Neuro-Symbolic Reasoning

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11 papers in the last four weeks, up 57% on the four weeks before. 0.1% of all new papers.

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May 23, 2026cs.CL

World-State Transformations for Neuro-symbolic Interactive Storytelling

Large Language Models (LLMs) have changed the possibilities of Interactive Storytelling systems that process free-text user input. However, as more of these systems are built, evidence continues to mount regarding the story coherence problems that arise when relying solely on them. Recent research suggests that LLMs can effectively predict state changes within rule-based Interactive Storytelling systems, triggering pre-programmed world-state transformations. In this paper, we conduct an exploratory evaluation of whether such transformations can serve as a catalyst for player expression while aiming to address the incoherence issues typical of purely LLM-based approaches. Building upon a neuro-symbolic architecture, we conducted experiments using an open-source model (Llama 3 70B) and a closed-source model (Gemini 1.5 Flash), with testing conducted in both English and Spanish. Eight participants played two scenarios, carefully designed to assess different evaluation objectives. Our observations suggest that transformations offer a way to maintain world-state consistency while encouraging players to interact creatively through their written inputs.

Santiago Góngora, Luis Chiruzzo, Gonzalo Méndez +1

Facultad de Informática, Universidad Complutense de Madrid, Spain

Interactive Storytelling Neuro-Symbolic Reasoning

May 21, 2026cs.AI

ImProver 2: Iteratively Self-Improving LMs for Neurosymbolic Proof Optimization

Formal mathematics libraries are rapidly expanding, creating a growing need to refactor verified proofs for maintainability and to improve training data quality for neural provers. However, scalable proof optimization is hindered by heterogeneous and heuristically specified objectives, scarce data, and high training and inference costs. To overcome these challenges, we introduce ImProver 2, a neurosymbolic framework for automated proof optimization in Lean 4. ImProver 2 combines a data-efficient expert-iteration pipeline with a scaffold that exposes formal structure alongside lightweight informal abstractions. We further introduce a suite of metrics capturing structural proof properties. Using ImProver 2, we train a 7B-parameter model that outperforms orders-of-magnitude larger models within the same model family, and is competitive with mid-tier frontier models across metrics. We additionally demonstrate that our neurosymbolic scaffold significantly improves performance across both small and frontier models. We show that with proper scaffolding and training, small models can effectively restructure research-level proofs over complex and varied metrics, matching substantially larger systems and establishing proof optimization as a scalable, learnable task.

Riyaz Ahuja, Tate Rowney, Jeremy Avigad +1

Carnegie Mellon University

LLM Self-Refinement Automated Theorem Proving Lean Theorem Proving Neuro-Symbolic Reasoning

May 20, 2026cs.LG

Sutra: Tensor-Op RNNs as a Compilation Target for Vector Symbolic Architectures

Sutra is a typed, purely functional programming language whose compiled forward pass is a PyTorch neural network. The compiler beta-reduces the whole program -- primitives, control flow, string I/O -- to one fused tensor-op graph over a frozen embedding substrate. Rotation binding, unbind, bundle, polynomial Kleene three-valued logic, and tail-recursive loops all lower to tensor operations; the Kleene connectives are Lagrange-interpolated polynomials exact on the {-1, 0, +1} truth grid. Validation is one fact tested two ways. (1) The same program runs on four frozen embeddings spanning two modalities -- three text encoders (nomic-embed-text, all-minilm, mxbai-embed-large) and one protein language model (ESM-2) -- and decodes bundles at 100% accuracy through width k=8 on every substrate, where the textbook Hadamard product has already collapsed (2.5% on mxbai-embed-large, 7.5% on all-minilm). (2) PyTorch autograd flows through the actually compiled graph: a fuzzy-rule classifier written in .su trains from random init (18.7 +/- 9.5%; chance = 20%, five classes) to 100.0 +/- 0.0% (three seeds) by backpropagating through the emitted graph, the symbolic source unmodified. A weighted variant additionally trains a scalar cosine gain and writes it back into the .su source as a numeric literal; recompiling reproduces the trained behaviour to ~2e-7 per logit, so the trained model is itself legible, recompilable code. The same artifact is therefore both a logic program and a trainable neural network.

Emma Leonhart

Logical Reasoning Differentiable Programming Vector Symbolic Architectures Neuro-Symbolic Reasoning

May 19, 2026cs.AI

High Quality Embeddings for Horn Logic Reasoning

Neural networks can be trained to rank the choices made by logical reasoners, resulting in more efficient searches for answers. A key step in this process is creating useful embeddings, i.e., numeric representations of logical statements. This paper introduces and evaluates several approaches to creating embeddings that result in better downstream results. We train embeddings using triplet loss, which requires examples consisting of an anchor, a positive example, and a negative example. We introduce three ideas: generating anchors that are more likely to have repeated terms, generating positive and negative examples in a way that ensures a good balance between easy, medium, and hard examples, and periodically emphasizing the hardest examples during training. We conduct several experiments to evaluate this approach, including a comparison of different embeddings across different knowledge bases, in an attempt to identify what characteristics make an embedding well-suited to a particular reasoning task.

