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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Latest papers 169

Jun 21, 2026cs.CV

SATURN: Symbolic Spatial Reasoning for Multi-Perspective Grounding

Vision-Language Models (VLMs) remain unreliable when spatial reasoning requires composing relations whose meanings depend on frames of reference. Existing neuro-symbolic methods make reasoning more explicit, but often depend on brittle geometric procedures and hard decisions over noisy perception. We propose SATURN, a neuro-symbolic framework for perspective-aware compositional spatial reasoning. SATURN reconstructs an approximate 3D scene, derives soft perspective-aware spatial predicates, and composes them with a training-free Pythonic symbolic executor, separating perception from reasoning while preserving uncertainty through multi-hop inference. We also introduce 3D FORCE, a diagnostic benchmark that controls reasoning depth, view, and perspective composition across spatial arrangement grounding (SAG) and referring expression grounding (REF). On 3D FORCE, VLMs and spatially trained models degrade sharply as depth and perspective complexity increase, whereas SATURN remains stable and outperforms strong baselines. On the real-world MindCube benchmark, SATURN achieves 78.57% overall accuracy, outperforming the strongest baseline by 14 pp.

Danial Kamali, Tanawan Premsri, Shreya Rajpal +3

Michigan State University · Lambda Labs

3D Spatial Reasoning Visually Grounded Reasoning Neuro-Symbolic Reasoning Spatial Reasoning 3D Visual Grounding

Jun 21, 2026cs.AI

VADAOrchestra: Neurosymbolic Orchestration of Adaptive Reasoning Workflows

Decision-making in real-world settings rarely follows a fixed script. Instead, it unfolds as a dynamic reasoning process in which the appropriate course of action evolves as new context and data become available. Traditional Business Process Management systems provide rigor, determinism, and auditability, yet they generally struggle to adapt their execution at runtime. Conversely, agentic systems based on Large Language Models (LLMs) bring flexibility to decision-making, but they are inherently opaque, often unreliable, and suffer from significant scalability constraints when operating over large datasets. To combine these complementary paradigms, we introduce VADAOrchestra, a neurosymbolic framework that models complex workflows as evolving reasoning processes. The framework adopts a hybrid approach: given a user query and a collection of data sources, an LLM-based orchestrator incrementally plans and adapts the workflow. This is encoded as a logic program in a fragment of Datalog+/- where predicates correspond to tool invocations and rules represent both predefined domain dependencies and logic constructs synthesized on demand to manipulate intermediate results. All logical inference tasks are then executed by a state-of-the-art Datalog+/- symbolic engine. This approach provides a verifiable reasoning trace, supporting the auditability and reproducibility of the entire process. Furthermore, by decoupling high-level orchestration from symbolic inference, it addresses scalability concerns, enabling complex reasoning over large datasets through targeted data querying. We evaluate VADAOrchestra on real-world financial use cases, demonstrating faithfulness, scalability, and explainability compared to standard agentic architectures.

Teodoro Baldazzi, Luigi Bellomarini, Andrea Coletta +4

TU Wien · Banca d’Italia · University of Warwick

AI-Assisted Decision Making LLM Agent Orchestration Agentic Workflows Neuro-Symbolic Reasoning

Jun 19, 2026cs.CV

A Neurosymbolic Framework for Interpretable Skeleton-Based Seizure Detection via Concept-Driven Logical Reasoning

Video-based seizure detection is essential for the management of epilepsy patients, offering a non-invasive complement to electroencephalography. While several deep learning approaches have been developed for video-based seizure detection, none are inherently interpretable, limiting their adoption and translation into clinical practice. We present, to our knowledge, the first exploration of a neurosymbolic framework for video-based seizure detection that directly addresses this gap. Our approach (1) extracts patient-centric skeleton sequences from epilepsy monitoring units via a prompt-guided foundation model, (2) predicts binary spatio-temporal concept activations grounded in clinical motor semiology guidelines, and (3) composes them via differentiable logic into interpretable Boolean rules with auditable contributions. Furthermore, to mitigate false positives arising from the traditional binary formulation (seizure vs.\ non-seizure), we sub-classify non-seizure segments into clinically relevant normal activities, providing the model with fine-grained discriminative supervision. Evaluated on two public seizure video benchmarks, our framework achieves 89.78% sensitivity with 0.06 false detections per hour on SAHZU and 85.27%,0.09 on IEEE, while producing complete three-level interpretability: every prediction decomposes into which motor primitives were detected, how they were logically composed, and how much each rule contributed to the clinical decision. We publicly release all annotations, extracted pose sequences, our data pipeline and code, https://github.com/Mr-TalhaIlyas/CDSD/.

