Daily Papers

Human reasoning can be understood as a cooperation between the intuitive, associative "System-1" and the deliberative, logical "System-2". For existing System-1-like methods in visual activity understanding, it is crucial to integrate System-2 processing to improve explainability, generalization, and data efficiency. One possible path of activity reasoning is building a symbolic system composed of symbols and rules, where one rule connects multiple symbols, implying human knowledge and reasoning abilities. Previous methods have made progress, but are defective with limited symbols from handcraft and limited rules from visual-based annotations, failing to cover the complex patterns of activities and lacking compositional generalization. To overcome the defects, we propose a new symbolic system with two ideal important properties: broad-coverage symbols and rational rules. Collecting massive human knowledge via manual annotations is expensive to instantiate this symbolic system. Instead, we leverage the recent advancement of LLMs (Large Language Models) as an approximation of the two ideal properties, i.e., Symbols from Large Language Models (Symbol-LLM). Then, given an image, visual contents from the images are extracted and checked as symbols and activity semantics are reasoned out based on rules via fuzzy logic calculation. Our method shows superiority in extensive activity understanding tasks. Code and data are available at https://mvig-rhos.com/symbol_llm.

This report overviews our ongoing work in enriching chain-of-thoughts datasets requiring arithmetical reasoning with the integration of non-parametric components, such as a calculator. We conduct an analysis of prominent relevant datasets such as GSM8K, Ape210K, AQuA-RAT, and MathQA and propose a machine-processable HTML-like format specifically tailored for working with semi-structured chains. By converting the datasets into this unified format, we enable the effective integration of large language models and symbolic systems, empowering them to tackle arithmetical reasoning tasks more efficiently.

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 .

Large Language Models (LLMs) excel in complex reasoning tasks but struggle with consistent rule application, exception handling, and explainability, particularly in domains like legal analysis that require both natural language understanding and precise logical inference. This paper introduces a structured prompting framework that decomposes reasoning into three verifiable steps: entity identification, property extraction, and symbolic rule application. By integrating neural and symbolic approaches, our method leverages LLMs' interpretive flexibility while ensuring logical consistency through formal verification. The framework externalizes task definitions, enabling domain experts to refine logical structures without altering the architecture. Evaluated on the LegalBench hearsay determination task, our approach significantly outperformed baselines, with OpenAI o-family models showing substantial improvements - o1 achieving an F1 score of 0.929 and o3-mini reaching 0.867 using structured decomposition with complementary predicates, compared to their few-shot baselines of 0.714 and 0.74 respectively. This hybrid neural-symbolic system offers a promising pathway for transparent and consistent rule-based reasoning, suggesting potential for explainable AI applications in structured legal reasoning tasks.

This paper addresses the problem of autonomous UAV search missions, where a UAV must locate specific Entities of Interest (EOIs) within a time limit, based on brief descriptions in large, hazard-prone environments with keep-out zones. The UAV must perceive, reason, and make decisions with limited and uncertain information. We propose NEUSIS, a compositional neuro-symbolic system designed for interpretable UAV search and navigation in realistic scenarios. NEUSIS integrates neuro-symbolic visual perception, reasoning, and grounding (GRiD) to process raw sensory inputs, maintains a probabilistic world model for environment representation, and uses a hierarchical planning component (SNaC) for efficient path planning. Experimental results from simulated urban search missions using AirSim and Unreal Engine show that NEUSIS outperforms a state-of-the-art (SOTA) vision-language model and a SOTA search planning model in success rate, search efficiency, and 3D localization. These results demonstrate the effectiveness of our compositional neuro-symbolic approach in handling complex, real-world scenarios, making it a promising solution for autonomous UAV systems in search missions.

As mathematical computing becomes more democratized in high-level languages, high-performance symbolic-numeric systems are necessary for domain scientists and engineers to get the best performance out of their machine without deep knowledge of code optimization. Naturally, users need different term types either to have different algebraic properties for them, or to use efficient data structures. To this end, we developed Symbolics.jl, an extendable symbolic system which uses dynamic multiple dispatch to change behavior depending on the domain needs. In this work we detail an underlying abstract term interface which allows for speed without sacrificing generality. We show that by formalizing a generic API on actions independent of implementation, we can retroactively add optimized data structures to our system without changing the pre-existing term rewriters. We showcase how this can be used to optimize term construction and give a 113x acceleration on general symbolic transformations. Further, we show that such a generic API allows for complementary term-rewriting implementations. We demonstrate the ability to swap between classical term-rewriting simplifiers and e-graph-based term-rewriting simplifiers. We showcase an e-graph ruleset which minimizes the number of CPU cycles during expression evaluation, and demonstrate how it simplifies a real-world reaction-network simulation to halve the runtime. Additionally, we show a reaction-diffusion partial differential equation solver which is able to be automatically converted into symbolic expressions via multiple dispatch tracing, which is subsequently accelerated and parallelized to give a 157x simulation speedup. Together, this presents Symbolics.jl as a next-generation symbolic-numeric computing environment geared towards modeling and simulation.

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.

Recent advances in Multimodal Large Language Models (MLLMs) have achieved remarkable progress in general domains and demonstrated promise in multimodal mathematical reasoning. However, applying MLLMs to geometry problem solving (GPS) remains challenging due to lack of accurate step-by-step solution data and severe hallucinations during reasoning. In this paper, we propose GeoGen, a pipeline that can automatically generates step-wise reasoning paths for geometry diagrams. By leveraging the precise symbolic reasoning, GeoGen produces large-scale, high-quality question-answer pairs. To further enhance the logical reasoning ability of MLLMs, we train GeoLogic, a Large Language Model (LLM) using synthetic data generated by GeoGen. Serving as a bridge between natural language and symbolic systems, GeoLogic enables symbolic tools to help verifying MLLM outputs, making the reasoning process more rigorous and alleviating hallucinations. Experimental results show that our approach consistently improves the performance of MLLMs, achieving remarkable results on benchmarks for geometric reasoning tasks. This improvement stems from our integration of the strengths of LLMs and symbolic systems, which enables a more reliable and interpretable approach for the GPS task. Codes are available at https://github.com/ycpNotFound/GeoGen.

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

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

This paper demonstrates that artificial intelligence can accelerate mathematical discovery by autonomously solving an open problem in theoretical physics. We present a neuro-symbolic system, combining the Gemini Deep Think large language model with a systematic Tree Search (TS) framework and automated numerical feedback, that successfully derived novel, exact analytical solutions for the power spectrum of gravitational radiation emitted by cosmic strings. Specifically, the agent evaluated the core integral I(N,α) for arbitrary loop geometries, directly improving upon recent AI-assisted attempts BCE+25 that only yielded partial asymptotic solutions. To substantiate our methodological claims regarding AI-accelerated discovery and to ensure transparency, we detail system prompts, search constraints, and intermittent feedback loops that guided the model. The agent identified a suite of 6 different analytical methods, the most elegant of which expands the kernel in Gegenbauer polynomials C_l^{(3/2)} to naturally absorb the integrand's singularities. The methods lead to an asymptotic result for I(N,α) at large N that both agrees with numerical results and also connects to the continuous Feynman parameterization of Quantum Field Theory. We detail both the algorithmic methodology that enabled this discovery and the resulting mathematical derivations.

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).

Premise selection is a fundamental problem of automated theorem proving. Previous works often use intricate symbolic methods, rely on domain knowledge, and require significant engineering effort to solve this task. In this work, we show that Magnushammer, a neural transformer-based approach, can outperform traditional symbolic systems by a large margin. Tested on the PISA benchmark, Magnushammer achieves 59.5% proof rate compared to a 38.3% proof rate of Sledgehammer, the most mature and popular symbolic-based solver. Furthermore, by combining Magnushammer with a neural formal prover based on a language model, we significantly improve the previous state-of-the-art proof rate from 57.0% to 71.0%.

Knowledge engineering is a discipline that focuses on the creation and maintenance of processes that generate and apply knowledge. Traditionally, knowledge engineering approaches have focused on knowledge expressed in formal languages. The emergence of large language models and their capabilities to effectively work with natural language, in its broadest sense, raises questions about the foundations and practice of knowledge engineering. Here, we outline the potential role of LLMs in knowledge engineering, identifying two central directions: 1) creating hybrid neuro-symbolic knowledge systems; and 2) enabling knowledge engineering in natural language. Additionally, we formulate key open research questions to tackle these directions.

While reasoning models (e.g., DeepSeek R1) trained with reinforcement learning (RL), excel in textual reasoning, they struggle in scenarios requiring structured problem-solving, such as geometric reasoning, concise computation, or complex equation solving-areas where computational tools like code interpreters (CI) demonstrate distinct advantages. To bridge this gap, we propose ReTool, which enhances long-form reasoning with tool-integrated learning, including two key features: (1) dynamic interleaving of real-time code execution within natural language reasoning processes, and (2) an automated RL paradigm that allows policy rollouts with multi-turn real-time code execution and teaches the model in learning when and how to invoke tools based on outcome feedback. ReTool employs a systematic training framework, beginning with synthetic cold-start data generation to produce code-augmented long-form reasoning traces for fine-tuning base models. Subsequent RL training leverages task outcomes as rewards to iteratively refine the model's tool use strategy, enabling autonomous discovery of optimal tool invocation patterns without human priors. Experiments on the challenging MATH Olympiad benchmark AIME demonstrate ReTool's superiority: Our 32B model achieves 67% accuracy with 400 training steps, outperforming text-based RL baseline (40% accuracy, 1080 steps) in efficiency and performance. Remarkably, ReTool-32B attains 72.5% accuracy in extended settings, surpassing OpenAI's o1-preview by 27.9%. Further analysis reveals emergent behaviors such as code self-correction, signaling an ''aha moment'' in which the model autonomously masters adaptive tool use. These findings highlight the promise of outcome-driven tool integration for advancing complex mathematical reasoning and offer new insights into hybrid neuro-symbolic systems.

AI for Mathematics (AI4Math) has emerged as a distinct field that leverages machine learning to navigate mathematical landscapes historically intractable for early symbolic systems. While mid-20th-century symbolic approaches successfully automated formal logic, they faced severe scalability limitations due to the combinatorial explosion of the search space. The recent integration of data-driven approaches has revitalized this pursuit. In this review, we provide a systematic overview of AI4Math, highlighting its primary focus on developing AI models to support mathematical research. Crucially, we emphasize that this is not merely the application of AI to mathematical activities; it also encompasses the development of stronger AI systems where the rigorous nature of mathematics serves as a premier testbed for advancing general reasoning capabilities. We categorize existing research into two complementary directions: problem-specific modeling, involving the design of specialized architectures for distinct mathematical tasks, and general-purpose modeling, focusing on foundation models capable of broader reasoning, retrieval, and exploratory workflows. We conclude by discussing key challenges and prospects, advocating for AI systems that go beyond facilitating formal correctness to enabling the discovery of meaningful results and unified theories, recognizing that the true value of a proof lies in the insights and tools it offers to the broader mathematical landscape.

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

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

Large Language Models (LLMs) show remarkable capabilities, yet their stochastic next-token prediction creates logical inconsistencies and reward hacking that formal symbolic systems avoid. To bridge this gap, we introduce a formal logic verification-guided framework that dynamically interleaves formal symbolic verification with the natural language generation process, providing real-time feedback to detect and rectify errors as they occur. Distinguished from previous neuro-symbolic methods limited by passive post-hoc validation, our approach actively penalizes intermediate fallacies during the reasoning chain. We operationalize this framework via a novel two-stage training pipeline that synergizes formal logic verification-guided supervised fine-tuning and policy optimization. Extensive evaluation on six benchmarks spanning mathematical, logical, and general reasoning demonstrates that our 7B and 14B models outperform state-of-the-art baselines by average margins of 10.4% and 14.2%, respectively. These results validate that formal verification can serve as a scalable mechanism to significantly push the performance boundaries of advanced LLM reasoning.