Yifan Zhang, Yasir White, Dean Clark +4

Lehigh University, Computer Science and Engineering, 113 Research Dr., Bethlehem, PA, 18015 · Los Angeles Pierce College, Computer Science, 6201 Winnetka Ave, Woodland Hills, CA 91367 · Colorado College, Computer Science, 14 E Cache La Poudre St, Colorado Springs, CO 80903

Logical Reasoning Metric Learning Neuro-Symbolic Reasoning

May 18, 2026cs.LG

Concise and Logically Consistent Conformal Sets for Neuro-Symbolic Concept-Based Models

Neuro-Symbolic Concept-based Models (NeSy-CBMs) are a family of architectures that integrate neural networks with symbolic reasoning for enhanced reliability in high-stakes applications. They work by first extracting high-level concepts from the input and then inferring a task label from these compatibly with given logical constraints. Yet, their label and concept predictions can be overconfident, making it difficult for stakeholders to gauge when the model's decisions can be trusted. We address this issue by integrating ideas from Conformal Prediction (CP), a framework providing rigorous, distribution-free coverage guarantees. We formalize three desiderata -- consistency, coverage, and conciseness -- that any conformal method for NeSy-CBMs should satisfy, and show that existing approaches fall short of at least one. We then introduce COCOCO, a post-hoc framework that conformalizes concepts and labels jointly and reconciles them via a single deduction-abduction revision step. COCOCO satisfies all three desiderata, retains distribution-free coverage, is robust to imperfect knowledge and supports user-specified size budgets. Our experiments on 8 data sets highlight how COCOCO compares favorably against competitors and natural baselines in terms of performance and set size.

Samuele Bortolotti, Emanuele Marconato, Andrea Pugnana +2

Department of Information Engineering and Computer Science, University of Trento, Italy · CIMeC, University of Trento, Rovereto, Italy

Concept Bottleneck Models Conformal Prediction Neuro-Symbolic Reasoning

May 17, 2026cs.AI

NeuSymMS: A Hybrid Neuro-Symbolic Memory System for Persistent, Self-Curating LLM Agents

We present NeuSymMS, an adaptive memory system that enables large language model (LLM) agents to learn, remember, and reason about users across sessions via a hybrid neuro-symbolic architecture. NeuSymMS couples neural fact extraction from unstructured dialogue using LLMs and a CLIPS-based expert system that classifies, deduplicates, and reconciles facts under explicit lifecycle rules. The system represents knowledge as subject-relation-value triples stored in relational database management system. It supports user/agents/agent-to-agent scoping, and implements a dual-horizon (short-term and long-term) memory model. IT leverages access-based promotion and time-based pruning of the memory on both horizpons. NeuSymMS maintains continuity of memory while avoiding context-window bloat and cross-entity contamination. We argue that this architecture offers a practical path to trustworthy, auditable memory for production agentic systems and discuss its novelty relative to log retrieval, summarization, and key-value approaches.

Mujahid Sultan, Sri Thuraisamy, Daya Rajaratnam

†MLSoft Inc., Toronto, Ontario, Canada · ∗iVedha Corporation, Toronto, Ontario, Canada

LLM Agent Memory Neuro-Symbolic Reasoning Long-Term Conversational Memory Agent Memory Management

May 15, 2026cs.AI

Reasoners or Translators? Contamination-aware Evaluation and Neuro-Symbolic Robustness in Tax Law

Recent advances in large language models (LLMs) have significantly enhanced automated legal reasoning. Yet, it remains unclear whether their performance reflects genuine legal reasoning ability or artifacts of data contamination. We present a comprehensive empirical study of tax law reasoning approaches and implement a contamination detection protocol to rigorously assess LLM reliability. We show that performance can be inflated by contamination. Building on this analysis, we conduct a systematic evaluation, comparing monolithic LLMs with hybrid systems that translate statutory text into formal representations and delegate inference to symbolic solvers. We build a novel test suite designed to probe generalization to unseen documents via case and rule variations. Our findings indicate that legal reasoning is inherently compositional and that neuro-symbolic frameworks offer a more reliable and robust foundation for legal AI, as well as improved generalization to unobserved situations.

Parisa Kordjamshidi, Samer Aslan, Madhavan Seshadri +2

Bloomberg · Michigan State University

Data Contamination in Language Models Neuro-Symbolic Reasoning Language Model Robustness Legal Reasoning

May 14, 2026cs.AI

From LLM-Generated Conjectures to Lean Formalizations: Automated Polynomial Inequality Proving via Sum-of-Squares Certificates

Automated proving of polynomial inequalities is a fundamental challenge in automated mathematical reasoning, where rich algebraic structure and a rapidly growing certificate search space hinder scalability. Purely symbolic approaches provide strong guarantees but often scale poorly as the number of variables or the degree increases, due to expensive algebraic manipulations and rapidly growing intermediate expressions. In parallel, LLM-guided methods have made notable progress, particularly on competition-style inequalities with a small number of variables. To address the remaining scalability challenges, we propose NSPI, a neuro-symbolic framework that combines the complementary strengths of LLMs and symbolic computation for polynomial-inequality proving. Concretely, an LLM proposes a conjecture in the form of an approximate polynomial Sum-Of-Squares (SOS) decomposition; we refine it via symbolic computation to obtain an exact polynomial SOS representation, which directly proves the target inequality, and we further certify the proof in Lean, yielding an end-to-end pipeline from heuristic discovery to machine-checked proof. Experiments on challenging benchmarks involving polynomials with up to 10 variables demonstrate the effectiveness and scalability of the proposed method.