Talha Ilyas, Deval Mehta, Zongyuan Ge

Department of ECSE, Faculty of Engineering, Monash University, Australia · AIM for Health Lab, Faculty of IT, Monash University, Australia · Department of DSAI, Faculty of IT, Monash University, Australia +1

Concept-Based Explanations Neural Network Interpretability Video Anomaly Detection Neuro-Symbolic Reasoning

Jun 18, 2026cs.AI

Neurosymbolic Clinical Trial Matching via LLM-Driven Abduction and Logical Verification

Large Language Models (LLMs) offer a promising path to automate Clinical Trial Matching (CTM), but still struggle with the deterministic verification required for complex eligibility criteria. Conversely, purely symbolic methods provide formal rigour but break down when faced with incomplete patient records and noisy clinical evidence. To bridge this gap, we investigate a hybrid framework for CTM combining LLMs with logical verification. In particular, we introduce an abductive neurosymbolic CTM framework (αNeSy-CTM), which leverages the linguistic and world knowledge in LLMs to support reasoning over noisy and underspecified clinical text. Extensive evaluation demonstrates that αNeSy-CTM substantially outperforms standalone LLM baselines, achieving up to 30% relative improvement over zero-shot baselines. In addition, our analyses confirm the impact of abductive reasoning on CTM, with αNeSy-CTM exhibiting improved accuracy, specificity, and robustness over a non-abductive neurosymbolic setting. Furthermore, αNeSy-CTM and Chain-of-Thought (CoT) reasoning prove highly complementary, highlighting the potential for a hybrid routing policy. Ultimately, this paper demonstrates the impact of neurosymbolic methods for automating CTM, providing a path toward the next generation of auditable, LLM-driven clinical applications.

Baiyang Qu, Leonardo Ranaldi, Xi Wang +1

Department of Computer Science, University of Leicester, UK · School of Informatics, University of Edinburgh, UK · School of Computer Science, University of Sheffield, UK

Abductive Reasoning Neuro-Symbolic Reasoning Clinical NLP

Jun 18, 2026cs.AI

DeepSWIP: Quotient-WMC Counterfactuals for Neural Probabilistic Logic Programs

Neurosymbolic systems such as DeepProbLog combine neural perception with probabilistic logic, but standard inference is associational. Counterfactual reasoning additionally requires a causal semantics for interventions and evidence. We introduce DeepSWIP, a single-world counterfactual semantics for DeepProbLog programs. Using neural materialization, we reduce fixed-context neural predicates to ordinary ProbLog choices, apply Single World Intervention Programs (SWIPs), and compute counterfactuals by weighted model counting (WMC) over a single transformed program. Under finite grounding and unique-supported-model assumptions, DeepSWIP is exact relative to the learned materialized FCM. The standard quotient-WMC form of ProbLog conditionals identifies active neural probabilities and explains intervention cleaning, calibration sensitivity, and rare-evidence instability. Experiments on MPI3D confirm the transformation against a DeepTwin construction against 12,000 queries, as predicted and a 2.14

\times

inference speedup from avoiding the Twin's endogenous duplication. A SUMO HOV experiment shows that neural calibration degradation biases plug-in estimates, while a correctly scoped randomized-policy AIPW estimator removes most first-order bias for population mean and ATE estimands. Code is at https://github.com/saibib/deep_SWIP.

Saimun Habib, Vaishak Belle, Fengxiang He

University of Edinburgh

Probabilistic Logic Structural Causal Models Neuro-Symbolic Reasoning Probabilistic Programming Counterfactual Reasoning

Jun 17, 2026cs.AI

NeSyCat Torch: A Differentiable Tensor Implementation of Categorical Semantics for Neurosymbolic Learning

Neurosymbolic semantics is fragmented: classical, fuzzy, probabilistic and neural systems each define truth by their own inductive rules. NeSyCat, extending ULLER, subsumes them under a single inductive definition of truth, parametric in a strong monad and an aggregation structure on truth-values. NeSyCat has so far lacked an account of predicates and functions learned by neural networks. We provide NeSyCat Torch as the missing link and interpret computational symbols via neural networks, implementing the framework in probabilistic programming and tensor-based backends. We use the distribution monad for reference semantics and metric evaluation, and complement it by a monad for numerically stable, differentiable training: the lazy log-tensor monad over the log-semiring. For efficient training in batches, we furthermore employ a batch monad. The axioms are the source code: written once in monad-based do-notation, monadic bind performs marginalisation, lazily pruning unneeded branches. On MNIST addition, our HaskTorch, JAX, and PyTorch implementations outperform LTN and DeepProbLog in speed and accuracy, while achieving nearly the accuracy of DeepStochLog. However, unlike DeepStochLog, we stay in a uniform framework that applies to many first-order NeSy approaches. Namely, the construction is parametric in the monad; instantiating it with, e.g., the Giry monad extends the approach to continuous probability (working out a neural representation here is left for future work).