Automating the translation of natural language to first-order logic (FOL) is crucial for knowledge representation and formal methods, yet remains challenging. We present a systematic evaluation of fine-tuned LLMs for this task, comparing architectures (encoder-decoder vs. decoder-only) and training strategies. Using the MALLS and Willow datasets, we explore techniques like vocabulary extension, predicate conditioning, and multilingual training, introducing metrics for exact match, logical equivalence, and predicate alignment. Our fine-tuned Flan-T5-XXL achieves 70% accuracy with predicate lists, outperforming GPT-4o and even the DeepSeek-R1-0528 model with CoT reasoning ability as well as symbolic systems like ccg2lambda. Key findings show: (1) predicate availability boosts performance by 15-20%, (2) T5 models surpass larger decoder-only LLMs, and (3) models generalize to unseen logical arguments (FOLIO dataset) without specific training. While structural logic translation proves robust, predicate extraction emerges as the main bottleneck.

Abstract symbolic writing systems are semiotic codes that are ubiquitous in modern society but are otherwise absent in the animal kingdom. Anthropological evidence suggests that the earliest forms of some writing systems originally consisted of iconic pictographs, which signify their referent via visual resemblance. While previous studies have examined the emergence and, separately, the evolution of pictographic writing systems through a computational lens, most employ non-naturalistic methodologies that make it difficult to draw clear analogies to human and animal cognition. We develop a multi-agent reinforcement learning testbed for emergent communication called a Signification Game, and formulate a model of inferential communication that enables agents to leverage visual theory of mind to communicate actions using pictographs. Our model, which is situated within a broader formalism for animal communication, sheds light on the cognitive and cultural processes that led to the development of early writing systems.

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.

LLMs can solve program synthesis tasks but remain inefficient and unreliable on hard instances requiring large combinatorial search. Given a small set of reasoning traces, we use coding agents to compile them into reusable symbolic program synthesizers over constrained DSLs. The resulting solvers require no LLM calls at test time and are strong standalone systems: symbolic solver ensembles reach 91.3% accuracy on PBEBench-Lite and 84.7% on PBEBench-Hard, outperforming LLMs with test-time scaling for the latter by +16.3 percentage points at zero LLM inference cost. They also complement LLM search, improving PBEBench-Hard accuracy from 68.4% to 85.8% while reducing reported token usage by 78%, and raising SLR-Bench hard-tier accuracy from 34.4% to 58.0% in a neuro-symbolic hybrid setting. Compared to directly using coding agents as per-instance solvers, induced solvers are substantially more Pareto-efficient, amortizing a small one-time construction cost over many zero-token executions. Finally, most solvers transfer zero-shot to a real historical linguistics task - predicting sound changes in natural language data - reaching 80.1% accuracy under ensembling and recovering some plausible linguistic rules. Together, these results show that reasoning traces can be compiled into reusable symbolic solvers that solve many tasks directly, complement LLM inference on hard cases, and provide a scalable route to domain-general solver induction. We release code and data for reproducibility.

Current 3D spatial reasoning methods face a fundamental trade-off: neuro-symbolic 3D (NS3D) concept learners achieve interpretable reasoning through compositional programs but are constrained to closed-set concept vocabularies and simple programs; end-to-end 3D multi-modal LLMs (3D MLLMs) could handle complex natural language and open-vocabulary concepts but suffer from black-box reasoning without explicit spatial verification. We introduce APEIRIA, a neuro-symbolic 3D MLLM to bridge two paradigms by distilling symbolic reasoning patterns into MLLMs with natural language chain-of-thought. Our three-stage curriculum progressively builds reasoning capabilities: a) 3D perception alignment grounds object visual-geometric features to the LLM, b) CoT-SFT teaches query decomposition and stepwise verification from symbolic program traces, and c) CoT-RL extends reasoning patterns to open-set concepts and deeply nested instructions. By transferring reasoning patterns rather than concept-specific knowledge, APEIRIA preserves key NS3D virtues: transparent reasoning and modular interchangeability of planning and perception components. Evaluations on grounding, question answering, and captioning show that APEIRIA surpasses prior NS3D methods and matches state-of-the-art 3D MLLMs on 3D spatial reasoning datasets, unifying symbolic methods' systematic reasoning with MLLMs' flexibility. Code is available at https://github.com/oceanflowlab/APEIRIA.

Large language models (LLMs) are rapidly approaching the level of proficiency in university-level symbolic mathematics required for applications in advanced science and technology. However, existing benchmarks fall short in assessing the core skills of LLMs in symbolic mathematics-such as integration, differential equations, and algebraic simplification. To address this gap, we introduce ASyMOB, a novel assessment framework focused exclusively on symbolic manipulation, featuring 17,092 unique math challenges, organized by similarity and complexity. ASyMOB enables analysis of LLM generalization capabilities by comparing performance in problems that differ by simple numerical or symbolic `perturbations'. Evaluated LLMs exhibit substantial degradation in performance for all perturbation types (up to -70.3%), suggesting reliance on memorized patterns rather than deeper understanding of symbolic math, even among models achieving high baseline accuracy. Comparing LLM performance to computer algebra systems, we identify examples where they fail while LLMs succeed, as well as problems solved only by combining both approaches. Models capable of integrated code execution yielded higher accuracy compared to their performance without code, particularly stabilizing weaker models (up to +33.1% for certain perturbation types). Notably, the most advanced models (o4-mini, Gemini 2.5 Flash) demonstrate not only high symbolic math proficiency (scoring 96.8% and 97.6% on the unperturbed set), but also remarkable robustness against perturbations, (-21.7% and -21.2% vs. average -50.4% for the other models). This may indicate a recent "phase transition" in the generalization capabilities of frontier LLMs. It remains to be seen whether the path forward lies in deeper integration with sophisticated external tools, or in developing models so capable that symbolic math systems like CAS become unnecessary.

I introduce a novel mathematical framework integrating topological dynamics, operator algebras, and ergodic geometry to study lattices of asynchronous metric dynamical systems. Each node in the lattice carries an internal flow represented by a one-parameter family of operators, evolving on its own time scale. I formalize stratified state spaces capturing multiple levels of synchronized behavior, define an asynchronous evolution metric that quantifies phase-offset distances between subsystems, and characterize emergent coherent topologies arising when subsystems synchronize. Within this framework, I develop formal operators for the evolution of each subsystem and give precise conditions under which phase-aligned synchronization occurs across the lattice. The main results include: (1) the existence and uniqueness of coherent (synchronized) states under a contractive coupling condition, (2) stability of these coherent states and criteria for their emergence as a collective phase transition in a continuous operator topology, and (3) the influence of symmetries, with group-invariant coupling leading to flow-invariant synchrony subspaces and structured cluster dynamics. Proofs are given for each theorem, demonstrating full mathematical rigor. In a final section, I discuss hypothetical applications of this framework to symbolic lattice systems (e.g. subshifts), to invariant group actions on dynamical lattices, and to operator fields over stratified manifolds in the spirit of noncommutative geometry. Throughout, I write in the first person to emphasize the exploratory nature of this work. The paper avoids any reference to cosmology or observers, focusing instead on clean, formal mathematics suitable for a broad array of dynamical systems.

Large language models (LLMs) are highly capable at language generation, but they remain unreliable when reasoning requires explicit symbolic structure, multi-step inference, and interpretable uncertainty. This paper presents a neuro-symbolic framework for translating natural-language reasoning problems into executable formal representations using first-order logic (FOL) and Narsese, the language of the Non-Axiomatic Reasoning System (NARS). To support this direction, we introduce NARS-Reasoning-v0.1, a benchmark of natural-language reasoning problems paired with FOL forms, executable Narsese programs, and three gold labels: True, False, and Uncertain. We develop a deterministic compilation pipeline from FOL to executable Narsese and validate retained examples through runtime execution in OpenNARS for Applications (ONA), ensuring that the symbolic targets are not only syntactically well formed but also behaviorally aligned with the intended answer. We further present Language-Structured Perception (LSP), a formulation in which an LLM is trained to produce reasoning-relevant symbolic structure rather than only a final verbal response. As an initial proof of concept, we also train and release a Phi-2 LoRA adapter on NARS-Reasoning-v0.1 for three-label reasoning classification, showing that the benchmark can support supervised adaptation in addition to executable evaluation. Overall, the paper positions executable symbolic generation and execution-based validation as a practical path toward more reliable neuro-symbolic reasoning systems.

Chord progression generation is practically important but understudied. Most large-scale symbolic music systems target melody, multi-track arrangement, or audio synthesis, and chord-only models tend to be relegated to conditioning components inside larger pipelines. This paper treats chord generation as a standalone task and addresses a question that arises whenever such a model is adapted across genres: how much old-domain data must be retained during fine-tuning to acquire a new domain without forgetting the old? I study jazz fine-tuning starting from a pop-pretrained 25M-parameter Music Transformer (84.24% top-1 chord accuracy on a held-out pop test set). The available jazz corpus is an order of magnitude smaller than the pop corpus, so every fine-tune run uses all 1,513 jazz training sequences. The swept variable is the volume of pop "rehearsal" data mixed alongside, taking values in {0, 1K, 2.5K, 5K, 10K}. Every fine-tuned model gains 7 to 9 points of jazz top-1. Pop accuracy collapses by 2.14 points under jazz-only fine-tuning, recovers to baseline at approximately 2.5K rehearsal samples (1.65x the jazz volume), and saturates beyond that point. A complementary observation: the metric-best run (F3, 2.5K mix) is not always the perceptually preferred one. The pop-leaning (10K) and jazz-leaning (1K) endpoints carry more committed stylistic identities that the author more often selects as finished output in informal listening. I discuss what this suggests for music co-creation tools but make no perceptual claim, since no formal listening study has been conducted. All six checkpoints are released on the HuggingFace Hub at https://huggingface.co/PearlLeeStudio.

Large Language Models (LLMs) are transforming scientific hypothesis generation and validation by enabling information synthesis, latent relationship discovery, and reasoning augmentation. This survey provides a structured overview of LLM-driven approaches, including symbolic frameworks, generative models, hybrid systems, and multi-agent architectures. We examine techniques such as retrieval-augmented generation, knowledge-graph completion, simulation, causal inference, and tool-assisted reasoning, highlighting trade-offs in interpretability, novelty, and domain alignment. We contrast early symbolic discovery systems (e.g., BACON, KEKADA) with modern LLM pipelines that leverage in-context learning and domain adaptation via fine-tuning, retrieval, and symbolic grounding. For validation, we review simulation, human-AI collaboration, causal modeling, and uncertainty quantification, emphasizing iterative assessment in open-world contexts. The survey maps datasets across biomedicine, materials science, environmental science, and social science, introducing new resources like AHTech and CSKG-600. Finally, we outline a roadmap emphasizing novelty-aware generation, multimodal-symbolic integration, human-in-the-loop systems, and ethical safeguards, positioning LLMs as agents for principled, scalable scientific discovery.

Rule extraction is a central problem in interpretable machine learning because it seeks to convert opaque predictive behavior into human-readable symbolic structure. This paper presents Chat Incremental Pattern Constructor (ChatIPC), a lightweight incremental symbolic learning system that extracts ordered token-transition rules from text, enriches them with definition based expansion, and constructs responses by similarity-guided candidate selection. The system may be viewed as a rule extractor operating over a token graph rather than a conventional classifier. I formalize the knowledge base, definition expansion, candidate scoring, repetition control, and response construction mechanisms used in ChatIPC. I further situate the method within the literature on rule extraction, decision tree induction, association rules, and interpretable sequence modeling. The paper emphasizes mathematical formulation and algorithmic clarity, and it provides pseudocode for the learning and construction pipeline.