Ruobing Zuo, Hanrui Zhao, Gaolei He +2

School of Software Engineering, East China Normal University, Shanghai, China · College of Computer Science and Technology, National University of Defense Technology, Changsha, China · School of Computer and Information Engineering, Henan University, Kaifeng, China

Mathematical Reasoning Neuro-Symbolic Reasoning LLM Mathematical Reasoning

May 14, 2026cs.LG

Natural Synthesis: Outperforming Reactive Synthesis Tools with Large Reasoning Models

Reactive synthesis, the problem of automatically constructing a hardware circuit from a logical specification, is a long-standing challenge in formal verification. It is elusive for two reasons: It is algorithmically hard, and writing formal specifications by hand is notoriously difficult. In this paper, we tackle both sides of the problem. For the algorithmic side, we present a neuro-symbolic approach to reactive synthesis that couples large reasoning models with model checkers to iteratively repair a synthesized Verilog implementation via sound symbolic feedback. Our approach solves more benchmarks than the best dedicated tools in the annual synthesis competition and extends to constructing parameterized systems, a problem known to be undecidable. On the specification side, we introduce an autoformalization step that shifts the specification task from temporal logic to natural language by introducing a hand-authored dataset of natural-language specifications for evaluation. We demonstrate performance comparable to that of starting from formal specifications, establishing natural synthesis as a viable end-to-end workflow.

Frederik Schmitt, Matthias Cosler, Niklas Metzger +4

1CISPA Helmholtz Center for Information Security · 2Technical University of Munich

Program Synthesis Formal Verification Neuro-Symbolic Reasoning Autoformalization Large Reasoning Models

May 14, 2026cs.LG

Logical Grammar Induction via Graph Kolmogorov Complexity: A Neuro-Symbolic Framework for Self-Healing Clinical Data Integrity

The reliability of Healthcare Information Systems (HIS) is frequently compromised by human-induced data entry errors, which existing statistical anomaly detection methods fail to distinguish from legitimate clinical extremes. This paper proposes Logic-GNN, a novel neuro-symbolic framework that treats clinical records as a structured

private language'' governed by latent logical games. By integrating Temporal Graph Neural Networks (TGNN) with Graph Kolmogorov Complexity, we induce a symbolic grammar that represents the underlying logic of medical interactions. We define anomalies as

grammatical violations'' that cause a significant expansion in the Minimum Description Length (MDL) of the clinical graph. Evaluated on the Sina System dataset (2M+ records), Logic-GNN achieves an F1-score of 0.94, outperforming state-of-the-art baselines by 12% in distinguishing between life-threatening medical outliers and data corruption. Our approach introduces a self-healing mechanism that suggests logical corrections to maintain data integrity in real-time HIS environments.

Abolfazl Zarghani, Amir Malekesfandiari

Department of Computer Engineering, Ferdowsi University of Mashhad, Mashhad, Iran

Healthcare Neuro-Symbolic Reasoning Anomaly Detection

May 13, 2026cs.AI

Bridging Legal Interpretation and Formal Logic: Faithfulness, Assumption, and the Future of AI Legal Reasoning

The growing adoption of large language models in legal practice brings both significant promise and serious risk. Legal professionals stand to benefit from AI that can reason over contracts, draft documents, and analyze sources at scale, yet the high-stakes nature of legal work demands a level of rigor that current AI systems do not provide. The central problem is not simply that LLMs hallucinate facts and references; it is that they systematically draw inferences that go beyond what the source text actually supports, presenting assumption-laden conclusions as if they were logically grounded. This proposal presents a neuro-symbolic approach to legal AI that combines the expressive power of large language models with the rigor of formal verification, aiming to make AI-assisted legal reasoning both capable and trustworthy, thus reducing the burden of manual verification without sacrificing the accountability that legal practice demands.

Olivia Peiyu Wang, Leilani H. Gilpin

University of California, Santa Cruz

LLM Grounding Neuro-Symbolic Reasoning Legal Reasoning

May 13, 2026cs.LO

Quantitative Linear Logic for Neuro-Symbolic Learning and Verification

Differentiable Logics are deployed in neuro-symbolic learning tasks as a way of embedding logical constraints in the training objective of neural networks. A differentiable logic consists of a syntax to write logical properties and a semantics to interpret them as real-valued functions to be folded in the loss function. A defining trade-off of the field is that between logical properties of the connectives, and analytic concerns for the semantics, with both aspects being relevant in applications. At one extreme we find fuzzy logics, that have well-established algebraic and proof-theoretic foundations, and at the other ad-hoc differentiable logics like Fischer's DL2, conceived for deep learning applications. However, no satisfactory foundation has emerged yet. We propose a resolution to this long-standing tension via a novel logic, Quantitative Linear Logic (QLL), with foundational ambitions. Our design is driven by naturality -- the idea that, since logical constraints are translated to losses, the semantics of the connectives should be pertinent operations used in ML practice (that is, sum and log-sum-exp) on additive quantities (like logits). We then judge the result on two aspects: logical adequacy -- that they satisfy most of the standard logical laws of Linear Logic; and empirical effectiveness -- test-time performance (as measured by adversarial attacks) is well-correlated to the actual verification of the logical constraints (as measured by off-the-shelf neural network verifiers), which makes QLL stand out among SoTA techniques.

