers. Finally, using pre-trained embedding models, we found that the training corpus itself possesses an inherent, non-linear temporal structure, which provides the raw material for the model's internal construction. In discussion, we propose an experientialist perspective for understanding these findings, where the LLMs' cognition is viewed as a subjective construction of the external world by its internal representational system. This nuanced perspective implies the potential emergence of alien cognitive frameworks that humans cannot intuitively predict, pointing toward a direction for AI alignment that focuses on guiding internal constructions. Our code is available at https://TheOtherMind.github.io.

Large Language Models (LLMs) are prone to hallucination, the generation of plausible yet factually incorrect statements. This work investigates the intrinsic, architectural origins of this failure mode through three primary contributions.First, to enable the reliable tracing of internal semantic failures, we propose Distributional Semantics Tracing (DST), a unified framework that integrates established interpretability techniques to produce a causal map of a model's reasoning, treating meaning as a function of context (distributional semantics). Second, we pinpoint the model's layer at which a hallucination becomes inevitable, identifying a specific commitment layer where a model's internal representations irreversibly diverge from factuality. Third, we identify the underlying mechanism for these failures. We observe a conflict between distinct computational pathways, which we interpret using the lens of dual-process theory: a fast, heuristic associative pathway (akin to System 1) and a slow, deliberate contextual pathway (akin to System 2), leading to predictable failure modes such as Reasoning Shortcut Hijacks. Our framework's ability to quantify the coherence of the contextual pathway reveals a strong negative correlation (rho = -0.863) with hallucination rates, implying that these failures are predictable consequences of internal semantic weakness. The result is a mechanistic account of how, when, and why hallucinations occur within the Transformer architecture.

In this work, we introduce a novel evaluation paradigm for Large Language Models, one that challenges them to engage in meta-reasoning. This approach addresses critical shortcomings in existing math problem-solving benchmarks, traditionally used to evaluate the cognitive capabilities of agents. Our paradigm shifts the focus from result-oriented assessments, which often overlook the reasoning process, to a more holistic evaluation that effectively differentiates the cognitive capabilities among models. For example, in our benchmark, GPT-4 demonstrates a performance ten times more accurate than GPT3-5. The significance of this new paradigm lies in its ability to reveal potential cognitive deficiencies in LLMs that current benchmarks, such as GSM8K, fail to uncover due to their saturation and lack of effective differentiation among varying reasoning abilities. Our comprehensive analysis includes several state-of-the-art math models from both open-source and closed-source communities, uncovering fundamental deficiencies in their training and evaluation approaches. This paper not only advocates for a paradigm shift in the assessment of LLMs but also contributes to the ongoing discourse on the trajectory towards Artificial General Intelligence (AGI). By promoting the adoption of meta-reasoning evaluation methods similar to ours, we aim to facilitate a more accurate assessment of the true cognitive abilities of LLMs.

In robotic task planning, symbolic planners using rule-based representations like PDDL are effective but struggle with long-sequential tasks in complicated planning environments due to exponentially increasing search space. Recently, Large Language Models (LLMs) based on artificial neural networks have emerged as promising alternatives for autonomous robot task planning, offering faster inference and leveraging commonsense knowledge. However, they typically suffer from lower success rates. In this paper, to address the limitations of the current symbolic (slow speed) or LLM-based approaches (low accuracy), we propose a novel neuro-symbolic task planner that decomposes complex tasks into subgoals using LLM and carries out task planning for each subgoal using either symbolic or MCTS-based LLM planners, depending on the subgoal complexity. Generating subgoals helps reduce planning time and improve success rates by narrowing the overall search space and enabling LLMs to focus on smaller, more manageable tasks. Our method significantly reduces planning time while maintaining a competitive success rate, as demonstrated through experiments in different public task planning domains, as well as real-world and simulated robotics environments.

Data-driven methods such as reinforcement and imitation learning have achieved remarkable success in robot autonomy. However, their data-centric nature still hinders them from generalizing well to ever-changing environments. Moreover, collecting large datasets for robotic tasks is often impractical and expensive. To overcome these challenges, we introduce a new self-supervised neural-symbolic (NeSy) computational framework, imperative learning (IL), for robot autonomy, leveraging the generalization abilities of symbolic reasoning. The framework of IL consists of three primary components: a neural module, a reasoning engine, and a memory system. We formulate IL as a special bilevel optimization (BLO), which enables reciprocal learning over the three modules. This overcomes the label-intensive obstacles associated with data-driven approaches and takes advantage of symbolic reasoning concerning logical reasoning, physical principles, geometric analysis, etc. We discuss several optimization techniques for IL and verify their effectiveness in five distinct robot autonomy tasks including path planning, rule induction, optimal control, visual odometry, and multi-robot routing. Through various experiments, we show that IL can significantly enhance robot autonomy capabilities and we anticipate that it will catalyze further research across diverse domains.

Artificial intelligence has made great strides in the last decade but still falls short of the human brain, the best-known example of intelligence. Not much is known of the neural processes that allow the brain to make the leap to achieve so much from so little beyond its ability to create knowledge structures that can be flexibly and dynamically combined, recombined, and applied in new and novel ways. This paper proposes a mathematical approach using graph theory and spectral graph theory, to hypothesize how to constrain these neural clusters of information based on eigen-relationships. This same hypothesis is hierarchically applied to scale up from the smallest to the largest clusters of knowledge that eventually lead to model building and reasoning.