This paper introduces a new metamodel-based knowledge representation that significantly improves autonomous learning and adaptation. While interest in hybrid machine learning / symbolic AI systems leveraging, for example, reasoning and knowledge graphs, is gaining popularity, we find there remains a need for both a clear definition of knowledge and a metamodel to guide the creation and manipulation of knowledge. Some of the benefits of the metamodel we introduce in this paper include a solution to the symbol grounding problem, cumulative learning, and federated learning. We have applied the metamodel to problems ranging from time series analysis, computer vision, and natural language understanding and have found that the metamodel enables a wide variety of learning mechanisms ranging from machine learning, to graph network analysis and learning by reasoning engines to interoperate in a highly synergistic way. Our metamodel-based projects have consistently exhibited unprecedented accuracy, performance, and ability to generalize. This paper is inspired by the state-of-the-art approaches to AGI, recent AGI-aspiring work, the granular computing community, as well as Alfred Korzybski's general semantics. One surprising consequence of the metamodel is that it not only enables a new level of autonomous learning and optimal functioning for machine intelligences, but may also shed light on a path to better understanding how to improve human cognition.

Although Answer Set Programming (ASP) allows constraining neural-symbolic (NeSy) systems, its employment is hindered by the prohibitive costs of computing stable models and the CPU-bound nature of state-of-the-art solvers. To this end, we propose Answer Set Networks (ASN), a NeSy solver. Based on Graph Neural Networks (GNN), ASNs are a scalable approach to ASP-based Deep Probabilistic Logic Programming (DPPL). Specifically, we show how to translate ASPs into ASNs and demonstrate how ASNs can efficiently solve the encoded problem by leveraging GPU's batching and parallelization capabilities. Our experimental evaluations demonstrate that ASNs outperform state-of-the-art CPU-bound NeSy systems on multiple tasks. Simultaneously, we make the following two contributions based on the strengths of ASNs. Namely, we are the first to show the finetuning of Large Language Models (LLM) with DPPLs, employing ASNs to guide the training with logic. Further, we show the "constitutional navigation" of drones, i.e., encoding public aviation laws in an ASN for routing Unmanned Aerial Vehicles in uncertain environments.

While large language models (LLMs) now excel at code generation, a key aspect of software development is the art of refactoring: consolidating code into libraries of reusable and readable programs. In this paper, we introduce LILO, a neurosymbolic framework that iteratively synthesizes, compresses, and documents code to build libraries tailored to particular problem domains. LILO combines LLM-guided program synthesis with recent algorithmic advances in automated refactoring from Stitch: a symbolic compression system that efficiently identifies optimal lambda abstractions across large code corpora. To make these abstractions interpretable, we introduce an auto-documentation (AutoDoc) procedure that infers natural language names and docstrings based on contextual examples of usage. In addition to improving human readability, we find that AutoDoc boosts performance by helping LILO's synthesizer to interpret and deploy learned abstractions. We evaluate LILO on three inductive program synthesis benchmarks for string editing, scene reasoning, and graphics composition. Compared to existing neural and symbolic methods - including the state-of-the-art library learning algorithm DreamCoder - LILO solves more complex tasks and learns richer libraries that are grounded in linguistic knowledge.

Artificial Intelligence (AI) has made incredible progress recently. On the one hand, advanced foundation models like ChatGPT can offer powerful conversation, in-context learning and code generation abilities on a broad range of open-domain tasks. They can also generate high-level solution outlines for domain-specific tasks based on the common sense knowledge they have acquired. However, they still face difficulties with some specialized tasks because they lack enough domain-specific data during pre-training or they often have errors in their neural network computations on those tasks that need accurate executions. On the other hand, there are also many existing models and systems (symbolic-based or neural-based) that can do some domain-specific tasks very well. However, due to the different implementation or working mechanisms, they are not easily accessible or compatible with foundation models. Therefore, there is a clear and pressing need for a mechanism that can leverage foundation models to propose task solution outlines and then automatically match some of the sub-tasks in the outlines to the off-the-shelf models and systems with special functionalities to complete them. Inspired by this, we introduce TaskMatrix.AI as a new AI ecosystem that connects foundation models with millions of APIs for task completion. Unlike most previous work that aimed to improve a single AI model, TaskMatrix.AI focuses more on using existing foundation models (as a brain-like central system) and APIs of other AI models and systems (as sub-task solvers) to achieve diversified tasks in both digital and physical domains. As a position paper, we will present our vision of how to build such an ecosystem, explain each key component, and use study cases to illustrate both the feasibility of this vision and the main challenges we need to address next.

We introduce ODEFormer, the first transformer able to infer multidimensional ordinary differential equation (ODE) systems in symbolic form from the observation of a single solution trajectory. We perform extensive evaluations on two datasets: (i) the existing "Strogatz" dataset featuring two-dimensional systems; (ii) ODEBench, a collection of one- to four-dimensional systems that we carefully curated from the literature to provide a more holistic benchmark. ODEFormer consistently outperforms existing methods while displaying substantially improved robustness to noisy and irregularly sampled observations, as well as faster inference. We release our code, model and benchmark dataset publicly.

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

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

Current video analytics approaches face a fundamental trade-off between flexibility and efficiency. End-to-end Vision Language Models (VLMs) often struggle with long-context processing and incur high computational costs, while neural-symbolic methods depend heavily on manual labeling and rigid rule design. In this paper, we introduce LazyVLM, a neuro-symbolic video analytics system that provides a user-friendly query interface similar to VLMs, while addressing their scalability limitation. LazyVLM enables users to effortlessly drop in video data and specify complex multi-frame video queries using a semi-structured text interface for video analytics. To address the scalability limitations of VLMs, LazyVLM decomposes multi-frame video queries into fine-grained operations and offloads the bulk of the processing to efficient relational query execution and vector similarity search. We demonstrate that LazyVLM provides a robust, efficient, and user-friendly solution for querying open-domain video data at scale.

This paper presents an integrated system that transforms symbolic music scores into expressive piano performance audio. By combining a Transformer-based Expressive Performance Rendering (EPR) model with a fine-tuned neural MIDI synthesiser, our approach directly generates expressive audio performances from score inputs. To the best of our knowledge, this is the first system to offer a streamlined method for converting score MIDI files lacking expression control into rich, expressive piano performances. We conducted experiments using subsets of the ATEPP dataset, evaluating the system with both objective metrics and subjective listening tests. Our system not only accurately reconstructs human-like expressiveness, but also captures the acoustic ambience of environments such as concert halls and recording studios. Additionally, the proposed system demonstrates its ability to achieve musical expressiveness while ensuring good audio quality in its outputs.

Generating high quality music that complements the visual content of a video is a challenging task. Most existing visual conditioned music generation systems generate symbolic music data, such as MIDI files, instead of raw audio waveform. Given the limited availability of symbolic music data, such methods can only generate music for a few instruments or for specific types of visual input. In this paper, we propose a novel approach called V2Meow that can generate high-quality music audio that aligns well with the visual semantics of a diverse range of video input types. Specifically, the proposed music generation system is a multi-stage autoregressive model which is trained with a number of O(100K) music audio clips paired with video frames, which are mined from in-the-wild music videos, and no parallel symbolic music data is involved. V2Meow is able to synthesize high-fidelity music audio waveform solely conditioned on pre-trained visual features extracted from an arbitrary silent video clip, and it also allows high-level control over the music style of generation examples via supporting text prompts in addition to the video frames conditioning. Through both qualitative and quantitative evaluations, we demonstrate that our model outperforms several existing music generation systems in terms of both visual-audio correspondence and audio quality.

Indian classical music relies on a sophisticated microtonal system of 22 shrutis (pitch intervals), which provides expressive nuance beyond the 12-tone equal temperament system. Existing symbolic music processing tools fail to account for these microtonal distinctions and culturally specific raga grammars that govern melodic movement. We present ShrutiSense, a comprehensive symbolic pitch processing system designed for Indian classical music, addressing two critical tasks: (1) correcting westernized or corrupted pitch sequences, and (2) completing melodic sequences with missing values. Our approach employs complementary models for different tasks: a Shruti-aware finite-state transducer (FST) that performs contextual corrections within the 22-shruti framework and a grammar-constrained Shruti hidden Markov model (GC-SHMM) that incorporates raga-specific transition rules for contextual completions. Comprehensive evaluation on simulated data across five ragas demonstrates that ShrutiSense (FST model) achieves 91.3% shruti classification accuracy for correction tasks, with example sequences showing 86.7-90.0% accuracy at corruption levels of 0.2 to 0.4. The system exhibits robust performance under pitch noise up to +/-50 cents, maintaining consistent accuracy across ragas (90.7-91.8%), thus preserving the cultural authenticity of Indian classical music expression.

Software is prone to security vulnerabilities. Program analysis tools to detect them have limited effectiveness in practice due to their reliance on human labeled specifications. Large language models (or LLMs) have shown impressive code generation capabilities but they cannot do complex reasoning over code to detect such vulnerabilities especially since this task requires whole-repository analysis. We propose IRIS, a neuro-symbolic approach that systematically combines LLMs with static analysis to perform whole-repository reasoning for security vulnerability detection. Specifically, IRIS leverages LLMs to infer taint specifications and perform contextual analysis, alleviating needs for human specifications and inspection. For evaluation, we curate a new dataset, CWE-Bench-Java, comprising 120 manually validated security vulnerabilities in real-world Java projects. A state-of-the-art static analysis tool CodeQL detects only 27 of these vulnerabilities whereas IRIS with GPT-4 detects 55 (+28) and improves upon CodeQL's average false discovery rate by 5% points. Furthermore, IRIS identifies 4 previously unknown vulnerabilities which cannot be found by existing tools. IRIS is available publicly at https://github.com/iris-sast/iris.

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.

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.

Dynamical systems (DS) theory is fundamental for many areas of science and engineering. It can provide deep insights into the behavior of systems evolving in time, as typically described by differential or recursive equations. A common approach to facilitate mathematical tractability and interpretability of DS models involves decomposing nonlinear DS into multiple linear DS separated by switching manifolds, i.e. piecewise linear (PWL) systems. PWL models are popular in engineering and a frequent choice in mathematics for analyzing the topological properties of DS. However, hand-crafting such models is tedious and only possible for very low-dimensional scenarios, while inferring them from data usually gives rise to unnecessarily complex representations with very many linear subregions. Here we introduce Almost-Linear Recurrent Neural Networks (AL-RNNs) which automatically and robustly produce most parsimonious PWL representations of DS from time series data, using as few PWL nonlinearities as possible. AL-RNNs can be efficiently trained with any SOTA algorithm for dynamical systems reconstruction (DSR), and naturally give rise to a symbolic encoding of the underlying DS that provably preserves important topological properties. We show that for the Lorenz and R\"ossler systems, AL-RNNs discover, in a purely data-driven way, the known topologically minimal PWL representations of the corresponding chaotic attractors. We further illustrate on two challenging empirical datasets that interpretable symbolic encodings of the dynamics can be achieved, tremendously facilitating mathematical and computational analysis of the underlying systems.