Thomas Flinkow, Ekaterina Komendantskaya, Matteo Capucci +1

Maynooth University, Maynooth, IE · University of Southampton, Southampton, UK · University of Strathclyde, Glasgow, UK +1

Neural Network Verification Neuro-Symbolic Reasoning Neurosymbolic Learning

May 13, 2026cs.SE

Neurosymbolic Auditing of Natural-Language Software Requirements

Natural-language software requirements are often ambiguous, inconsistent, and underspecified; in safety-critical domains, these defects propagate into formal models that verify the wrong specification and into implementations that ship unsafe behavior. We show that large language models, equipped with an SMT solver, can audit such requirements: translating them into formal logic, detecting ambiguity through stochastic variation in the generated formalization, and exposing inconsistency, vacuousness, and safety violations through solver queries on the resulting specification. We present VERIMED, a neurosymbolic pipeline that operationalizes this idea for medical-device software requirements, and report two findings. First, stochastic variation across independent formalizations is a signal of ambiguity: requirements that admit multiple plausible interpretations produce SMT-inequivalent formalizations, and bidirectional SMT equivalence checking turns this disagreement into a solver-checkable test. Second, the usefulness of symbolic feedback depends on its granularity: in counterexample-guided repair on a hemodialysis question-answering benchmark, concrete SMT counterexamples raise verified accuracy from 55.4% to 98.5%. Over an extensive experimental evaluation on open-source hemodialysis safety requirements, we show that the LLM-based approach in VERIMED successfully reduces ambiguity-sensitive requirements and enables rigorous auditing of software requirements through SMT-based queries.

Bethel Hall, William Eiers

Stevens Institute of Technology

Requirements Engineering Formal Verification Satisfiability Modulo Theories Neuro-Symbolic Reasoning

May 11, 2026cs.CV

Hilbert-Geo: Solving Solid Geometric Problems by Neural-Symbolic Reasoning

Geometric problem solving, as a typical multimodal reasoning problem, has attracted much attention and made great progress recently, however most of works focus on plane geometry while usually fail in solid geometry due to 3D spatial diagrams and complex reasoning. To bridge this gap, we introduce Hilbert-Geo, the first unified formal language framework for solid geometry, including an extensive predicate library and a dedicated theorem bank. Based on this framework, we propose a Parse2Reason method containing two steps of first parsing then reasoning. In the parsing step, we utilize conditional description language (CDL), a formalized language composed of predicates specifically designed to construct geometric conditions, to represent both problem description (natural text) and solid diagrams (visual image). In the reasoning step, we leverage those formal CDL and the theorem bank to perform relational inference and algebraic computation, generating strictly correct, verifiable, and human-readable reasoning processes. Notably, our proposed Hilbert-Geo is also applicable to plane geometry. To advance geometric reasoning, we curate two expert-annotated dataset SolidFGeo2k and PlaneFGeo3k, which are furnished with geometric formal language annotations, solutions and answers. Extensive experiments show that our proposed method achieves the state-of-the-art (SOTA) performance 77.3% in SolidFGeo2k and 84.1% in MathVerse-Solid (one small subset in MathVerse dedicated to solid geometry), substantially outperforming leading MLLMs, such as Gemini-2.5-pro (54.2% on SolidFGeo2k) and GPT-5 (62.9% on MathVerse-Solid). In addition, our method achieves the SOTA accuracy 80.2% in PlaneFGeo3k, demonstrating the generality of the Hilbert-Geo in geometric reasoning. Our code and datasets are released at https://github.com/PremiLab-Math/Hilbert-Geo.

Ruoran Xu, Haoyu Cheng, Bin Dong +1

Xi’an Jiaotong-Liverpool University · Ricoh Software Research Center Beijing Co.,Ltd.

Symbolic Reasoning Multimodal Reasoning Mathematical Reasoning Neuro-Symbolic Reasoning

May 11, 2026cs.AI

Deep Arguing

Deep learning has become the dominant approach for creating high capacity, scalable models across diverse data modalities. However, because these models rely on a large number of learned parameters, tightly couple feature extraction with task objectives, and often lack explicit reasoning mechanisms, it is difficult for humans to understand how they arrive at their predictions. Understanding what representations emerge and why they arise from the training data remains an open challenge. We introduce Deep Arguing, a novel neurosymbolic approach that integrates deep learning with argumentation construction and reasoning for interpretable classification with different data modalities. In our approach deep neural networks construct an argumentation structure wherein data points support their assigned label and attack different ones. Using differentiable argumentation semantics for reasoning, the model is trained end-to-end to jointly learn feature representation and argumentative interactions. This results in argumentation structures providing faithful case-based explanations for predictions. Structure constraints over the argumentation graph guide learning, improving both interpretability and predictive performance. Experiments with tabular and imaging datasets show that Deep Arguing achieves performance competitive with standard baselines whilst offering interpretable argumentative reasoning.