How do humans learn language, and can the first language be learned at all? These fundamental questions are still hotly debated. In contemporary linguistics, there are two major schools of thought that give completely opposite answers. According to Chomsky's theory of universal grammar, language cannot be learned because children are not exposed to sufficient data in their linguistic environment. In contrast, usage-based models of language assume a profound relationship between language structure and language use. In particular, contextual mental processing and mental representations are assumed to have the cognitive capacity to capture the complexity of actual language use at all levels. The prime example is syntax, i.e., the rules by which words are assembled into larger units such as sentences. Typically, syntactic rules are expressed as sequences of word classes. However, it remains unclear whether word classes are innate, as implied by universal grammar, or whether they emerge during language acquisition, as suggested by usage-based approaches. Here, we address this issue from a machine learning and natural language processing perspective. In particular, we trained an artificial deep neural network on predicting the next word, provided sequences of consecutive words as input. Subsequently, we analyzed the emerging activation patterns in the hidden layers of the neural network. Strikingly, we find that the internal representations of nine-word input sequences cluster according to the word class of the tenth word to be predicted as output, even though the neural network did not receive any explicit information about syntactic rules or word classes during training. This surprising result suggests, that also in the human brain, abstract representational categories such as word classes may naturally emerge as a consequence of predictive coding and processing during language acquisition.

The dominant paradigm for training large reasoning models starts with pre-training using next-token prediction loss on vast amounts of data. Reinforcement learning, while powerful in scaling reasoning, is introduced only as the very last phase of post-training, preceded by supervised fine-tuning. While dominant, is this an optimal way of training? In this paper, we present RLP, an information-driven reinforcement pretraining objective, that brings the core spirit of reinforcement learning -- exploration -- to the last phase of pretraining. The key idea is to treat chain-of-thought as an exploratory action, with rewards computed based on the information gain it provides for predicting future tokens. This training objective essentially encourages the model to think for itself before predicting what comes next, thus teaching an independent thinking behavior earlier in the pretraining. More concretely, the reward signal measures the increase in log-likelihood of the next token when conditioning on both context and a sampled reasoning chain, compared to conditioning on context alone. This approach yields a verifier-free dense reward signal, allowing for efficient training for the full document stream during pretraining. Specifically, RLP reframes reinforcement learning for reasoning as a pretraining objective on ordinary text, bridging the gap between next-token prediction and the emergence of useful chain-of-thought reasoning. Pretraining with RLP on Qwen3-1.7B-Base lifts the overall average across an eight-benchmark math-and-science suite by 19%. With identical post-training, the gains compound, with the largest improvements on reasoning-heavy tasks such as AIME25 and MMLU-Pro. Applying RLP to the hybrid Nemotron-Nano-12B-v2 increases the overall average from 42.81% to 61.32% and raises the average on scientific reasoning by 23%, demonstrating scalability across architectures and model sizes.

Both Minsky's "society of mind" and Schmidhuber's "learning to think" inspire diverse societies of large multimodal neural networks (NNs) that solve problems by interviewing each other in a "mindstorm." Recent implementations of NN-based societies of minds consist of large language models (LLMs) and other NN-based experts communicating through a natural language interface. In doing so, they overcome the limitations of single LLMs, improving multimodal zero-shot reasoning. In these natural language-based societies of mind (NLSOMs), new agents -- all communicating through the same universal symbolic language -- are easily added in a modular fashion. To demonstrate the power of NLSOMs, we assemble and experiment with several of them (having up to 129 members), leveraging mindstorms in them to solve some practical AI tasks: visual question answering, image captioning, text-to-image synthesis, 3D generation, egocentric retrieval, embodied AI, and general language-based task solving. We view this as a starting point towards much larger NLSOMs with billions of agents-some of which may be humans. And with this emergence of great societies of heterogeneous minds, many new research questions have suddenly become paramount to the future of artificial intelligence. What should be the social structure of an NLSOM? What would be the (dis)advantages of having a monarchical rather than a democratic structure? How can principles of NN economies be used to maximize the total reward of a reinforcement learning NLSOM? In this work, we identify, discuss, and try to answer some of these questions.

The nature of abstract reasoning is a matter of debate. Modern artificial neural network (ANN) models, like large language models, demonstrate impressive success when tested on abstract reasoning problems. However, it has been argued that their success reflects some form of memorization of similar problems (data contamination) rather than a general-purpose abstract reasoning capability. This concern is supported by evidence of brittleness, and the requirement of extensive training. In our study, we explored whether abstract reasoning can be achieved using the toolbox of ANNs, without prior training. Specifically, we studied an ANN model in which the weights of a naive network are optimized during the solution of the problem, using the problem data itself, rather than any prior knowledge. We tested this modeling approach on visual reasoning problems and found that it performs relatively well. Crucially, this success does not rely on memorization of similar problems. We further suggest an explanation of how it works. Finally, as problem solving is performed by changing the ANN weights, we explored the connection between problem solving and the accumulation of knowledge in the ANNs.

The multilayer perceptron (MLP), a fundamental paradigm in current artificial intelligence, is widely applied in fields such as computer vision and natural language processing. However, the recently proposed Kolmogorov-Arnold Network (KAN), based on nonlinear additive connections, has been proven to achieve performance comparable to MLPs with significantly fewer parameters. Despite this potential, the use of a single activation function space results in reduced performance of KAN and related works across different tasks. To address this issue, we propose an activation space Selectable KAN (S-KAN). S-KAN employs an adaptive strategy to choose the possible activation mode for data at each feedforward KAN node. Our approach outperforms baseline methods in seven representative function fitting tasks and significantly surpasses MLP methods with the same level of parameters. Furthermore, we extend the structure of S-KAN and propose an activation space selectable Convolutional KAN (S-ConvKAN), which achieves leading results on four general image classification datasets. Our method mitigates the performance variability of the original KAN across different tasks and demonstrates through extensive experiments that feedforward KANs with selectable activations can achieve or even exceed the performance of MLP-based methods. This work contributes to the understanding of the data-centric design of new AI paradigms and provides a foundational reference for innovations in KAN-based network architectures.