Engineering design operates through hierarchical abstraction from system specifications to component implementations, requiring visual understanding coupled with mathematical reasoning at each level. While Multi-modal Large Language Models (MLLMs) excel at natural image tasks, their ability to extract mathematical models from technical diagrams remains unexplored. We present CircuitSense, a comprehensive benchmark evaluating circuit understanding across this hierarchy through 8,006+ problems spanning component-level schematics to system-level block diagrams. Our benchmark uniquely examines the complete engineering workflow: Perception, Analysis, and Design, with a particular emphasis on the critical but underexplored capability of deriving symbolic equations from visual inputs. We introduce a hierarchical synthetic generation pipeline consisting of a grid-based schematic generator and a block diagram generator with auto-derived symbolic equation labels. Comprehensive evaluation of six state-of-the-art MLLMs, including both closed-source and open-source models, reveals fundamental limitations in visual-to-mathematical reasoning. Closed-source models achieve over 85\% accuracy on perception tasks involving component recognition and topology identification, yet their performance on symbolic derivation and analytical reasoning falls below 19\%, exposing a critical gap between visual parsing and symbolic reasoning. Models with stronger symbolic reasoning capabilities consistently achieve higher design task accuracy, confirming the fundamental role of mathematical understanding in circuit synthesis and establishing symbolic reasoning as the key metric for engineering competence.

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

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.

The coronavirus disease (COVID-19) has resulted in a pandemic crippling the a breadth of services critical to daily life. Segmentation of lung infections in computerized tomography (CT) slices could be be used to improve diagnosis and understanding of COVID-19 in patients. Deep learning systems lack interpretability because of their black box nature. Inspired by human communication of complex ideas through language, we propose a symbolic framework based on emergent languages for the segmentation of COVID-19 infections in CT scans of lungs. We model the cooperation between two artificial agents - a Sender and a Receiver. These agents synergistically cooperate using emergent symbolic language to solve the task of semantic segmentation. Our game theoretic approach is to model the cooperation between agents unlike Generative Adversarial Networks (GANs). The Sender retrieves information from one of the higher layers of the deep network and generates a symbolic sentence sampled from a categorical distribution of vocabularies. The Receiver ingests the stream of symbols and cogenerates the segmentation mask. A private emergent language is developed that forms the communication channel used to describe the task of segmentation of COVID infections. We augment existing state of the art semantic segmentation architectures with our symbolic generator to form symbolic segmentation models. Our symbolic segmentation framework achieves state of the art performance for segmentation of lung infections caused by COVID-19. Our results show direct interpretation of symbolic sentences to discriminate between normal and infected regions, infection morphology and image characteristics. We show state of the art results for segmentation of COVID-19 lung infections in CT.

Generating music from text descriptions is a user-friendly mode since the text is a relatively easy interface for user engagement. While some approaches utilize texts to control music audio generation, editing musical elements in generated audio is challenging for users. In contrast, symbolic music offers ease of editing, making it more accessible for users to manipulate specific musical elements. In this paper, we propose MuseCoco, which generates symbolic music from text descriptions with musical attributes as the bridge to break down the task into text-to-attribute understanding and attribute-to-music generation stages. MuseCoCo stands for Music Composition Copilot that empowers musicians to generate music directly from given text descriptions, offering a significant improvement in efficiency compared to creating music entirely from scratch. The system has two main advantages: Firstly, it is data efficient. In the attribute-to-music generation stage, the attributes can be directly extracted from music sequences, making the model training self-supervised. In the text-to-attribute understanding stage, the text is synthesized and refined by ChatGPT based on the defined attribute templates. Secondly, the system can achieve precise control with specific attributes in text descriptions and offers multiple control options through attribute-conditioned or text-conditioned approaches. MuseCoco outperforms baseline systems in terms of musicality, controllability, and overall score by at least 1.27, 1.08, and 1.32 respectively. Besides, there is a notable enhancement of about 20% in objective control accuracy. In addition, we have developed a robust large-scale model with 1.2 billion parameters, showcasing exceptional controllability and musicality.

The Scholarly Question Answering over Linked Data (Scholarly QALD) at The International Semantic Web Conference (ISWC) 2023 challenge presents two sub-tasks to tackle question answering (QA) over knowledge graphs (KGs). We answer the KGQA over DBLP (DBLP-QUAD) task by proposing a neuro-symbolic (NS) framework based on PSYCHIC, an extractive QA model capable of identifying the query and entities related to a KG question. Our system achieved a F1 score of 00.18% on question answering and came in third place for entity linking (EL) with a score of 71.00%.

The unprecedented surge in video data production in recent years necessitates efficient tools to extract meaningful frames from videos for downstream tasks. Long-term temporal reasoning is a key desideratum for frame retrieval systems. While state-of-the-art foundation models, like VideoLLaMA and ViCLIP, are proficient in short-term semantic understanding, they surprisingly fail at long-term reasoning across frames. A key reason for this failure is that they intertwine per-frame perception and temporal reasoning into a single deep network. Hence, decoupling but co-designing semantic understanding and temporal reasoning is essential for efficient scene identification. We propose a system that leverages vision-language models for semantic understanding of individual frames but effectively reasons about the long-term evolution of events using state machines and temporal logic (TL) formulae that inherently capture memory. Our TL-based reasoning improves the F1 score of complex event identification by 9-15% compared to benchmarks that use GPT4 for reasoning on state-of-the-art self-driving datasets such as Waymo and NuScenes.

To improve the performance and explainability of LLM-based natural language reasoning, structured reasoning can be applied to generate explicitly structured proofs. Among different methods for structured reasoning, we specifically focus on backward chaining, where the proof goal is recursively decomposed to subgoals by searching and applying rules. We argue that current LLM-based backward chaining systems (e.g. Least-to-most prompting and LAMBADA) are incomplete, as they omit crucial algorithmic components identified from the classic backward chaining algorithm in computational logic (SLD Resolution). To this end, we propose a novel backward chaining system, SymBa (Symbolic Backward Chaining), which integrates a symbolic solver and an LLM. In SymBa, the solver controls the proof process, and the LLM is only called when the solver requires new information to complete the proof. Empowered by completeness, SymBa achieves a significant improvement in seven deductive, relational, and arithmetic reasoning benchmarks compared to the baselines.

In this work, we present Score MUsic Graph (SMUG)-Explain, a framework for generating and visualizing explanations of graph neural networks applied to arbitrary prediction tasks on musical scores. Our system allows the user to visualize the contribution of input notes (and note features) to the network output, directly in the context of the musical score. We provide an interactive interface based on the music notation engraving library Verovio. We showcase the usage of SMUG-Explain on the task of cadence detection in classical music. All code is available on https://github.com/manoskary/SMUG-Explain.

We explore the use of large language models (LLMs) for music generation using a retrieval system to select relevant examples. We find promising initial results for music generation in a dialogue with the user, especially considering the ease with which such a system can be implemented. The code is available online.

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.

AI agents that interact with their environments through tools enable powerful applications, but in high-stakes business settings, unintended actions can cause unacceptable harm, such as privacy breaches and financial loss. Existing mitigations, such as training-based methods and neural guardrails, improve agent reliability but cannot provide guarantees. We study symbolic guardrails as a practical path toward strong safety and security guarantees for AI agents. Our three-part study includes a systematic review of 80 state-of-the-art agent safety and security benchmarks to identify the policies they evaluate, an analysis of which policy requirements can be guaranteed by symbolic guardrails, and an evaluation of how symbolic guardrails affect safety, security, and agent success on τ^2-Bench, CAR-bench, and MedAgentBench. We find that 85\% of benchmarks lack concrete policies, relying instead on underspecified high-level goals or common sense. Among the specified policies, 74\% of policy requirements can be enforced by symbolic guardrails, often using simple, low-cost mechanisms. These guardrails improve safety and security without sacrificing agent utility. Overall, our results suggest that symbolic guardrails are a practical and effective way to guarantee some safety and security requirements, especially for domain-specific AI agents. We release all codes and artifacts at https://github.com/hyn0027/agent-symbolic-guardrails.

Tokenization is the first - and often underappreciated - layer of computation in language models. While Chain-of-Thought (CoT) prompting enables transformer models to approximate recurrent computation by externalizing intermediate steps, we show that the success of such reasoning is fundamentally bounded by the structure of tokenized inputs. This work presents a theoretical and empirical investigation into how tokenization schemes, particularly subword-based methods like byte-pair encoding (BPE), impede symbolic computation by merging or obscuring atomic reasoning units. We introduce the notion of Token Awareness to formalize how poor token granularity disrupts logical alignment and prevents models from generalizing symbolic procedures. Through systematic evaluation on arithmetic and symbolic tasks, we demonstrate that token structure dramatically affect reasoning performance, causing failure even with CoT, while atomically-aligned formats unlock strong generalization, allowing small models (e.g., GPT-4o-mini) to outperform larger systems (e.g., o1) in structured reasoning. Our findings reveal that symbolic reasoning ability in LLMs is not purely architectural, but deeply conditioned on token-level representations.

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

This paper introduces text2midi, an end-to-end model to generate MIDI files from textual descriptions. Leveraging the growing popularity of multimodal generative approaches, text2midi capitalizes on the extensive availability of textual data and the success of large language models (LLMs). Our end-to-end system harnesses the power of LLMs to generate symbolic music in the form of MIDI files. Specifically, we utilize a pretrained LLM encoder to process captions, which then condition an autoregressive transformer decoder to produce MIDI sequences that accurately reflect the provided descriptions. This intuitive and user-friendly method significantly streamlines the music creation process by allowing users to generate music pieces using text prompts. We conduct comprehensive empirical evaluations, incorporating both automated and human studies, that show our model generates MIDI files of high quality that are indeed controllable by text captions that may include music theory terms such as chords, keys, and tempo. We release the code and music samples on our demo page (https://github.com/AMAAI-Lab/Text2midi) for users to interact with text2midi.

While the recent Chain-of-Thought (CoT) technique enhances the reasoning ability of large language models (LLMs) with the theory of mind, it might still struggle in handling logical reasoning that relies much on symbolic expressions and rigid deducing rules. To strengthen the logical reasoning capability of LLMs, we propose a novel Symbolic Chain-of-Thought, namely SymbCoT, a fully LLM-based framework that integrates symbolic expressions and logic rules with CoT prompting. Technically, building upon an LLM, SymbCoT 1) first translates the natural language context into the symbolic format, and then 2) derives a step-by-step plan to solve the problem with symbolic logical rules, 3) followed by a verifier to check the translation and reasoning chain. Via thorough evaluations on 5 standard datasets with both First-Order Logic and Constraint Optimization symbolic expressions, SymbCoT shows striking improvements over the CoT method consistently, meanwhile refreshing the current state-of-the-art performances. We further demonstrate that our system advances in more faithful, flexible, and explainable logical reasoning. To our knowledge, this is the first to combine symbolic expressions and rules into CoT for logical reasoning with LLMs. Code is open at https://github.com/Aiden0526/SymbCoT.

This technical report presents a new paradigm for full-song symbolic music generation. Existing symbolic models operate on note-attribute tokens and suffer from extremely long sequences, limited context length, and weak support for long-range structure. We address these issues by introducing PhraseVAE and PhraseLDM, the first latent diffusion framework designed for full-song multitrack symbolic music. PhraseVAE compresses an arbitrary variable-length polyphonic note sequence into a single compact 64-dimensional phrase-level latent representation with high reconstruction fidelity, allowing a well-structured latent space and efficient generative modeling. Built on this latent space, PhraseLDM generates an entire multi-track song in a single pass without any autoregressive components. The system eliminates bar-wise sequential modeling, supports up to 128 bars of music (8 minutes at 64 bpm), and produces complete songs with coherent local texture, idiomatic instrument patterns, and clear global structure. With only 45M parameters, our framework generates a full song within seconds while maintaining competitive musical quality and generation diversity. Together, these results show that phrase-level latent diffusion provides an effective and scalable solution to long-sequence modeling in symbolic music generation. We hope this work encourages future symbolic music research to move beyond note-attribute tokens and to consider phrase-level units as a more effective and musically meaningful modeling target.