Adam Gould, Francesca Toni

Department of Computing Imperial College London

Neural Network Interpretability Computational Argumentation Classification Neuro-Symbolic Reasoning

May 11, 2026cs.AI

GuardAD: Safeguarding Autonomous Driving MLLMs via Markovian Safety Logic

Multimodal large language models (MLLMs) are increasingly integrated into autonomous driving (AD) systems; however, they remain vulnerable to diverse safety threats, particularly in accident-prone scenarios. Recent safeguard mechanisms have shown promise by incorporating logical constraints, yet most rely on static formulations that lack temporally grounded safety reasoning over evolving traffic interactions, resulting in limited robustness in dynamic driving environments. To address these limitations, we propose GuardAD, a model-agnostic safeguard that formulates AD safety as an evolving Markovian logical state. GuardAD introduces Neuro-Symbolic Logic Formalization, which represents safety predicates over heterogeneous traffic participants and continuously induces them via n-th order Markovian Logic Induction. This design enables the inference of emerging and latent hazards beyond single-step observations. Rather than simply vetoing unsafe actions, GuardAD performs Logic-Driven Action Revision, where inferred safety states actively guide action refinement without modifying the underlying MLLM. Extensive experiments on multiple benchmarks and AD-MLLMs demonstrate that GuardAD substantially reduces accident rates (-32.07%) while slightly improving task performance (+6.85%). Moreover, closed-loop simulation evaluations, together with physical-world vehicle studies, further validate the effectiveness and potential of GuardAD.

Tianyuan Zhang, Peng Yue, Zihao Peng +8

Beihang University · Zhongguancun Laboratory · Peking University

Autonomous Driving LLM Safety Neuro-Symbolic Reasoning Runtime Assurance

May 11, 2026quant-ph

SCALAR: A Neurosymbolic Framework for Automated Conjecture and Reasoning in Quantum Circuit Analysis

In this paper, we present SCALAR (Symbolic Conjecture and LLM-Assisted Reasoning), a neurosymbolic framework for automated conjecture generation in quantum circuit analysis built on top of the CUDA-Q open source framework. The system integrates quantum simulation, symbolic conjecture generation, and LLM-based interpretation. We evaluate SCALAR on 82 MaxCut instances from the MQLib benchmark dataset and extend the analysis to 2,000 randomly generated graphs across four topologies: regular, Erdos-Renyi, Barabasi-Albert, and Watts-Strogatz. The framework generates conjectured bounds relating optimal QAOA parameters to graph invariants, including known relationships such as periodicity constraints on the phase separation parameter

γ

. SCALAR also recovers previously reported parameter transfer phenomena across structurally similar instances. Additionally, the system identifies correlations between graph structural features and optimization landscape properties, which we characterize through invariant-based descriptors. Using CUDA-Q tensor network simulator, we scale experiments to instances of up to 77 qubits. We discuss the accuracy, generality, and limitations of the generated conjectures, including sensitivity to graph class and quantum circuit depth.

Sean Feeney, Pooja Rao, Andreas Klappenecker +5

Department of Computer Science, Texas A&M University, College Station, USA · NVIDIA Corporation, Santa Clara, USA · Computing and Artificial Intelligence Division (CAI-3), Los Alamos National Laboratory, Los Alamos, USA

AI-Assisted Scientific Research Neuro-Symbolic Reasoning Quantum Approximate Optimization Algorithm

May 11, 2026cs.CV

A neurosymbolic Approach with Epistemic Deep Learning for Hierarchical Image Classification

Deep neural networks achieve high accuracy on image classification tasks. Yet, they often produce overconfident predictions as which fail to express epistemic uncertainty, and frequently violate logical or structural constraints present in the data. These limitations are particularly pronounced in hierarchical classification, where predictions across fine and coarse levels must remain coherent. We propose, for the first time, a unified neurosymbolic and epistemic modelling framework that augments Swin Transformers with focal set reasoning and differentiable fuzzy logic. Rather than treating labels as isolated categories, our method induces data-driven focal sets within the learnt embedding space, which helps capture epistemic uncertainty over multiple plausible fine-grained classes. These focal sets form the basis of a belief-theoretic layer that uses fuzzy membership functions and t-norm conjunctions to encourage consistency between fine- and coarse-grained predictions. A learnable loss further balances calibration, mass regularisation, and logical consistency, allowing the model to adaptively trade off symbolic structure with data-driven evidence. In experiments on hierarchical image classification, our framework maintains accuracy on par with transformer baselines while providing more calibrated and interpretable predictions, reducing overconfidence and enforcing high logical consistency across hierarchical outputs. Our experimental results show that combining focal set reasoning with fuzzy logic provides a practical step toward deep learning models that are both accurate and epistemically aware.

Ezel Kilicdere, Shireen Kudukkil Manchingal, Fabio Cuzzolin

Datasand IT and Consultancy Ltd. · Institute for AI, Data Analysis and Systems (AIDAS) School of Engineering, Computing and Mathematics, Oxford Brookes University, UK

Hierarchical Classification Evidential Deep Learning Neuro-Symbolic Reasoning Image Classification

May 10, 2026cs.AI

LLM-Guided Monte Carlo Tree Search over Knowledge Graphs: Composing Mechanistic Explanations for Drug-Disease Pairs

Extracting multi-step explanations from knowledge graphs poses a combinatorial challenge requiring both heuristic guidance (as candidates proliferate with depth) and credit assignment (as path quality emerges over extended sequences). Frontier LLMs, strong on knowledge/reasoning benchmarks, offer a compelling source of such heuristics, yet their knowledge comes sans guarantees and compositional performance degrades as chains lengthen. We thus present TESSERA, a 3-part neuro-symbolic framework that uses LLMs in a circumscribed role: for local discriminative judgement rather than autonomous multi-step generation; the knowledge graph then defines the hypothesis space enforcing hard structural constraints, and MCTS coordinates the long-horizon search with principled credit assignment via backpropagation. LLMs perform dual roles as a prior policy biasing exploration and a comparative state evaluator supplying reward signals. Evaluation on drug mechanism elucidation across two complementary knowledge graphs demonstrates fidelity to curated biology while surfacing coherent alternative mechanisms, with ablations confirming discriminative contribution from both LLM components. Beyond its current application, our framework offers a general paradigm for compositional reasoning over structured knowledge.