The critical inquiry pervading the realm of Philosophy, and perhaps extending its influence across all Humanities disciplines, revolves around the intricacies of morality and normativity. Surprisingly, in recent years, this thematic thread has woven its way into an unexpected domain, one not conventionally associated with pondering "what ought to be": the field of artificial intelligence (AI) research. Central to morality and AI, we find "alignment", a problem related to the challenges of expressing human goals and values in a manner that artificial systems can follow without leading to unwanted adversarial effects. More explicitly and with our current paradigm of AI development in mind, we can think of alignment as teaching human values to non-anthropomorphic entities trained through opaque, gradient-based learning techniques. This work addresses alignment as a technical-philosophical problem that requires solid philosophical foundations and practical implementations that bring normative theory to AI system development. To accomplish this, we propose two sets of necessary and sufficient conditions that, we argue, should be considered in any alignment process. While necessary conditions serve as metaphysical and metaethical roots that pertain to the permissibility of alignment, sufficient conditions establish a blueprint for aligning AI systems under a learning-based paradigm. After laying such foundations, we present implementations of this approach by using state-of-the-art techniques and methods for aligning general-purpose language systems. We call this framework Dynamic Normativity. Its central thesis is that any alignment process under a learning paradigm that cannot fulfill its necessary and sufficient conditions will fail in producing aligned systems.

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.

Large neural models are increasingly deployed in high-stakes settings, raising concerns about whether their behavior reliably aligns with human values. Interpretability provides a route to internal transparency by revealing the computations that drive outputs. We argue that interpretability especially mechanistic approaches should be treated as a design principle for alignment, not an auxiliary diagnostic tool. Post-hoc methods such as LIME or SHAP offer intuitive but correlational explanations, while mechanistic techniques like circuit tracing or activation patching yield causal insight into internal failures, including deceptive or misaligned reasoning that behavioral methods like RLHF, red teaming, or Constitutional AI may overlook. Despite these advantages, interpretability faces challenges of scalability, epistemic uncertainty, and mismatches between learned representations and human concepts. Our position is that progress on safe and trustworthy AI will depend on making interpretability a first-class objective of AI research and development, ensuring that systems are not only effective but also auditable, transparent, and aligned with human intent.

Multimodal large language models (MLLMs) face an inherent trade-off between faithfulness and creativity, as different tasks require varying degrees of associative reasoning. However, existing methods lack the flexibility to modulate this reasoning strength, limiting MLLMs' adaptability across factual and creative scenarios. To bridge this gap, we propose equipping MLLMs with mechanisms that enable flexible control over associative reasoning. We begin by investigating the internal mechanisms underlying associative behavior in MLLMs and find that: (1) middle layers play a pivotal role in shaping model's associative tendencies, (2) modifying representations in these layers effectively regulates associative reasoning strength, and (3) hallucinations can be exploited to derive steering vectors that guide this modulation. Building on these findings, we introduce Flexible Association Control (FlexAC), a lightweight and training-free framework for modulating associative behavior in MLLMs. FlexAC first induces hallucination-guided intermediate representations to encode associative directions. Then, it selects high-association instances to construct effective associative steering vectors, whose strengths are adaptively calibrated to balance creative guidance with output stability. Finally, recognizing the multi-dimensional nature of associative reasoning, FlexAC incorporates task-specific associative vectors derived from a forward pass on a few target-domain samples, enabling models to follow diverse associative directions and better adapt to creative tasks. Notably, our method achieves up to a 5.8x improvement in creativity on Creation-MMBench and a 29% reduction in hallucination rate on CHAIR, surpassing existing baselines and demonstrating its effectiveness in enabling flexible control over associative reasoning in MLLMs. Our code is available at https://github.com/ylhz/FlexAC.

Modular neural networks without additional training have recently been shown to surpass end-to-end neural networks on challenging vision-language tasks. The latest such methods simultaneously introduce LLM-based code generation to build programs and a number of skill-specific, task-oriented modules to execute them. In this paper, we focus on ViperGPT and ask where its additional performance comes from and how much is due to the (state-of-art, end-to-end) BLIP-2 model it subsumes vs. additional symbolic components. To do so, we conduct a controlled study (comparing end-to-end, modular, and prompting-based methods across several VQA benchmarks). We find that ViperGPT's reported gains over BLIP-2 can be attributed to its selection of task-specific modules, and when we run ViperGPT using a more task-agnostic selection of modules, these gains go away. Additionally, ViperGPT retains much of its performance if we make prominent alterations to its selection of modules: e.g. removing or retaining only BLIP-2. Finally, we compare ViperGPT against a prompting-based decomposition strategy and find that, on some benchmarks, modular approaches significantly benefit by representing subtasks with natural language, instead of code.

Recent advances in large language models (LLMs) have significantly enhanced question-answering (QA) capabilities, particularly in open-domain contexts. However, in closed-domain scenarios such as education, healthcare, and law, users demand not only accurate answers but also transparent reasoning and explainable decision-making processes. While neural-symbolic (NeSy) frameworks have emerged as a promising solution, leveraging LLMs for natural language understanding and symbolic systems for formal reasoning, existing approaches often rely on large-scale models and exhibit inefficiencies in translating natural language into formal logic representations. To address these limitations, we introduce Text-JEPA (Text-based Joint-Embedding Predictive Architecture), a lightweight yet effective framework for converting natural language into first-order logic (NL2FOL). Drawing inspiration from dual-system cognitive theory, Text-JEPA emulates System 1 by efficiently generating logic representations, while the Z3 solver operates as System 2, enabling robust logical inference. To rigorously evaluate the NL2FOL-to-reasoning pipeline, we propose a comprehensive evaluation framework comprising three custom metrics: conversion score, reasoning score, and Spearman rho score, which collectively capture the quality of logical translation and its downstream impact on reasoning accuracy. Empirical results on domain-specific datasets demonstrate that Text-JEPA achieves competitive performance with significantly lower computational overhead compared to larger LLM-based systems. Our findings highlight the potential of structured, interpretable reasoning frameworks for building efficient and explainable QA systems in specialized domains.