Recent advances in Multimodal Large Language Models (MLLMs) have demonstrated impressive capabilities across various vision-language tasks. However, their reasoning abilities in the multimodal symbolic music domain remain largely unexplored. We introduce WildScore, the first in-the-wild multimodal symbolic music reasoning and analysis benchmark, designed to evaluate MLLMs' capacity to interpret real-world music scores and answer complex musicological queries. Each instance in WildScore is sourced from genuine musical compositions and accompanied by authentic user-generated questions and discussions, capturing the intricacies of practical music analysis. To facilitate systematic evaluation, we propose a systematic taxonomy, comprising both high-level and fine-grained musicological ontologies. Furthermore, we frame complex music reasoning as multiple-choice question answering, enabling controlled and scalable assessment of MLLMs' symbolic music understanding. Empirical benchmarking of state-of-the-art MLLMs on WildScore reveals intriguing patterns in their visual-symbolic reasoning, uncovering both promising directions and persistent challenges for MLLMs in symbolic music reasoning and analysis. We release the dataset and code.

Though end-to-end neural approaches have recently been dominating NLP tasks in both performance and ease-of-use, they lack interpretability and robustness. We propose Binder, a training-free neural-symbolic framework that maps the task input to a program, which (1) allows binding a unified API of language model (LM) functionalities to a programming language (e.g., SQL, Python) to extend its grammar coverage and thus tackle more diverse questions, (2) adopts an LM as both the program parser and the underlying model called by the API during execution, and (3) requires only a few in-context exemplar annotations. Specifically, we employ GPT-3 Codex as the LM. In the parsing stage, with only a few in-context exemplars, Codex is able to identify the part of the task input that cannot be answerable by the original programming language, correctly generate API calls to prompt Codex to solve the unanswerable part, and identify where to place the API calls while being compatible with the original grammar. In the execution stage, Codex can perform versatile functionalities (e.g., commonsense QA, information extraction) given proper prompts in the API calls. Binder achieves state-of-the-art results on WikiTableQuestions and TabFact datasets, with explicit output programs that benefit human debugging. Note that previous best systems are all finetuned on tens of thousands of task-specific samples, while Binder only uses dozens of annotations as in-context exemplars without any training. Our code is available at https://github.com/HKUNLP/Binder .

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

Pre-trained language models (LMs) have shown remarkable reasoning performance using explanations (or ``chain-of-thought'' (CoT)) for in-context learning. On the other hand, these reasoning tasks are usually presumed to be more approachable for symbolic programming. To make progress towards understanding in-context learning, we curate synthetic datasets containing equivalent (natural, symbolic) data pairs, where symbolic examples contain first-order logic rules and predicates from knowledge bases (KBs). Then we revisit neuro-symbolic approaches and use Language Models as Logic Programmer (LMLP) that learns from demonstrations containing logic rules and corresponding examples to iteratively reason over KBs, recovering Prolog's backward chaining algorithm. Comprehensive experiments are included to systematically compare LMLP with CoT in deductive reasoning settings, showing that LMLP enjoys more than 25% higher accuracy than CoT on length generalization benchmarks even with fewer parameters.

VQA is an ambitious task aiming to answer any image-related question. However, in reality, it is hard to build such a system once for all since the needs of users are continuously updated, and the system has to implement new functions. Thus, Continual Learning (CL) ability is a must in developing advanced VQA systems. Recently, a pioneer work split a VQA dataset into disjoint answer sets to study this topic. However, CL on VQA involves not only the expansion of label sets (new Answer sets). It is crucial to study how to answer questions when deploying VQA systems to new environments (new Visual scenes) and how to answer questions requiring new functions (new Question types). Thus, we propose CLOVE, a benchmark for Continual Learning On Visual quEstion answering, which contains scene- and function-incremental settings for the two aforementioned CL scenarios. In terms of methodology, the main difference between CL on VQA and classification is that the former additionally involves expanding and preventing forgetting of reasoning mechanisms, while the latter focusing on class representation. Thus, we propose a real-data-free replay-based method tailored for CL on VQA, named Scene Graph as Prompt for Symbolic Replay. Using a piece of scene graph as a prompt, it replays pseudo scene graphs to represent the past images, along with correlated QA pairs. A unified VQA model is also proposed to utilize the current and replayed data to enhance its QA ability. Finally, experimental results reveal challenges in CLOVE and demonstrate the effectiveness of our method. The dataset and code will be available at https://github.com/showlab/CLVQA.

Approximating nonlinear differential equations using a neural network provides a robust and efficient tool for various scientific computing tasks, including real-time predictions, inverse problems, optimal controls, and surrogate modeling. Previous works have focused on embedding dynamical systems into networks through two approaches: learning a single solution operator (i.e., the mapping from input parametrized functions to solutions) or learning the governing system of equations (i.e., the constitutive model relative to the state variables). Both of these approaches yield different representations for the same underlying data or function. Additionally, observing that families of differential equations often share key characteristics, we seek one network representation across a wide range of equations. Our method, called Predicting Operators and Symbolic Expressions (PROSE), learns maps from multimodal inputs to multimodal outputs, capable of generating both numerical predictions and mathematical equations. By using a transformer structure and a feature fusion approach, our network can simultaneously embed sets of solution operators for various parametric differential equations using a single trained network. Detailed experiments demonstrate that the network benefits from its multimodal nature, resulting in improved prediction accuracy and better generalization. The network is shown to be able to handle noise in the data and errors in the symbolic representation, including noisy numerical values, model misspecification, and erroneous addition or deletion of terms. PROSE provides a new neural network framework for differential equations which allows for more flexibility and generality in learning operators and governing equations from data.

Recent years have seen many audio-domain text-to-music generation models that rely on large amounts of text-audio pairs for training. However, symbolic-domain controllable music generation has lagged behind partly due to the lack of a large-scale symbolic music dataset with extensive metadata and captions. In this work, we present MetaScore, a new dataset consisting of 963K musical scores paired with rich metadata, including free-form user-annotated tags, collected from an online music forum. To approach text-to-music generation, We employ a pretrained large language model (LLM) to generate pseudo-natural language captions for music from its metadata tags. With the LLM-enhanced MetaScore, we train a text-conditioned music generation model that learns to generate symbolic music from the pseudo captions, allowing control of instruments, genre, composer, complexity and other free-form music descriptors. In addition, we train a tag-conditioned system that supports a predefined set of tags available in MetaScore. Our experimental results show that both the proposed text-to-music and tags-to-music models outperform a baseline text-to-music model in a listening test. While a concurrent work Text2MIDI also supports free-form text input, our models achieve comparable performance. Moreover, the text-to-music system offers a more natural interface than the tags-to-music model, as it allows users to provide free-form natural language prompts.

Given ample experimental data from a system governed by differential equations, it is possible to use deep learning techniques to construct the underlying differential operators. In this work we perform symbolic discovery of differential operators in a situation where there is sparse experimental data. This small data regime in machine learning can be made tractable by providing our algorithms with prior information about the underlying dynamics. Physics Informed Neural Networks (PINNs) have been very successful in this regime (reconstructing entire ODE solutions using only a single point or entire PDE solutions with very few measurements of the initial condition). We modify the PINN approach by adding a neural network that learns a representation of unknown hidden terms in the differential equation. The algorithm yields both a surrogate solution to the differential equation and a black-box representation of the hidden terms. These hidden term neural networks can then be converted into symbolic equations using symbolic regression techniques like AI Feynman. In order to achieve convergence of these neural networks, we provide our algorithms with (noisy) measurements of both the initial condition as well as (synthetic) experimental data obtained at later times. We demonstrate strong performance of this approach even when provided with very few measurements of noisy data in both the ODE and PDE regime.

Precise recognition of search intent in Retrieval-Augmented Generation (RAG) systems remains a challenging goal, especially under resource constraints and for complex queries with nested structures and dependencies. This paper presents QCompiler, a neuro-symbolic framework inspired by linguistic grammar rules and compiler design, to bridge this gap. It theoretically designs a minimal yet sufficient Backus-Naur Form (BNF) grammar G[q] to formalize complex queries. Unlike previous methods, this grammar maintains completeness while minimizing redundancy. Based on this, QCompiler includes a Query Expression Translator, a Lexical Syntax Parser, and a Recursive Descent Processor to compile queries into Abstract Syntax Trees (ASTs) for execution. The atomicity of the sub-queries in the leaf nodes ensures more precise document retrieval and response generation, significantly improving the RAG system's ability to address complex queries.

Large language models (LLMs) have demonstrated impressive capabilities across diverse tasks, yet their ability to perform structured symbolic planning remains limited, particularly in domains requiring formal representations like the Planning Domain Definition Language (PDDL). In this paper, we present a novel instruction tuning framework, PDDL-Instruct, designed to enhance LLMs' symbolic planning capabilities through logical chain-of-thought reasoning. Our approach focuses on teaching models to rigorously reason about action applicability, state transitions, and plan validity using explicit logical inference steps. By developing instruction prompts that guide models through the precise logical reasoning required to determine when actions can be applied in a given state, we enable LLMs to self-correct their planning processes through structured reflection. The framework systematically builds verification skills by decomposing the planning process into explicit reasoning chains about precondition satisfaction, effect application, and invariant preservation. Experimental results on multiple planning domains show that our chain-of-thought reasoning based instruction-tuned models are significantly better at planning, achieving planning accuracy of up to 94% on standard benchmarks, representing a 66% absolute improvement over baseline models. This work bridges the gap between the general reasoning capabilities of LLMs and the logical precision required for automated planning, offering a promising direction for developing better AI planning systems.

We propose Hier-SLAM++, a comprehensive Neuro-Symbolic semantic 3D Gaussian Splatting SLAM method with both RGB-D and monocular input featuring an advanced hierarchical categorical representation, which enables accurate pose estimation as well as global 3D semantic mapping. The parameter usage in semantic SLAM systems increases significantly with the growing complexity of the environment, making scene understanding particularly challenging and costly. To address this problem, we introduce a novel and general hierarchical representation that encodes both semantic and geometric information in a compact form into 3D Gaussian Splatting, leveraging the capabilities of large language models (LLMs) as well as the 3D generative model. By utilizing the proposed hierarchical tree structure, semantic information is symbolically represented and learned in an end-to-end manner. We further introduce a novel semantic loss designed to optimize hierarchical semantic information through both inter-level and cross-level optimization. Additionally, we propose an improved SLAM system to support both RGB-D and monocular inputs using a feed-forward model. To the best of our knowledge, this is the first semantic monocular Gaussian Splatting SLAM system, significantly reducing sensor requirements for 3D semantic understanding and broadening the applicability of semantic Gaussian SLAM system. We conduct experiments on both synthetic and real-world datasets, demonstrating superior or on-par performance with state-of-the-art NeRF-based and Gaussian-based SLAM systems, while significantly reducing storage and training time requirements.