Rishabh Jakhar, Michel Dumontier, Remzi Celebi

Institute of Data Science, Department of Advanced Computing Sciences, Maastricht University, The Netherlands

LLM Reasoning with Graphs Scientific Discovery Monte Carlo Tree Search Neuro-Symbolic Reasoning Knowledge Graph Question Answering Large Language Model-Guided Scientific Discovery+1

May 10, 2026cs.CV

GeoSym127K: Scalable Symbolically-verifiable Synthesis for Multimodal Geometric Reasoning

Large Multimodal Models (LMMs) often struggle with geometric reasoning due to visual hallucinations and a lack of mathematically precise Chain-of-Thought (CoT) data. To address this, we propose the GeoSym Engine, an automated and scalable neuro-symbolic framework. By leveraging a type-conditional grammar and an analytic SymGT Solver, it derives exact symbolic ground truths and seamlessly integrates with a robust rendering pipeline to produce high-precision geometric diagrams. Using this engine, we construct GeoSym127K, a difficulty-stratified dataset featuring 51K high-resolution images, 127K questions with symbolic ground truths, and 55K answer-verified CoT QA pairs. We also introduce GeoSym-Bench, an expert-curated suite of 511 complex samples for rigorous evaluation. Through extensive supervised fine-tuning (SFT), we demonstrate that GeoSym drives concentrated improvements specifically on diagram-dependent and multi-step geometry tasks. Our Qwen3-VL-8B model gains an absolute +22.21% on the MathVerse Vision-Only subset and reaches 61.52% (+6.19% improvement) on WeMath, mitigating long-horizon logic fragmentation and outperforming advanced closed-source models like Doubao-1.8. Furthermore, applying Reinforcement Learning with Verifiable Rewards (RLVR) via GRPO reveals that initializing from structural SFT checkpoints substantially elevates the performance ceiling over zero-shot RL. Driven by deterministic exact-match signals, this showcases the robust scaling potential of our verifiable reasoning synthesis. Datasets and code are available at https://huggingface.co/datasets/Tomie0506/GeoSym127K and https://github.com/Tomie56/GeoSym127K.

Jinhao Jing, Zheng Ma, Jinwei Liang +9

SenseTime Research · The Chinese University of Hong Kong, Shenzhen · University of California, Los Angeles +3

Mathematical Reasoning Benchmarks Synthetic Data Generation Multimodal Reasoning VLM Reasoning Neuro-Symbolic Reasoning

May 9, 2026cs.LG

Lattice Deduction Transformers

We introduce the Lattice Deduction Transformer (LDT), a recurrent transformer that approximates logically sound deduction by projecting its latent state through a lattice between forward passes. We train on-policy in a process that mirrors deduction in a search-based constraint solver and supervise training via a domain-agnostic, abstract-interpretation-based approximation of the set of solution candidates. An

800

K-parameter LDT achieves

100\%

accuracy on Sudoku-Extreme and Snowflake Sudoku, at a fraction of the training cost of prior small recurrent reasoners, while remaining empirically sound: the model returns a correct answer or abstains. A

1.8

M-parameter variant reaches

99.9\%

accuracy on Maze-Hard. Frontier LLMs score

0\%

on all three benchmarks.

Liam Davis, Leopold Haller, Alberto Alfarano +1

Amherst College · Axiom · Barnard College, Columbia University

Recurrent Transformers Neuro-Symbolic Reasoning Constraint Satisfaction

May 8, 2026cs.AI

Abductive Reasoning with Probabilistic Commonsense

Recent efforts to improve the reasoning abilities of Large Language Models (LLMs) have focused on integrating formal logic solvers within neurosymbolic frameworks. A key challenge is that formal solvers lack commonsense world knowledge, preventing them from making reasoning steps that humans find obvious. Prior methods address this by using LLMs to supply missing commonsense assumptions, but these approaches implicitly assume universal agreement on such commonsense facts. In reality, commonsense beliefs vary across individuals. We propose a probabilistic framework for abductive commonsense reasoning that explicitly models this variation, aiming to determine whether most people would judge a statement as true or false. We introduce Probabilistic Abductive CommonSense (PACS), a novel algorithm that uses an LLM and a formal solver to sample proofs as observations of individuals' distinct commonsense beliefs, and aggregates conclusions across these samples. Empirically, PACS outperforms chain-of-thought reasoning, prior neurosymbolic methods, and search-based approaches across multiple benchmarks.

Joseph Cotnareanu, Chiara Roverato, Han Zhou +3

McGill University · International Laboratory on Learning Systems · Mila - Quebec Artificial Intelligence Institute +1

Abductive Reasoning Neuro-Symbolic Reasoning LLM Reasoning

May 8, 2026cs.AI

Tacit Knowledge Extraction via Logic Augmented Generation and Active Inference

Tacit knowledge plays a central role in human expertise, yet it remains difficult to capture, formalize, and reuse in machine-interpretable form. This challenge is especially relevant in procedural domains, where successful execution depends not only on explicit instructions, but also on implicit assumptions, contextual constraints, embodied skills, and experience-based judgments rarely documented. As a result, current knowledge engineering pipelines struggle to transform tacit and process-centric knowledge into formally specified, machine-interpretable representations that can be queried, validated, reasoned over, and reused. In this paper, we introduce a neuro-symbolic framework that combines Logic-Augmented Generation and an Active-Inference-inspired approach for ontology-grounded Knowledge Graph construction. We evaluate the approach in a knowledge transfer case study in manufacturing, using assembly-like repair procedures from instructional videos as a reproducible proxy domain. Results show that the proposed solution improves completeness and semantic quality, advancing neuro-symbolic knowledge engineering for industrial domains.