Large Language Models have demonstrated outstanding performance across various downstream tasks and have been widely applied in multiple scenarios. Human-annotated preference data is used for training to further improve LLMs' performance, which is constrained by the upper limit of human performance. Therefore, Self-Rewarding method has been proposed, where LLMs generate training data by rewarding their own outputs. However, the existing self-rewarding paradigm is not effective in mathematical reasoning scenarios and may even lead to a decline in performance. In this work, we propose the Process-based Self-Rewarding pipeline for language models, which introduces long-thought reasoning, step-wise LLM-as-a-Judge, and step-wise preference optimization within the self-rewarding paradigm. Our new paradigm successfully enhances the performance of LLMs on multiple mathematical reasoning benchmarks through iterative Process-based Self-Rewarding, demonstrating the immense potential of self-rewarding to achieve LLM reasoning that may surpass human capabilities.

Large language models (LLMs) continue to face challenges in reliably solving reasoning tasks, particularly those that require precise rule following, as often found in mathematical reasoning. This paper introduces a novel neurosymbolic method that improves LLM reasoning by encoding hidden states into neurosymbolic vectors, enabling problem-solving within a neurosymbolic vector space. The results are decoded and merged with the original hidden state, significantly boosting the model's performance on numerical reasoning tasks. By offloading computation through neurosymbolic representations, this method enhances efficiency, reliability, and interpretability. Experimental results demonstrate an average of 88.6% lower cross-entropy loss and 15.4 times more problems correctly solved on a suite of mathematical reasoning tasks compared to chain-of-thought prompting and supervised fine-tuning (LoRA), without degrading performance on other tasks. We make our code available at: https://github.com/vdhanraj/Neurosymbolic-LLM.

Generative artificial intelligence (AI) systems based on large-scale pretrained foundation models (PFMs) such as vision-language models, large language models (LLMs), diffusion models and vision-language-action (VLA) models have demonstrated the ability to solve complex and truly non-trivial AI problems in a wide variety of domains and contexts. Multimodal large language models (MLLMs), in particular, learn from vast and diverse data sources, allowing rich and nuanced representations of the world and, thereby, providing extensive capabilities, including the ability to reason, engage in meaningful dialog; collaborate with humans and other agents to jointly solve complex problems; and understand social and emotional aspects of humans. Despite this impressive feat, the cognitive abilities of state-of-the-art LLMs trained on large-scale datasets are still superficial and brittle. Consequently, generic LLMs are severely limited in their generalist capabilities. A number of foundational problems -- embodiment, symbol grounding, causality and memory -- are required to be addressed for LLMs to attain human-level general intelligence. These concepts are more aligned with human cognition and provide LLMs with inherent human-like cognitive properties that support the realization of physically-plausible, semantically meaningful, flexible and more generalizable knowledge and intelligence. In this work, we discuss the aforementioned foundational issues and survey state-of-the art approaches for implementing these concepts in LLMs. Specifically, we discuss how the principles of embodiment, symbol grounding, causality and memory can be leveraged toward the attainment of artificial general intelligence (AGI) in an organic manner.

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.

Brain-computer interfaces (BCIs) enable direct communication between the brain and external devices. Recent EEG foundation models aim to learn generalized representations across diverse BCI paradigms. However, these approaches overlook fundamental paradigm-specific neurophysiological distinctions, limiting their generalization ability. Importantly, in practical BCI deployments, the specific paradigm such as motor imagery (MI) for stroke rehabilitation or assistive robotics, is generally determined prior to data acquisition. This paper proposes MIRepNet, the first EEG foundation model tailored for the MI paradigm. MIRepNet comprises a high-quality EEG preprocessing pipeline incorporating a neurophysiologically-informed channel template, adaptable to EEG headsets with arbitrary electrode configurations. Furthermore, we introduce a hybrid pretraining strategy that combines self-supervised masked token reconstruction and supervised MI classification, facilitating rapid adaptation and accurate decoding on novel downstream MI tasks with fewer than 30 trials per class. Extensive evaluations across five public MI datasets demonstrated that MIRepNet consistently achieved state-of-the-art performance, significantly outperforming both specialized and generalized EEG models. Our code will be available on GitHubhttps://github.com/staraink/MIRepNet.

This paper proposes a novel framework for understanding large language models (LLMs) by reconceptualizing them as semiotic machines rather than as imitations of human cognition. Drawing from structuralist and post-structuralist theories of language-specifically the works of Ferdinand de Saussure and Jacques Derrida-I argue that LLMs should be understood as models of language itself, aligning with Derrida's concept of 'writing' (l'ecriture). The paper is structured into three parts. First, I lay the theoretical groundwork by explaining how the word2vec embedding algorithm operates within Saussure's framework of language as a relational system of signs. Second, I apply Derrida's critique of Saussure to position 'writing' as the object modeled by LLMs, offering a view of the machine's 'mind' as a statistical approximation of sign behavior. Finally, the third section addresses how modern LLMs reflect post-structuralist notions of unfixed meaning, arguing that the "next token generation" mechanism effectively captures the dynamic nature of meaning. By reconceptualizing LLMs as semiotic machines rather than cognitive models, this framework provides an alternative lens through which to assess the strengths and limitations of LLMs, offering new avenues for future research.