Existing memory systems enable Large Language Models (LLMs) to support long-horizon human-LLM interactions by persisting historical interactions beyond limited context windows. However, while recent approaches have succeeded in constructing effective memories, they often disrupt the inherent logical and temporal relationships within interaction sessions, resulting in fragmented memory units and degraded reasoning performance. In this paper, we propose MetaMem, a novel framework that augments memory systems with a self-evolving meta-memory, aiming to teach LLMs how to effectively utilize memorized knowledge. During meta-memory optimization, MetaMem iteratively distills transferable knowledge utilization experiences across different tasks by self-reflecting on reasoning processes and performing actions to update the current meta-memory state. The accumulated meta-memory units serve as explicit knowledge utilization experiences, guiding the LLM to systematically identify and integrate critical evidence from scattered memory fragments. Extensive experiments demonstrate the effectiveness of MetaMem, which significantly outperforms strong baselines by over 3.6%. All codes and datasets are available at https://github.com/OpenBMB/MetaMem.

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.

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.

Current multimodal approaches predominantly treat visual generation as an external process, relying on pixel rendering or code execution, thereby overlooking the native visual representation capabilities latent within Large Language Models (LLMs). In this work, we unlock this potential through ASCII art, a compact, efficient, and text-native visual format. We introduce SVE-ASCII, a unified framework designed to elicit and benchmark Symbolic Visual Expression directly within the pure text space. To address the scarcity of systematic resources, we construct ASCIIArt-7K, a high-quality dataset synthesized via a novel "Seed-and-Evolve" pipeline that augments human-curated anchors through in-context stylistic editing. We further implement a unified instruction-tuning strategy that jointly optimizes for both Generation (Text-to-ASCII) and Understanding (ASCII-to-Text). Crucially, our experiments reveal a critical phenomenon regarding task duality: while it is established that perception aids generation, we provide compelling evidence that generative training significantly enhances visual comprehension. This confirms a mutually reinforcing cycle in symbolic visual processing, a relationship previously hypothesized but rarely empirically demonstrated in the visual domain. We release our dataset, the ASCIIArt-Bench benchmark, and the SVE-ASCII model, establishing a robust baseline for native text-based visual intelligence.

The advent of large language models (LLMs) has unlocked great opportunities in complex data management tasks, particularly in question answering (QA) over complicated multi-table relational data. Despite significant progress, systematically evaluating LLMs on multi-table QA remains a critical challenge due to the inherent complexity of analyzing heterogeneous table structures and potential large scale of serialized relational data. Existing benchmarks primarily focus on single-table QA, failing to capture the intricacies of reasoning across multiple relational tables, as required in real-world domains such as finance, healthcare, and e-commerce. To address this gap, we present TQA-Bench, a new multi-table QA benchmark designed to evaluate the capabilities of LLMs in tackling complex QA tasks over relational data. Our benchmark incorporates diverse relational database instances sourced from real-world public datasets and introduces a flexible sampling mechanism to create tasks with varying multi-table context lengths, ranging from 8K to 64K tokens. To ensure robustness and reliability, we integrate symbolic extensions into the evaluation framework, enabling the assessment of LLM reasoning capabilities beyond simple data retrieval or probabilistic pattern matching. We systematically evaluate a range of LLMs, both open-source and closed-source, spanning model scales from 7 billion to 70 billion parameters. Our extensive experiments reveal critical insights into the performance of LLMs in multi-table QA, highlighting both challenges and opportunities for advancing their application in complex, data-driven environments. Our benchmark implementation and results are available at https://github.com/Relaxed-System-Lab/TQA-Bench.

Since large language models have approached human-level performance on many tasks, it has become increasingly harder for researchers to find tasks that are still challenging to the models. Failure cases usually come from the long-tail distribution - data that an oracle language model could assign a probability on the lower end of its distribution. Current methodology such as prompt engineering or crowdsourcing are insufficient for creating long-tail examples because humans are constrained by cognitive bias. We propose a Logic-Induced-Knowledge-Search (LINK) framework for systematically generating long-tail knowledge statements. Grounded by a symbolic rule, we search for long-tail values for each variable of the rule by first prompting a LLM, then verifying the correctness of the values with a critic, and lastly pushing for the long-tail distribution with a reranker. With this framework we construct a dataset, Logic-Induced-Long-Tail (LINT), consisting of 200 symbolic rules and 50K knowledge statements spanning across four domains. Human annotations find that 84% of the statements in LINT are factually correct. In contrast, ChatGPT and GPT4 struggle with directly generating long-tail statements under the guidance of logic rules, each only getting 56% and 78% of their statements correct. Moreover, their "long-tail" generations in fact fall into the higher likelihood range, and thus are not really long-tail. Our findings suggest that LINK is effective for generating data in the long-tail distribution while enforcing quality. LINT can be useful for systematically evaluating LLMs' capabilities in the long-tail distribution. We challenge the models with a simple entailment classification task using samples from LINT. We find that ChatGPT and GPT4's capability in identifying incorrect knowledge drop by ~3% in the long-tail distribution compared to head distribution.

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.

Training on verifiable symbolic data is a promising way to expand the reasoning frontier of language models beyond what standard pre-training corpora provide. Yet existing procedural generators often rely on fixed puzzles or templates and do not deliver the distributional breadth needed at scale. We introduce Reasoning Core, a scalable suite that procedurally generates verifiable symbolic reasoning data across core formal domains: PDDL planning over randomized domains, first-order logic with equality, context-free grammar parsing and generation, causal reasoning over random Bayesian networks, and systems of equations. Each task is paired with an external solver for rigorous verification and admits continuous difficulty control for curriculum design. Examples can optionally include solver-derived reasoning traces, enabling supervised training from the earliest pre-training stages, and the same interface provides verifiable reward functions for reinforcement learning. Our experiments show that mixing Reasoning Core data into pre-training improves downstream reasoning while preserving, or slightly improving, language modeling quality. Zero-shot evaluations confirm these tasks challenge frontier models such as GPT-5. The code and data are publicly available under the MIT license.

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

The 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".

Multi-step symbolic reasoning is critical for advancing downstream performance on financial tasks. Yet, benchmarks for systematically evaluating this capability are lacking. Existing datasets like FinQA and ConvFinQA supervise only final numerical answers, without assessing intermediate reasoning steps. To address this, we introduce FinChain, the first symbolic benchmark designed for verifiable Chain-of- Thought (CoT) financial reasoning. Spanning 54 topics across 12 financial domains, Fin- Chain offers five parameterized templates per topic, each varying in reasoning complexity and domain expertise required. Each dataset instance includes an executable Python trace, enabling automatic generation of extensive training data and easy adaptation to other domains. We also introduce ChainEval, a new metric for automatic evaluation of both final answers and intermediate reasoning. Benchmarking 30 LLMs on our dataset, we find that even state-of-the-art models have considerable room for improvement in multi-step financial reasoning. All templates and evaluation metrics for FinChain are available at https: //github.com/mbzuai-nlp/finchain.

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 symbolic discovery of Ordinary Differential Equations (ODEs) from trajectory data plays a pivotal role in AI-driven scientific discovery. Existing symbolic methods predominantly rely on fixed, pre-collected training datasets, which often result in suboptimal performance, as demonstrated in our case study in Figure 1. Drawing inspiration from active learning, we investigate strategies to query informative trajectory data that can enhance the evaluation of predicted ODEs. However, the butterfly effect in dynamical systems reveals that small variations in initial conditions can lead to drastically different trajectories, necessitating the storage of vast quantities of trajectory data using conventional active learning. To address this, we introduce Active Symbolic Discovery of Ordinary Differential Equations via Phase Portrait Sketching (APPS). Instead of directly selecting individual initial conditions, our APPS first identifies an informative region within the phase space and then samples a batch of initial conditions from this region. Compared to traditional active learning methods, APPS mitigates the gap of maintaining a large amount of data. Extensive experiments demonstrate that APPS consistently discovers more accurate ODE expressions than baseline methods using passively collected datasets.

Optimizing Register Transfer Level (RTL) code is crucial for improving the power, performance, and area (PPA) of digital circuits in the early stages of synthesis. Manual rewriting, guided by synthesis feedback, can yield high-quality results but is time-consuming and error-prone. Most existing compiler-based approaches have difficulty handling complex design constraints. Large Language Model (LLM)-based methods have emerged as a promising alternative to address these challenges. However, LLM-based approaches often face difficulties in ensuring alignment between the generated code and the provided prompts. This paper presents SymRTLO, a novel neuron-symbolic RTL optimization framework that seamlessly integrates LLM-based code rewriting with symbolic reasoning techniques. Our method incorporates a retrieval-augmented generation (RAG) system of optimization rules and Abstract Syntax Tree (AST)-based templates, enabling LLM-based rewriting that maintains syntactic correctness while minimizing undesired circuit behaviors. A symbolic module is proposed for analyzing and optimizing finite state machine (FSM) logic, allowing fine-grained state merging and partial specification handling beyond the scope of pattern-based compilers. Furthermore, a fast verification pipeline, combining formal equivalence checks with test-driven validation, further reduces the complexity of verification. Experiments on the RTL-Rewriter benchmark with Synopsys Design Compiler and Yosys show that SymRTLO improves power, performance, and area (PPA) by up to 43.9%, 62.5%, and 51.1%, respectively, compared to the state-of-the-art methods.

Solving complex mathematical problems via system-2 reasoning is a natural human skill, yet it remains a significant challenge for current large language models (LLMs). We identify the scarcity of deliberate multi-step reasoning data as a primary limiting factor. To this end, we introduce Enriched Instruction Tuning (EIT), a method that enriches existing human-annotated mathematical datasets by synergizing human and AI feedback to create fine-grained reasoning trajectories. These datasets are then used to fine-tune open-source LLMs, enhancing their mathematical reasoning abilities without reliance on any symbolic verification program. Concretely, EIT is composed of two critical steps: Enriching with Reasoning Plan (ERP) and Enriching with Reasoning Step (ERS). The former generates a high-level plan that breaks down complex instructions into a sequence of simpler objectives, while ERS fills in reasoning contexts often overlooked by human annotators, creating a smoother reasoning trajectory for LLM fine-tuning. Unlike existing CoT prompting methods that generate reasoning chains only depending on LLM's internal knowledge, our method leverages human-annotated initial answers as ``meta-knowledge'' to help LLMs generate more detailed and precise reasoning processes, leading to a more trustworthy LLM expert for complex mathematical problems. In experiments, EIT achieves an accuracy of 84.1% on GSM8K and 32.5% on MATH, surpassing state-of-the-art fine-tuning and prompting methods, and even matching the performance of tool-augmented methods.

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.

In this paper, we present MusPy, an open source Python library for symbolic music generation. MusPy provides easy-to-use tools for essential components in a music generation system, including dataset management, data I/O, data preprocessing and model evaluation. In order to showcase its potential, we present statistical analysis of the eleven datasets currently supported by MusPy. Moreover, we conduct a cross-dataset generalizability experiment by training an autoregressive model on each dataset and measuring held-out likelihood on the others---a process which is made easier by MusPy's dataset management system. The results provide a map of domain overlap between various commonly used datasets and show that some datasets contain more representative cross-genre samples than others. Along with the dataset analysis, these results might serve as a guide for choosing datasets in future research. Source code and documentation are available at https://github.com/salu133445/muspy .

Large language models (LLMs) excel at program synthesis, yet their ability to produce symbolic graphics programs (SGPs) that render into precise visual content remains underexplored. We study symbolic graphics programming, where the goal is to generate an SGP from a natural-language description. This task also serves as a lens into how LLMs understand the visual world by prompting them to generate images rendered from SGPs. Among various SGPs, our paper sticks to scalable vector graphics (SVGs). We begin by examining the extent to which LLMs can generate SGPs. To this end, we introduce SGP-GenBench, a comprehensive benchmark covering object fidelity, scene fidelity, and compositionality (attribute binding, spatial relations, numeracy). On SGP-GenBench, we discover that frontier proprietary models substantially outperform open-source models, and performance correlates well with general coding capabilities. Motivated by this gap, we aim to improve LLMs' ability to generate SGPs. We propose a reinforcement learning (RL) with verifiable rewards approach, where a format-validity gate ensures renderable SVG, and a cross-modal reward aligns text and the rendered image via strong vision encoders (e.g., SigLIP for text-image and DINO for image-image). Applied to Qwen-2.5-7B, our method substantially improves SVG generation quality and semantics, achieving performance on par with frontier systems. We further analyze training dynamics, showing that RL induces (i) finer decomposition of objects into controllable primitives and (ii) contextual details that improve scene coherence. Our results demonstrate that symbolic graphics programming offers a precise and interpretable lens on cross-modal grounding.