Lorenzo Lamazzi, Aldo Gangemi, Alessio Giberti +4

CNR - Institute of Cognitive Sciences and Technologies, Bologna, Italy · Department of Philosophy, University of Bologna, Bologna, Italy · MISTER Smart Innovation, Bologna, Italy +1

KG Construction Knowledge Representation Neuro-Symbolic Reasoning

May 8, 2026cs.CV

Neurosymbolic Framework for Concept-Driven Logical Reasoning in Skeleton-Based Human Action Recognition

Skeleton-based human activity recognition has achieved strong empirical performance, yet most existing models remain black boxes and difficult to interpret. In this work, we introduce a neurosymbolic formulation of skeleton-based HAR that reframes action recognition as concept-driven first-order logical reasoning over motion primitives. Our framework bridges representation learning and symbolic inference by grounding first-order logic predicates in learnable spatial and temporal motion concepts. Specifically, we employ a standard spatio-temporal skeleton encoder to extract latent motion representations, which are then mapped to interpretable concept predicates via a spatio-temporal concept decoder that explicitly separates pose-centric and dynamics-centric abstractions. These concept predicates are composed through differentiable first-order logic layers, enabling the model to learn human-readable logical rules that govern action semantics. To impose semantic structure on the learned concepts, we align skeleton representations with LLM-derived descriptions of atomic motion primitives, establishing a shared conceptual space for perception and reasoning. Extensive experiments on NTU RGB+D 60/120 and NW-UCLA demonstrate that our approach achieves competitive recognition performance while providing explicit, interpretable explanations grounded in logical structure. Our results highlight neurosymbolic reasoning as an effective paradigm for interpretable spatio-temporal action understanding. Code: https://github.com/Mr-TalhaIlyas/REASON

Talha Ilyas, Deval Mehta, Zongyuan Ge

Department of ECSE, Faculty of Engineering, Monash University, Australia · Department of DSAI, Faculty of Information Technology, Monash University, Australia · AIM for Health Lab, Faculty of Information Technology, Monash University, Australia

Skeleton-Based Action Recognition Logical Reasoning Human Activity Recognition Interpretable ML Neuro-Symbolic Reasoning

May 8, 2026cs.AI

2.5-D Decomposition for LLM-Based Spatial Construction

Autonomous systems that build structures from natural-language instructions need reliable spatial reasoning, yet large language models (LLMs) make systematic coordinate errors when generating three-dimensional block placements. We present a neuro-symbolic pipeline based on 2.5-D decomposition: the LLM plans in the two-dimensional horizontal plane while a deterministic executor computes all vertical placements from column occupancy, eliminating an entire class of errors. On the Build What I Mean benchmark (160 rounds), GPT-4o-mini with this pipeline achieves 94.6% mean structural accuracy across 12 independent runs, within 3.0 percentage points of the 97.6% ceiling imposed by architect-agent errors that no builder-side improvement can address. This outperforms both GPT-4o at 90.3% and the best competing system at 76.3%. A controlled ablation confirms that 2.5-D decomposition is the dominant contributor, accounting for 28.7 percentage points of accuracy. The pipeline transfers directly to edge hardware: Nemotron-3 120B on an NVIDIA Jetson Thor AGX achieves 96.0% mean structural accuracy with the identical pipeline, slightly exceeding the cloud result. Expanding the system prompt by four targeted examples to exceed the model's 8,320-token prefix cache page size, combined with low-effort reasoning, reduces mean per-request latency by 3X to 19.7 seconds at 95.6% accuracy. The underlying principle, removing deterministic dimensions from the LLM's output space, applies to any autonomous construction or assembly task where gravity or other physical constraints fix one or more degrees of freedom. A transfer experiment on 500 IGLU collaborative building tasks confirms the effect generalizes beyond the primary benchmark.

Paul Whitten, Li-Jen Chen, Sharath Baddam

Rockwell Automation Mayfield Heights, OH, USA

LLM Planning 3D Spatial Reasoning Neuro-Symbolic Reasoning

May 6, 2026cs.CL

ReaComp: Compiling LLM Reasoning into Symbolic Solvers for Efficient Program Synthesis

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.

Atharva Naik, Yash Mathur, Prakam +2

Carnegie Mellon University · Independent Researcher

Symbolic Reasoning LLM-Based Program Synthesis Program Synthesis Neuro-Symbolic Reasoning

May 6, 2026cs.CL

UFAL-CUNI at SemEval-2026 Task 11: An Efficient Modular Neuro-symbolic Method for Syllogistic Reasoning

This paper describes our system submitted to SemEval-2026 Task 11: Disentangling Content and Formal Reasoning in Large Language Models. We present an efficient modular neuro-symbolic approach, combining a symbolic prover with small reasoning LLMs (4B parameters). The system consists of an LLM-based parser that translates natural language syllogisms to a first-order logic (FOL) representation, an automated theorem prover, and two optional modules: machine translation for multilingual inputs and a symbolic retrieval component for the identification of relevant premises. The system achieves competitive accuracy and relatively low content effect on most subtasks. Our ablations show that this approach outperforms LLM-based zero-shot baselines in this parameter size range, but also reveal limited multilingual capabilities of small LLMs. Finally, we include a discussion of the task's main ranking metric and analyze its limitations.