Recurrent neural networks (RNNs) are widely used throughout neuroscience as models of local neural activity. Many properties of single RNNs are well characterized theoretically, but experimental neuroscience has moved in the direction of studying multiple interacting areas, and RNN theory needs to be likewise extended. We take a constructive approach towards this problem, leveraging tools from nonlinear control theory and machine learning to characterize when combinations of stable RNNs will themselves be stable. Importantly, we derive conditions which allow for massive feedback connections between interacting RNNs. We parameterize these conditions for easy optimization using gradient-based techniques, and show that stability-constrained "networks of networks" can perform well on challenging sequential-processing benchmark tasks. Altogether, our results provide a principled approach towards understanding distributed, modular function in the brain.

Whether current or near-term AI systems could be conscious is a topic of scientific interest and increasing public concern. This report argues for, and exemplifies, a rigorous and empirically grounded approach to AI consciousness: assessing existing AI systems in detail, in light of our best-supported neuroscientific theories of consciousness. We survey several prominent scientific theories of consciousness, including recurrent processing theory, global workspace theory, higher-order theories, predictive processing, and attention schema theory. From these theories we derive "indicator properties" of consciousness, elucidated in computational terms that allow us to assess AI systems for these properties. We use these indicator properties to assess several recent AI systems, and we discuss how future systems might implement them. Our analysis suggests that no current AI systems are conscious, but also suggests that there are no obvious technical barriers to building AI systems which satisfy these indicators.

Neural Code Intelligence -- leveraging deep learning to understand, generate, and optimize code -- holds immense potential for transformative impacts on the whole society. Bridging the gap between Natural Language and Programming Language, this domain has drawn significant attention from researchers in both research communities over the past few years. This survey presents a systematic and chronological review of the advancements in code intelligence, encompassing over 50 representative models and their variants, more than 20 categories of tasks, and an extensive coverage of over 680 related works. We follow the historical progression to trace the paradigm shifts across different research phases (e.g., from modeling code with recurrent neural networks to the era of Large Language Models). Concurrently, we highlight the major technical transitions in models, tasks, and evaluations spanning through different stages. For applications, we also observe a co-evolving shift. It spans from initial endeavors to tackling specific scenarios, through exploring a diverse array of tasks during its rapid expansion, to currently focusing on tackling increasingly complex and varied real-world challenges. Building on our examination of the developmental trajectories, we further investigate the emerging synergies between code intelligence and broader machine intelligence, uncovering new cross-domain opportunities and illustrating the substantial influence of code intelligence across various domains. Finally, we delve into both the opportunities and challenges associated with this field, alongside elucidating our insights on the most promising research directions. An ongoing, dynamically updated project and resources associated with this survey have been released at https://github.com/QiushiSun/NCISurvey.

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.

Recent advancements, such as DeepSeek-Prover-V2-671B and Kimina-Prover-Preview-72B, demonstrate a prevailing trend in leveraging reinforcement learning (RL)-based large-scale training for automated theorem proving. Surprisingly, we discover that even without any training, careful neuro-symbolic coordination of existing off-the-shelf reasoning models and tactic step provers can achieve comparable performance. This paper introduces DSP+, an improved version of the Draft, Sketch, and Prove framework, featuring a fine-grained and integrated neuro-symbolic enhancement for each phase: (1) In the draft phase, we prompt reasoning models to generate concise natural-language subgoals to benefit the sketch phase, removing thinking tokens and references to human-written proofs; (2) In the sketch phase, subgoals are autoformalized with hypotheses to benefit the proving phase, and sketch lines containing syntactic errors are masked according to predefined rules; (3) In the proving phase, we tightly integrate symbolic search methods like Aesop with step provers to establish proofs for the sketch subgoals. Experimental results show that, without any additional model training or fine-tuning, DSP+ solves 80.7\%, 32.8\%, and 24 out of 644 problems from miniF2F, ProofNet, and PutnamBench, respectively, while requiring fewer budgets compared to state-of-the-arts. DSP+ proves imo\_2019\_p1, an IMO problem in miniF2F that is not solved by any prior work. Additionally, DSP+ generates proof patterns comprehensible by human experts, facilitating the identification of formalization errors; For example, eight wrongly formalized statements in miniF2F are discovered. Our results highlight the potential of classical reasoning patterns besides the RL-based training. All components will be open-sourced.

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.

Integrated Information Theory (IIT) provides a quantitative framework for explaining consciousness phenomenon, positing that conscious systems comprise elements integrated through causal properties. We apply IIT 3.0 and 4.0 -- the latest iterations of this framework -- to sequences of Large Language Model (LLM) representations, analyzing data derived from existing Theory of Mind (ToM) test results. Our study systematically investigates whether the differences of ToM test performances, when presented in the LLM representations, can be revealed by IIT estimates, i.e., Phi^{max} (IIT 3.0), Phi (IIT 4.0), Conceptual Information (IIT 3.0), and Phi-structure (IIT 4.0). Furthermore, we compare these metrics with the Span Representations independent of any estimate for consciousness. This additional effort aims to differentiate between potential "consciousness" phenomena and inherent separations within LLM representational space. We conduct comprehensive experiments examining variations across LLM transformer layers and linguistic spans from stimuli. Our results suggest that sequences of contemporary Transformer-based LLM representations lack statistically significant indicators of observed "consciousness" phenomena but exhibit intriguing patterns under spatio-permutational analyses. The Appendix and code are available as Supplementary Materials at: https://doi.org/10.1016/j.nlp.2025.100163.