LLMs can perform multi-step reasoning through Chain-of-Thought (CoT), but they cannot reliably verify their own logic. Even when they reach correct answers, the underlying reasoning may be flawed, undermining trust in high-stakes scenarios. To mitigate this issue, we introduce VeriCoT, a neuro-symbolic method that extracts and verifies formal logical arguments from CoT reasoning. VeriCoT formalizes each CoT reasoning step into first-order logic and identifies premises that ground the argument in source context, commonsense knowledge, or prior reasoning steps. The symbolic representation enables automated solvers to verify logical validity while the NL premises allow humans and systems to identify ungrounded or fallacious reasoning steps. Experiments on the ProofWriter, LegalBench, and BioASQ datasets show VeriCoT effectively identifies flawed reasoning, and serves as a strong predictor of final answer correctness. We also leverage VeriCoT's verification signal for (1) inference-time self-reflection, (2) supervised fine-tuning (SFT) on VeriCoT-distilled datasets and (3) preference fine-tuning (PFT) with direct preference optimization (DPO) using verification-based pairwise rewards, further improving reasoning validity and accuracy.

The rapid evolution of autonomous, agentic artificial intelligence within financial services has introduced an existential architectural crisis: large language models (LLMs) are probabilistic, non-deterministic systems operating in domains that demand absolute, mathematically verifiable compliance guarantees. Existing guardrail solutions -- including NVIDIA NeMo Guardrails and Guardrails AI -- rely on probabilistic classifiers and syntactic validators that are fundamentally inadequate for enforcing complex multi-variable regulatory constraints mandated by the SEC, FINRA, and OCC. This paper presents the Lean-Agent Protocol, a formal-verification-based AI guardrail platform that leverages the Aristotle neural-symbolic model developed by Harmonic AI to auto-formalize institutional policies into Lean 4 code. Every proposed agentic action is treated as a mathematical conjecture: execution is permitted if and only if the Lean 4 kernel proves that the action satisfies pre-compiled regulatory axioms. This architecture provides cryptographic-level compliance certainty at microsecond latency, directly satisfying SEC Rule 15c3-5, OCC Bulletin 2011-12, FINRA Rule 3110, and CFPB explainability mandates. A three-phase implementation roadmap from shadow verification through enterprise-scale deployment is provided.

The recent explosion of generative AI-Music systems has raised numerous concerns over data copyright, licensing music from musicians, and the conflict between open-source AI and large prestige companies. Such issues highlight the need for publicly available, copyright-free musical data, in which there is a large shortage, particularly for symbolic music data. To alleviate this issue, we present PDMX: a large-scale open-source dataset of over 250K public domain MusicXML scores collected from the score-sharing forum MuseScore, making it the largest available copyright-free symbolic music dataset to our knowledge. PDMX additionally includes a wealth of both tag and user interaction metadata, allowing us to efficiently analyze the dataset and filter for high quality user-generated scores. Given the additional metadata afforded by our data collection process, we conduct multitrack music generation experiments evaluating how different representative subsets of PDMX lead to different behaviors in downstream models, and how user-rating statistics can be used as an effective measure of data quality. Examples can be found at https://pnlong.github.io/PDMX.demo/.

Existing work in automatic music generation has primarily focused on end-to-end systems that produce complete compositions or continuations. However, because musical composition is typically an iterative process, such systems make it difficult to engage in the back-and-forth between human and machine that is essential to computer-assisted creativity. In this study, we address the task of personalizable, multi-track, long-context, and controllable symbolic music infilling to enhance the process of computer-assisted composition. We present MIDI-RWKV, a novel model based on the RWKV-7 linear architecture, to enable efficient and coherent musical cocreation on edge devices. We also demonstrate that MIDI-RWKV admits an effective method of finetuning its initial state for personalization in the very-low-sample regime. We evaluate MIDI-RWKV and its state tuning on several quantitative and qualitative metrics, and release model weights and code at https://github.com/christianazinn/MIDI-RWKV.

Symbolic music evaluation for large language models remains fragmented across representations, datasets, and metrics. We introduce LilyBench, a LilyPond-based benchmark that jointly evaluates symbolic music generation and music understanding on the same family of open-weight LLMs. The benchmark includes a 200-prompt generation suite and ten understanding tasks adapted from ABC-Eval, covering syntax, metadata prediction, structural sequencing, and music recognition. Generation quality is evaluated using compile rate, MusPy descriptor distributions via Jensen-Shannon similarity, and LilyBERT-based Fréchet Music Distance (FMD). Experiments on four open-weight models show that executable LilyPond generation is achievable in zero-shot settings, while structural understanding tasks remain challenging despite strong performance on composer and genre recognition. Our experiments also reveal systematic disagreements between descriptor-based and embedding-based metrics, suggesting that symbolic music evaluation benefits from metric triangulation rather than single-score ranking. We release the benchmark, prompt bank, and evaluation code to support future research in symbolic music generation and understanding at https://github.com/CSCPadova/lilybench

In nature, the behaviors of many complex systems can be described by parsimonious math equations. Automatically distilling these equations from limited data is cast as a symbolic regression process which hitherto remains a grand challenge. Keen efforts in recent years have been placed on tackling this issue and demonstrated success in symbolic regression. However, there still exist bottlenecks that current methods struggle to break when the discrete search space tends toward infinity and especially when the underlying math formula is intricate. To this end, we propose a novel Reinforcement Symbolic Regression Machine (RSRM) that masters the capability of uncovering complex math equations from only scarce data. The RSRM model is composed of three key modules: (1) a Monte Carlo tree search (MCTS) agent that explores optimal math expression trees consisting of pre-defined math operators and variables, (2) a Double Q-learning block that helps reduce the feasible search space of MCTS via properly understanding the distribution of reward, and (3) a modulated sub-tree discovery block that heuristically learns and defines new math operators to improve representation ability of math expression trees. Biding of these modules yields the state-of-the-art performance of RSRM in symbolic regression as demonstrated by multiple sets of benchmark examples. The RSRM model shows clear superiority over several representative baseline models.

Pre-trained language models (PLM) have advanced the state-of-the-art across NLP applications, but lack domain-specific knowledge that does not naturally occur in pre-training data. Previous studies augmented PLMs with symbolic knowledge for different downstream NLP tasks. However, knowledge bases (KBs) utilized in these studies are usually large-scale and static, in contrast to small, domain-specific, and modifiable knowledge bases that are prominent in real-world task-oriented dialogue (TOD) systems. In this paper, we showcase the advantages of injecting domain-specific knowledge prior to fine-tuning on TOD tasks. To this end, we utilize light-weight adapters that can be easily integrated with PLMs and serve as a repository for facts learned from different KBs. To measure the efficacy of proposed knowledge injection methods, we introduce Knowledge Probing using Response Selection (KPRS) -- a probe designed specifically for TOD models. Experiments on KPRS and the response generation task show improvements of knowledge injection with adapters over strong baselines.

Large language models (LLMs) have shown remarkable reasoning capabilities given chain-of-thought prompts (examples with intermediate reasoning steps). Existing benchmarks measure reasoning ability indirectly, by evaluating accuracy on downstream tasks such as mathematical reasoning. However, it is unclear how these models obtain the answers and whether they rely on simple heuristics rather than the generated chain-of-thought. To enable systematic exploration of the reasoning ability of LLMs, we present a new synthetic question-answering dataset called PrOntoQA, where each example is generated from a synthetic world model represented in first-order logic. This allows us to parse the generated chain-of-thought into symbolic proofs for formal analysis. Our analysis on InstructGPT and GPT-3 shows that LLMs are quite capable of making correct individual deduction steps, and so are generally capable of reasoning, even in fictional contexts. However, they have difficulty with proof planning: When multiple valid deduction steps are available, they are not able to systematically explore the different options.

We present AlphaApollo, a self-evolving agentic reasoning system that aims to address two bottlenecks in foundation model (FM) reasoning-limited model-intrinsic capacity and unreliable test-time iteration. AlphaApollo orchestrates multiple models with professional tools to enable deliberate, verifiable reasoning. It couples (i) a computation tool (Python with numerical and symbolic libraries) and (ii) a retrieval tool (task-relevant external information) to execute exact calculations and ground decisions. The system further supports multi-round, multi-model solution evolution via a shared state map that records candidates, executable checks, and feedback for iterative refinement. In evaluations on AIME 2024/2025 across multiple models, AlphaApollo delivers consistent gains: +5.15% Average@32 and +23.34% Pass@32 for Qwen2.5-14B-Instruct, and +8.91% Average@32 with +26.67% Pass@32 for Llama-3.3-70B-Instruct. Tool-use analysis shows that more than 80% of tool calls are successfully executed, with consistent outperformance of non-tool baselines, thereby lifting the capability ceiling of FMs. More empirical results and implementation details will be updated at https://github.com/tmlr-group/AlphaApollo.

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

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.

Cyber-physical systems like autonomous vehicles are tested in simulation before deployment, using domain-specific programs for scenario specification. To aid the testing of autonomous vehicles in simulation, we design a natural language interface, using an instruction-following large language model, to assist a non-coding domain expert in synthesising the desired scenarios and vehicle behaviours. We show that using it to convert utterances to the symbolic program is feasible, despite the very small training dataset. Human experiments show that dialogue is critical to successful simulation generation, leading to a 4.5 times higher success rate than a generation without engaging in extended conversation.

We propose AnyTOD, an end-to-end, zero-shot task-oriented dialog (TOD) system capable of handling unseen tasks without task-specific training. We view TOD as a program executed by a language model (LM), where program logic and ontology is provided by a designer as a schema. To enable generalization to unseen schemas and programs without prior training, AnyTOD adopts a neuro-symbolic approach. A neural LM keeps track of events occurring during a conversation and a symbolic program implementing the dialog policy is executed to recommend next actions AnyTOD should take. This approach drastically reduces data annotation and model training requirements, addressing the enduring challenge of rapidly adapting a TOD system to unseen tasks and domains. We demonstrate state-of-the-art results on STAR, ABCD and SGD benchmarks. We also demonstrate strong zero-shot transfer ability in low-resource settings, such as zero-shot on MultiWOZ. In addition, we release STARv2, an updated version of the STAR dataset with richer annotations, for benchmarking zero-shot end-to-end TOD models.