Ivan Kartáč, Kristýna Onderková, Jan Bronec +3

Institute of Formal and Applied Linguistics, Faculty of Mathematics and Physics, Charles University

Logical Reasoning Symbolic Reasoning Neuro-Symbolic Reasoning

May 6, 2026cs.AI

A Foundation Model for Zero-Shot Logical Rule Induction

Inductive Logic Programming (ILP) learns interpretable logical rules from data. Existing methods are transductive: their learned parameters are bound to specific predicates and require retraining for each new task. We introduce Neural Rule Inducer (NRI), a pretrained model for zero-shot rule induction. Rather than encoding literal identities, NRI represents literals using domain-agnostic statistical properties such as class-conditional rates, entropy, and co-occurrence, which generalize across variable identities and counts without retraining. The model consists of a statistical encoder and a parallel slot-based decoder. Parallel decoding preserves the permutation invariance of logical disjunction; an autoregressive decoder would instead impose an arbitrary clause order. Product T-norm relaxation makes rule execution differentiable, allowing end-to-end training on prediction accuracy alone. We evaluate NRI on rule recovery, robustness to label noise and spurious correlations, and zero-shot transfer to real-world benchmarks, and we believe this work opens up the possibility of foundation models for symbolic reasoning. Code and the reference checkpoint are available at https://github.com/phuayj/neural-rule-inducer.

Yin Jun Phua

Institute of Science Tokyo

Zero-Shot Learning Neuro-Symbolic Reasoning Inductive Logic Programming

May 6, 2026cs.CV

Information Coordination as a Bridge: A Neuro-Symbolic Architecture for Reliable Autonomous Driving Scene Understanding

Reliable autonomous driving requires scene understanding that is semantically consistent across heterogeneous sensors and verifiable at the reasoning stage. However, many recent LLM-driven driving systems attach the language model as a post-processor and force it to reason over redundant or conflicting perception outputs, which can amplify hallucinated entities and unsafe conclusions. This paper proposes InfoCoordiBridge, a BEV-centric neuro-symbolic architecture that inserts an explicit coordination bridge between perception and language reasoning. InfoCoordiBridge comprises (i) a unified multi-agent perception layer that outputs typed structured facts together with modality-focused synopses, (ii) an ICA module that aligns and fuses multi-source outputs into a single SceneSummary, and (iii) an SSRE module that performs SceneSummary-grounded reasoning with verification. Experiments on nuScenes and Waymo show that ICA preserves competitive 3D detection accuracy while substantially improving fusion consistency, reducing redundancy to below 1% and achieving about 98% attribute agreement. On NuScenes-QA and a template-aligned Waymo-QA benchmark, SSRE improves factual grounding and reduces hallucinated entity mentions compared with representative VLM and agentic baselines. Overall, by coordinating multi-sensor outputs into a single conflict-aware SceneSummary before prompting, InfoCoordiBridge prevents redundant and cross-modally inconsistent perception evidence from propagating into high-level reasoning.

Shuo Liu, Lei Shi, Haowen Liu +3

School of Computer and Artificial Intelligence, Zhengzhou University, 450001, Zhengzhou, China · School of Cyber Science and Engineering, Zhengzhou University, 450001, Zhengzhou, China · Songshan Laboratory, 450003, Zhengzhou, China

Object Hallucination in VLMs Autonomous Driving Perception VLM Reasoning Neuro-Symbolic Reasoning Multimodal Sensor Fusion

May 5, 2026cs.LG

Weakly Supervised Concept Learning for Object-centric Visual Reasoning

Neurosymbolic systems promise to combine deep neural network's (DNN) processing of raw sensor inputs with few-shot performance of symbolic artificial intelligence. Two-stage approaches explicitly decouple DNN based perception from subsequent rule based reasoning. This avoids optimization and interpretability issues of end to end differentiable approaches, but requires costly labels for the perception output. This paper introduces an efficient weak supervision scheme for the perception stage to ground its output symbols for logical induction in object-centric reasoning tasks. It combines a slot-based architecture for object-centricity with a Variational Autoencoder (VAE) for self-supervision, competing with concept guidance on latent dimensions for human interpretable grounding. The resulting predictions are translated into symbolic background knowledge for reasoning frameworks, such as Inductive Logic Programming (ILP), Decision Trees, and Bayesian Networks. Our extensive empirical evaluation on synthetic and real world datasets shows that our approach can discover complex, abstract rules for object centric reasoning whilst reducing supervision to as little as 1% of labels, and being robust even under substantial domain shift. Notably, at 1% supervision it even outperforms state of the art foundation model baselines in domain generalization

Sparsh Tiwari, Bettina Finzel, Gesina Schwalbe

University of Lübeck, Germany · University of Bamberg, Germany · University of Ulm, Germany

Visual Reasoning Object-Centric Representation Learning Weakly Supervised Learning Visually Grounded Reasoning Neuro-Symbolic Reasoning