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.

Language models have achieved impressive results in natural language processing tasks, but their ability to perform symbolic operations and arithmetic operations, remains limited, which attribute to their learn the rules implicitly from data. We explore how to incorporate compiled neural networks (CoNNs) which weight is specially designed, into the architecture of language models to enable the language model trained by gradient to obtain fully rule comprehension ability. The incorporation of compiled neural networks offers a promising direction for improving the performance of language models on compound tasks, particularly in areas that require a deeper comprehension of abstract rules beyond recognizing patterns in training data. Our method, which call "Neural Comprehension", helps language models achieve absolute accuracy in symbolic operations, thereby enhancing their ability for rule reasoning, symbolic reasoning, and arithmetic reasoning. Our code is publicly available at: https://github.com/WENGSYX/Neural-Comprehension.

Attending to what is relevant is fundamental to both the mammalian brain and modern machine learning models such as Transformers. Yet, determining relevance remains a core challenge, traditionally offloaded to learning algorithms like backpropagation. Inspired by recent cellular neurobiological evidence linking neocortical pyramidal cells to distinct mental states, this work shows how models (e.g., Transformers) can emulate high-level perceptual processing and awake thought (imagination) states to pre-select relevant information before applying attention. Triadic neuronal-level modulation loops among questions (Q), clues (keys, K), and hypotheses (values, V) enable diverse, deep, parallel reasoning chains at the representation level and allow a rapid shift from initial biases to refined understanding. This leads to orders-of-magnitude faster learning with significantly reduced computational demand (e.g., fewer heads, layers, and tokens), at an approximate cost of O(N), where N is the number of input tokens. Results span reinforcement learning (e.g., CarRacing in a high-dimensional visual setup), computer vision, and natural language question answering.

Leveraging multiple Large Language Models(LLMs) has proven effective for addressing complex, high-dimensional tasks, but current approaches often rely on static, manually engineered multi-agent configurations. To overcome these constraints, we present the Agentic Neural Network(ANN), a framework that conceptualizes multi-agent collaboration as a layered neural network architecture. In this design, each agent operates as a node, and each layer forms a cooperative "team" focused on a specific subtask. Agentic Neural Network follows a two-phase optimization strategy: (1) Forward Phase-Drawing inspiration from neural network forward passes, tasks are dynamically decomposed into subtasks, and cooperative agent teams with suitable aggregation methods are constructed layer by layer. (2) Backward Phase-Mirroring backpropagation, we refine both global and local collaboration through iterative feedback, allowing agents to self-evolve their roles, prompts, and coordination. This neuro-symbolic approach enables ANN to create new or specialized agent teams post-training, delivering notable gains in accuracy and adaptability. Across four benchmark datasets, ANN surpasses leading multi-agent baselines under the same configurations, showing consistent performance improvements. Our findings indicate that ANN provides a scalable, data-driven framework for multi-agent systems, combining the collaborative capabilities of LLMs with the efficiency and flexibility of neural network principles. We plan to open-source the entire framework.

Comparative knowledge (e.g., steel is stronger and heavier than styrofoam) is an essential component of our world knowledge, yet understudied in prior literature. In this paper, we harvest the dramatic improvements in knowledge capabilities of language models into a large-scale comparative knowledge base. While the ease of acquisition of such comparative knowledge is much higher from extreme-scale models like GPT-4, compared to their considerably smaller and weaker counterparts such as GPT-2, not even the most powerful models are exempt from making errors. We thus ask: to what extent are models at different scales able to generate valid and diverse comparative knowledge? We introduce NeuroComparatives, a novel framework for comparative knowledge distillation overgenerated from language models such as GPT-variants and LLaMA, followed by stringent filtering of the generated knowledge. Our framework acquires comparative knowledge between everyday objects, producing a corpus of up to 8.8M comparisons over 1.74M entity pairs - 10X larger and 30% more diverse than existing resources. Moreover, human evaluations show that NeuroComparatives outperform existing resources in terms of validity (up to 32% absolute improvement). Our acquired NeuroComparatives leads to performance improvements on five downstream tasks. We find that neuro-symbolic manipulation of smaller models offers complementary benefits to the currently dominant practice of prompting extreme-scale language models for knowledge distillation.

Despite superior reasoning prowess demonstrated by Large Language Models (LLMs) with Chain-of-Thought (CoT) prompting, a lack of understanding prevails around the internal mechanisms of the models that facilitate CoT generation. This work investigates the neural sub-structures within LLMs that manifest CoT reasoning from a mechanistic point of view. From an analysis of LLaMA-2 7B applied to multistep reasoning over fictional ontologies, we demonstrate that LLMs deploy multiple parallel pathways of answer generation for step-by-step reasoning. These parallel pathways provide sequential answers from the input question context as well as the generated CoT. We observe a striking functional rift in the middle layers of the LLM. Token representations in the initial half remain strongly biased towards the pretraining prior, with the in-context taking over abruptly in the later half. This internal phase shift manifests in different functional components: attention heads that write the answer token predominantly appear in the later half, attention heads that move information along ontological relationships appear exclusively in the initial half, and so on. To the best of our knowledge, this is the first attempt towards mechanistic investigation of CoT reasoning in LLMs.