Electronic health record (EHR) systems are used extensively throughout the healthcare domain. However, data interchangeability between EHR systems is limited due to the use of different coding standards across systems. Existing methods of mapping coding standards based on manual human experts mapping, dictionary mapping, symbolic NLP and classification are unscalable and cannot accommodate large scale EHR datasets. In this work, we present Text2Node, a cross-domain mapping system capable of mapping medical phrases to concepts in a large taxonomy (such as SNOMED CT). The system is designed to generalize from a limited set of training samples and map phrases to elements of the taxonomy that are not covered by training data. As a result, our system is scalable, robust to wording variants between coding systems and can output highly relevant concepts when no exact concept exists in the target taxonomy. Text2Node operates in three main stages: first, the lexicon is mapped to word embeddings; second, the taxonomy is vectorized using node embeddings; and finally, the mapping function is trained to connect the two embedding spaces. We compared multiple algorithms and architectures for each stage of the training, including GloVe and FastText word embeddings, CNN and Bi-LSTM mapping functions, and node2vec for node embeddings. We confirmed the robustness and generalisation properties of Text2Node by mapping ICD-9-CM Diagnosis phrases to SNOMED CT and by zero-shot training at comparable accuracy. This system is a novel methodological contribution to the task of normalizing and linking phrases to a taxonomy, advancing data interchangeability in healthcare. When applied, the system can use electronic health records to generate an embedding that incorporates taxonomical medical knowledge to improve clinical predictive models.

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.

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.

Standard natural language processing (NLP) pipelines operate on symbolic representations of language, which typically consist of sequences of discrete tokens. However, creating an analogous representation for ancient logographic writing systems is an extremely labor intensive process that requires expert knowledge. At present, a large portion of logographic data persists in a purely visual form due to the absence of transcription -- this issue poses a bottleneck for researchers seeking to apply NLP toolkits to study ancient logographic languages: most of the relevant data are images of writing. This paper investigates whether direct processing of visual representations of language offers a potential solution. We introduce LogogramNLP, the first benchmark enabling NLP analysis of ancient logographic languages, featuring both transcribed and visual datasets for four writing systems along with annotations for tasks like classification, translation, and parsing. Our experiments compare systems that employ recent visual and text encoding strategies as backbones. The results demonstrate that visual representations outperform textual representations for some investigated tasks, suggesting that visual processing pipelines may unlock a large amount of cultural heritage data of logographic languages for NLP-based analyses.

In the domain of symbolic music research, the progress of developing scalable systems has been notably hindered by the scarcity of available training data and the demand for models tailored to specific tasks. To address these issues, we propose MelodyT5, a novel unified framework that leverages an encoder-decoder architecture tailored for symbolic music processing in ABC notation. This framework challenges the conventional task-specific approach, considering various symbolic music tasks as score-to-score transformations. Consequently, it integrates seven melody-centric tasks, from generation to harmonization and segmentation, within a single model. Pre-trained on MelodyHub, a newly curated collection featuring over 261K unique melodies encoded in ABC notation and encompassing more than one million task instances, MelodyT5 demonstrates superior performance in symbolic music processing via multi-task transfer learning. Our findings highlight the efficacy of multi-task transfer learning in symbolic music processing, particularly for data-scarce tasks, challenging the prevailing task-specific paradigms and offering a comprehensive dataset and framework for future explorations in this domain.

Large Language Models (LLMs) exhibit impressive reasoning abilities, yet their reliance on structured step-by-step processing reveals a critical limitation. While human cognition fluidly adapts between intuitive, heuristic (System 1) and analytical, deliberative (System 2) reasoning depending on the context, LLMs lack this dynamic flexibility. This rigidity can lead to brittle and unreliable performance when faced with tasks that deviate from their trained patterns. To address this, we create a dataset of 2,000 samples with valid System 1 and System 2 answers, explicitly align LLMs with these reasoning styles, and evaluate their performance across reasoning benchmarks. Our results reveal an accuracy-efficiency trade-off: System 2-aligned models excel in arithmetic and symbolic reasoning, while System 1-aligned models perform better in commonsense tasks. A mechanistic analysis of model responses shows that System 1 models employ more definitive answers, whereas System 2 models demonstrate greater uncertainty. Interpolating between these extremes produces a monotonic transition in reasoning accuracy, preserving coherence. This work challenges the assumption that step-by-step reasoning is always optimal and highlights the need for adapting reasoning strategies based on task demands.

Emotions are fundamental to the creation and perception of music performances. However, achieving human-like expression and emotion through machine learning models for performance rendering remains a challenging task. In this work, we present SyMuPe, a novel framework for developing and training affective and controllable symbolic piano performance models. Our flagship model, PianoFlow, uses conditional flow matching trained to solve diverse multi-mask performance inpainting tasks. By design, it supports both unconditional generation and infilling of music performance features. For training, we use a curated, cleaned dataset of 2,968 hours of aligned musical scores and expressive MIDI performances. For text and emotion control, we integrate a piano performance emotion classifier and tune PianoFlow with the emotion-weighted Flan-T5 text embeddings provided as conditional inputs. Objective and subjective evaluations against transformer-based baselines and existing models show that PianoFlow not only outperforms other approaches, but also achieves performance quality comparable to that of human-recorded and transcribed MIDI samples. For emotion control, we present and analyze samples generated under different text conditioning scenarios. The developed model can be integrated into interactive applications, contributing to the creation of more accessible and engaging music performance systems.

Chemical reasoning inherently integrates visual, textual, and symbolic modalities, yet existing benchmarks rarely capture this complexity, often relying on simple image-text pairs with limited chemical semantics. As a result, the actual ability of Multimodal Large Language Models (MLLMs) to process and integrate chemically meaningful information across modalities remains unclear. We introduce ChemVTS-Bench, a domain-authentic benchmark designed to systematically evaluate the Visual-Textual-Symbolic (VTS) reasoning abilities of MLLMs. ChemVTS-Bench contains diverse and challenging chemical problems spanning organic molecules, inorganic materials, and 3D crystal structures, with each task presented in three complementary input modes: (1) visual-only, (2) visual-text hybrid, and (3) SMILES-based symbolic input. This design enables fine-grained analysis of modality-dependent reasoning behaviors and cross-modal integration. To ensure rigorous and reproducible evaluation, we further develop an automated agent-based workflow that standardizes inference, verifies answers, and diagnoses failure modes. Extensive experiments on state-of-the-art MLLMs reveal that visual-only inputs remain challenging, structural chemistry is the hardest domain, and multimodal fusion mitigates but does not eliminate visual, knowledge-based, or logical errors, highlighting ChemVTS-Bench as a rigorous, domain-faithful testbed for advancing multimodal chemical reasoning. All data and code will be released to support future research.

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

We introduce MathSticks, a benchmark for Visual Symbolic Compositional Reasoning (VSCR), which unifies visual perception, symbolic manipulation, and arithmetic consistency. Each task presents an incorrect matchstick equation that must be corrected by moving one or two sticks under strict conservation rules. The benchmark includes both text-guided and purely visual settings, systematically covering digit scale, move complexity, solution multiplicity, and operator variation, with 1.4M generated instances and a curated test set. Evaluations of 14 vision--language models reveal substantial limitations: closed-source models succeed only on simple cases, open-source models fail in the visual regime, while humans exceed 90\% accuracy. These findings establish MathSticks as a rigorous testbed for advancing compositional reasoning across vision and symbols. Our code and dataset are publicly available at https://github.com/Yuheng2000/MathSticks.

First-order logic (FOL) reasoning, which involves sequential deduction, is pivotal for intelligent systems and serves as a valuable task for evaluating reasoning capabilities, particularly in chain-of-thought (CoT) contexts. Existing benchmarks often rely on extensive human annotation or handcrafted templates, making it difficult to achieve the necessary complexity, scalability, and diversity for robust evaluation. To address these limitations, we propose a novel framework called ProverGen that synergizes the generative strengths of Large Language Models (LLMs) with the rigor and precision of symbolic provers, enabling the creation of a scalable, diverse, and high-quality FOL reasoning dataset, ProverQA. ProverQA is also distinguished by its inclusion of accessible and logically coherent intermediate reasoning steps for each problem. Our evaluation shows that state-of-the-art LLMs struggle to solve ProverQA problems, even with CoT prompting, highlighting the dataset's challenging nature. We also finetune Llama3.1-8B-Instruct on a separate training set generated by our framework. The finetuned model demonstrates consistent improvements on both in-distribution and out-of-distribution test sets, suggesting the value of our proposed data generation framework. Code available at: https://github.com/opendatalab/ProverGen

Text Normalization and Semantic Parsing have numerous applications in natural language processing, such as natural language programming, paraphrasing, data augmentation, constructing expert systems, text matching, and more. Despite the prominent achievements of deep learning in Large Language Models (LLMs), the interpretability of neural network architectures is still poor, which affects their credibility and hence limits the deployments of risk-sensitive scenarios. In certain scenario-specific domains with scarce data, rapidly obtaining a large number of supervised learning labels is challenging, and the workload of manually labeling data would be enormous. Catastrophic forgetting in neural networks further leads to low data utilization rates. In situations where swift responses are vital, the density of the model makes local deployment difficult and the response time long, which is not conducive to local applications of these fields. Inspired by the multiplication rule, a principle of combinatorial mathematics, and human thinking patterns, a multilayer framework along with its algorithm, the Digestion Algorithm in Hierarchical Symbolic Forests (DAHSF), is proposed to address these above issues, combining text normalization and semantic parsing workflows. The Chinese Scripting Language "Fire Bunny Intelligent Development Platform V2.0" is an important test and application of the technology discussed in this paper. DAHSF can run locally in scenario-specific domains on little datasets, with model size and memory usage optimized by at least two orders of magnitude, thus improving the execution speed, and possessing a promising optimization outlook.

The advent of powerful neural classifiers has increased interest in problems that require both learning and reasoning. These problems are critical for understanding important properties of models, such as trustworthiness, generalization, interpretability, and compliance to safety and structural constraints. However, recent research observed that tasks requiring both learning and reasoning on background knowledge often suffer from reasoning shortcuts (RSs): predictors can solve the downstream reasoning task without associating the correct concepts to the high-dimensional data. To address this issue, we introduce rsbench, a comprehensive benchmark suite designed to systematically evaluate the impact of RSs on models by providing easy access to highly customizable tasks affected by RSs. Furthermore, rsbench implements common metrics for evaluating concept quality and introduces novel formal verification procedures for assessing the presence of RSs in learning tasks. Using rsbench, we highlight that obtaining high quality concepts in both purely neural and neuro-symbolic models is a far-from-solved problem. rsbench is available at: https://unitn-sml.github.io/rsbench.

Olympiad-level benchmarks in mathematics and physics are crucial testbeds for advanced AI reasoning, but chemistry, with its unique multimodal symbolic language, has remained an open challenge. We introduce ChemO, a new benchmark built from the International Chemistry Olympiad (IChO) 2025. ChemO features two key innovations for automated assessment: Assessment-Equivalent Reformulation (AER), which converts problems requiring visual outputs (e.g., drawing molecules) into computationally tractable formats, and Structured Visual Enhancement (SVE), a diagnostic mechanism to disentangle a model's visual perception capabilities from its core chemical reasoning. To tackle this benchmark, we propose ChemLabs, a hierarchical multi-agent framework that mimics human expert collaboration through specialized agents for problem decomposition, perception, reasoning, and auditing. Experiments on state-of-the-art multimodal models demonstrate that combining SVE with our multi-agent system yields dramatic performance gains. Our top configuration achieves a score of 93.6 out of 100, surpassing an estimated human gold medal threshold and establishing a new state-of-the-art in automated chemical problem-solving. ChemO Dataset: https://huggingface.co/datasets/IDEA-AI4SCI/ChemO

Despite their spectacular progress, language models still struggle on complex reasoning tasks, such as advanced mathematics. We consider a long-standing open problem in mathematics: discovering a Lyapunov function that ensures the global stability of a dynamical system. This problem has no known general solution, and algorithmic solvers only exist for some small polynomial systems. We propose a new method for generating synthetic training samples from random solutions, and show that sequence-to-sequence transformers trained on such datasets perform better than algorithmic solvers and humans on polynomial systems, and can discover new Lyapunov functions for non-polynomial systems.

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.