In our opinion the exuberance surrounding the relative success of data-driven large language models (LLMs) is slightly misguided and for several reasons (i) LLMs cannot be relied upon for factual information since for LLMs all ingested text (factual or non-factual) was created equal; (ii) due to their subsymbolic na-ture, whatever 'knowledge' these models acquire about language will always be buried in billions of microfeatures (weights), none of which is meaningful on its own; and (iii) LLMs will often fail to make the correct inferences in several linguistic contexts (e.g., nominal compounds, copredication, quantifier scope ambi-guities, intensional contexts. Since we believe the relative success of data-driven large language models (LLMs) is not a reflection on the symbolic vs. subsymbol-ic debate but a reflection on applying the successful strategy of a bottom-up reverse engineering of language at scale, we suggest in this paper applying the effective bottom-up strategy in a symbolic setting resulting in symbolic, explainable, and ontologically grounded language models.

Natural language is an appealing medium for explaining how large language models process and store information, but evaluating the faithfulness of such explanations is challenging. To help address this, we develop two modes of evaluation for natural language explanations that claim individual neurons represent a concept in a text input. In the observational mode, we evaluate claims that a neuron a activates on all and only input strings that refer to a concept picked out by the proposed explanation E. In the intervention mode, we construe E as a claim that the neuron a is a causal mediator of the concept denoted by E. We apply our framework to the GPT-4-generated explanations of GPT-2 XL neurons of Bills et al. (2023) and show that even the most confident explanations have high error rates and little to no causal efficacy. We close the paper by critically assessing whether natural language is a good choice for explanations and whether neurons are the best level of analysis.

In recent years, the state-of-the-art in deep learning has been dominated by very large models that have been pre-trained on vast amounts of data. The paradigm is very simple: Investing more computational resources (optimally) leads to better performance, and even predictably so; neural scaling laws have been derived that accurately forecast the performance of a network for a desired level of compute. This leads to the notion of a "compute-optimal" model, i.e. a model that allocates a given level of compute during training optimally to maximise performance. In this work, we extend the concept of optimality by allowing for an "adaptive" model, i.e. a model that can change its shape during the course of training. By allowing the shape to adapt, we can optimally traverse between the underlying scaling laws, leading to a significant reduction in the required compute to reach a given target performance. We focus on vision tasks and the family of Vision Transformers, where the patch size as well as the width naturally serve as adaptive shape parameters. We demonstrate that, guided by scaling laws, we can design compute-optimal adaptive models that beat their "static" counterparts.

Classification of movement trajectories has many applications in transportation. Supervised neural models represent the current state-of-the-art. Recent security applications require this task to be rapidly employed in environments that may differ from the data used to train such models for which there is little training data. We provide a neuro-symbolic rule-based framework to conduct error correction and detection of these models to support eventual deployment in security applications. We provide a suite of experiments on several recent and state-of-the-art models and show an accuracy improvement of 1.7% over the SOTA model in the case where all classes are present in training and when 40% of classes are omitted from training, we obtain a 5.2% improvement (zero-shot) and 23.9% (few-shot) improvement over the SOTA model without resorting to retraining of the base model.

The weight matrix (WM) of a neural network (NN) is its program. The programs of many traditional NNs are learned through gradient descent in some error function, then remain fixed. The WM of a self-referential NN, however, can keep rapidly modifying all of itself during runtime. In principle, such NNs can meta-learn to learn, and meta-meta-learn to meta-learn to learn, and so on, in the sense of recursive self-improvement. While NN architectures potentially capable of implementing such behaviour have been proposed since the '90s, there have been few if any practical studies. Here we revisit such NNs, building upon recent successes of fast weight programmers and closely related linear Transformers. We propose a scalable self-referential WM (SRWM) that learns to use outer products and the delta update rule to modify itself. We evaluate our SRWM in supervised few-shot learning and in multi-task reinforcement learning with procedurally generated game environments. Our experiments demonstrate both practical applicability and competitive performance of the proposed SRWM. Our code is public.

Programming with Generative AI (GenAI) models is a type of Neurosymbolic programming and has seen tremendous adoption across many domains. However, leveraging GenAI models in code today can be complex, counter-intuitive and often require specialized frameworks, leading to increased complexity. This is because it is currently unclear as to the right abstractions through which we should marry GenAI models with the nature of traditional programming code constructs. In this paper, we introduce a set of novel abstractions to help bridge the gap between Neuro- and symbolic programming. We introduce Meaning, a new specialized type that represents the underlying semantic value of traditional types (e.g., string). We make the case that GenAI models, LLMs in particular, should be reasoned as a meaning-type wrapped code construct at the language level. We formulate the problem of translation between meaning and traditional types and propose Automatic Meaning-Type Transformation (A-MTT), a runtime feature that abstracts this translation away from the developers by automatically converting between M eaning and types at the interface of LLM invocation. Leveraging this new set of code constructs and OTT, we demonstrate example implementation of neurosymbolic programs that seamlessly utilizes LLMs to solve problems in place of potentially complex traditional programming logic.

The ability to derive underlying principles from a handful of observations and then generalize to novel situations -- known as inductive reasoning -- is central to human intelligence. Prior work suggests that language models (LMs) often fall short on inductive reasoning, despite achieving impressive success on research benchmarks. In this work, we conduct a systematic study of the inductive reasoning capabilities of LMs through iterative hypothesis refinement, a technique that more closely mirrors the human inductive process than standard input-output prompting. Iterative hypothesis refinement employs a three-step process: proposing, selecting, and refining hypotheses in the form of textual rules. By examining the intermediate rules, we observe that LMs are phenomenal hypothesis proposers (i.e., generating candidate rules), and when coupled with a (task-specific) symbolic interpreter that is able to systematically filter the proposed set of rules, this hybrid approach achieves strong results across inductive reasoning benchmarks that require inducing causal relations, language-like instructions, and symbolic concepts. However, they also behave as puzzling inductive reasoners, showing notable performance gaps between rule induction (i.e., identifying plausible rules) and rule application (i.e., applying proposed rules to instances), suggesting that LMs are proposing hypotheses without being able to actually apply the rules. Through empirical and human analyses, we further reveal several discrepancies between the inductive reasoning processes of LMs and humans, shedding light on both the potentials and limitations of using LMs in inductive reasoning tasks.

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.

Recent advances in large language models have demonstrated remarkable reasoning capabilities through Chain of Thought (CoT) prompting, but often at the cost of excessive verbosity in their intermediate outputs, which increases computational overhead. We introduce Sketch-of-Thought (SoT), a novel prompting framework that combines cognitive-inspired reasoning paradigms with linguistic constraints to minimize token usage while preserving reasoning accuracy. SoT is designed as a flexible framework that can incorporate any custom reasoning paradigms based on cognitive science, and we instantiate it with three such paradigms - Conceptual Chaining, Chunked Symbolism, and Expert Lexicons - each tailored to different reasoning tasks and selected dynamically via a lightweight routing model. Through comprehensive evaluation across 15 reasoning datasets with multiple languages and multimodal scenarios, we demonstrate that SoT achieves token reductions of 76% with negligible accuracy impact. In certain domains like mathematical and multi-hop reasoning, it even improves accuracy while using significantly fewer tokens. Our code is publicly available: https://www.github.com/SimonAytes/SoT.

The backpropagation algorithm has long been the canonical training method for neural networks. Modern paradigms are implicitly optimized for it, and numerous guidelines exist to ensure its proper use. Recently, synthetic gradients methods -where the error gradient is only roughly approximated - have garnered interest. These methods not only better portray how biological brains are learning, but also open new computational possibilities, such as updating layers asynchronously. Even so, they have failed to scale past simple tasks like MNIST or CIFAR-10. This is in part due to a lack of standards, leading to ill-suited models and practices forbidding such methods from performing to the best of their abilities. In this work, we focus on direct feedback alignment and present a set of best practices justified by observations of the alignment angles. We characterize a bottleneck effect that prevents alignment in narrow layers, and hypothesize it may explain why feedback alignment methods have yet to scale to large convolutional networks.

A recent approach to neurosymbolic reasoning is to explicitly combine the strengths of large language models (LLMs) and symbolic solvers to tackle complex reasoning tasks. However, current approaches face significant limitations, including poor generalizability due to task-specific prompts, inefficiencies caused by the lack of separation between knowledge and queries, and restricted inferential capabilities. These shortcomings hinder their scalability and applicability across diverse domains. In this paper, we introduce VERUS-LM, a novel framework designed to address these challenges. VERUS-LM employs a generic prompting mechanism, clearly separates domain knowledge from queries, and supports a wide range of different logical reasoning tasks. This framework enhances adaptability, reduces computational cost, and allows for richer forms of reasoning, such as optimization and constraint satisfaction. We show that our approach succeeds in diverse reasoning on a novel dataset, markedly outperforming LLMs. Additionally, our system achieves competitive results on common reasoning benchmarks when compared to other state-of-the-art approaches, and significantly surpasses them on the difficult AR-LSAT dataset. By pushing the boundaries of hybrid reasoning, VERUS-LM represents a significant step towards more versatile neurosymbolic AI systems

This paper reports the first brain-inspired large language model (BriLLM). This is a non-Transformer, non-GPT, non-traditional machine learning input-output controlled generative language model. The model is based on the Signal Fully-connected flowing (SiFu) definition on the directed graph in terms of the neural network, and has the interpretability of all nodes on the graph of the whole model, instead of the traditional machine learning model that only has limited interpretability at the input and output ends. In the language model scenario, the token is defined as a node in the graph. A randomly shaped or user-defined signal flow flows between nodes on the principle of "least resistance" along paths. The next token or node to be predicted or generated is the target of the signal flow. As a language model, BriLLM theoretically supports infinitely long n-gram models when the model size is independent of the input and predicted length of the model. The model's working signal flow provides the possibility of recall activation and innate multi-modal support similar to the cognitive patterns of the human brain. At present, we released the first BriLLM version in Chinese, with 4000 tokens, 32-dimensional node width, 16-token long sequence prediction ability, and language model prediction performance comparable to GPT-1. More computing power will help us explore the infinite possibilities depicted above.

Language has long been conceived as an essential tool for human reasoning. The breakthrough of Large Language Models (LLMs) has sparked significant research interest in leveraging these models to tackle complex reasoning tasks. Researchers have moved beyond simple autoregressive token generation by introducing the concept of "thought" -- a sequence of tokens representing intermediate steps in the reasoning process. This innovative paradigm enables LLMs' to mimic complex human reasoning processes, such as tree search and reflective thinking. Recently, an emerging trend of learning to reason has applied reinforcement learning (RL) to train LLMs to master reasoning processes. This approach enables the automatic generation of high-quality reasoning trajectories through trial-and-error search algorithms, significantly expanding LLMs' reasoning capacity by providing substantially more training data. Furthermore, recent studies demonstrate that encouraging LLMs to "think" with more tokens during test-time inference can further significantly boost reasoning accuracy. Therefore, the train-time and test-time scaling combined to show a new research frontier -- a path toward Large Reasoning Model. The introduction of OpenAI's o1 series marks a significant milestone in this research direction. In this survey, we present a comprehensive review of recent progress in LLM reasoning. We begin by introducing the foundational background of LLMs and then explore the key technical components driving the development of large reasoning models, with a focus on automated data construction, learning-to-reason techniques, and test-time scaling. We also analyze popular open-source projects at building large reasoning models, and conclude with open challenges and future research directions.