Daniel Romero Schellhorn, Till Mossakowski, Björn Gehrke

University of Osnabrück, Osnabrück, Germany

Neuro-Symbolic Reasoning Neurosymbolic Learning Probabilistic Programming

Jun 16, 2026cs.MA

A Neuro-Symbolic Approach to Strategy Synthesis for Strategic Logics

Reasoning about what agents can achieve through strategic interaction is a core challenge in Multi-Agent Systems (MAS). Logics for strategic ability, such as ATL, provide rigorous methods, but their adoption is often hindered by the computational cost of strategy synthesis. We introduce a neuro-symbolic framework that integrates large language models (LLMs) into the model-checking pipeline for MAS. The LLM acts as a strategy-generation oracle, proposing candidate strategies that are then formally validated by a standard MAS model checker. This generate-and-certify architecture uses LLM guidance to navigate large combinatorial strategy spaces while preserving formal soundness: generated strategies are accepted only when certified by the verifier. We instantiate the framework for bounded strategic reasoning in NatATL and introduce the first NatATL strategy-synthesis dataset, consisting of 4211 instances. Experiments with an open-weight Qwen3-32B model show that our certified pipeline achieves 92% accuracy on strategy-synthesis outcomes.

Marco Aruta, Vadim Malvone, Aniello Murano +2

University of Naples Federico II, Naples, Italy · LTCI, Télécom Paris, Institut Polytechnique de Paris, Palaiseau, France · Università degli Studi di Salerno, Salerno, Italy

Formal Verification Multi-Agent Systems Neuro-Symbolic Reasoning

Jun 16, 2026cs.AI

A homotopy-type-theoretic generalization of neurosymbolic inference

A wide range of neurosymbolic (NeSy) systems compute one functional: a belief-weighted sum of a logical quantity over a space of

σ

-structures, of which weighted model counting, fuzzy logic, and probabilistic logic are special cases. This account is built on sets, and a set deliberately forgets two things that are important for NeSy: when two

σ

-structures are the same up to a symmetry of the theory, and how many distinct proofs witness a query. Types, in the sense of homotopy type theory, preserve this information and turn the functional into a belief-weighted homotopy cardinality, a notion of size that counts each object in inverse proportion to its symmetries. We develop the framework from scratch for NeSy systems, prove a conservativity theorem that recovers the classical functional when symmetries are trivial, and show that the symmetry our framework exposes is exactly the one behind reasoning shortcuts. The payoff is concrete: the shortcut-aware concept posterior that recent methods reach by ensembling or expressive density estimation is the only symmetry-invariant point of the confusion-set simplex, computable in closed form by averaging a single model over the symmetry group. On MNIST reasoning-shortcut benchmarks this single-model wrapper is better calibrated than a diversity-trained ensemble, while leaving label accuracy and identifiable concepts untouched. Code is freely available at https://github.com/bio-ontology-research-group/hott-nesy.

Fernando Zhapa-Camacho, Robert Hoehndorf

Computer, Electrical and Mathematical Sciences & Engineering Division, King Abdullah University of Science and Technology, 4700 KAUST, 23955, Thuwal, Saudi Arabia · KAUST Center of Excellence for Smart Health (KCSH) · KAUST Center of Excellence for Generative AI

Symbolic Reasoning Neuro-Symbolic Reasoning Neuro-Symbolic AI

Jun 15, 2026cs.CL

Robust Dual-Signal Fusion: Hybrid Neuro-Symbolic Gating with Compressed Chain-of-Thought Refinement for Irony Detection in Social Media Texts

Small-scale Large Language Models (LLMs) natively default to literal semantic interpretations, making few-shot irony detection a persistent challenge in noisy, user-generated text. In this study, we show that, despite this limitation, inference from compact LLMs can still be effectively harnessed for this task. We introduce the Robust Dual-Signal (RDS) Fusion framework, a hybrid neuro-symbolic architecture that utilizes a compressed Chain-of-Thought (CoT) of an LLM, alongside a static, pretrained RoBERTa and a symbolic prior module in two downstream fusions. RDS Fusion demonstrates better performance than an unrestricted reasoning ablation, while requiring substantially lower inference time. We also find that in our experiments, unrestricted reasoning does not yield better results than restricted reasoning. Evaluated on a strictly held-out TweetEval test set (

N=734

), RDS Fusion achieves

78.1\%

accuracy and a Macro F1 of

0.777

, which is comparable to a finetuned BERTweet-base. On the heavily imbalanced iSarcasm dataset, the frozen CoT pipeline suppresses

22.5\%

of baseline false positives, yielding a Macro F1 of

0.6726

and Ironic F1 of

0.4821

, outperforming multiple heavily supervised SemEval transformer ensembles. Paired McNemar's tests show that, while adding the symbolic prior to the neural baseline yields an insignificant gain, and the RDS Fusion is statistically insignificant compared to the combined RoBERTa and symbolic prior ablation; the concurrent fusion achieves a statistically significant improvement over the standalone baseline (

p=0.005

).

Ankit Bhattacharjee, Krityapriya Bhaumik

Indian Institute of Technology Kharagpur, India

CoT Reasoning Neuro-Symbolic Reasoning

Jun 15, 2026cs.CL

VeriGraph: Towards Verifiable Data-Analytic Agents

LLM-based agents have demonstrated strong capabilities in data-intensive analytical tasks, yet their outputs are rarely verifiable: a reliance on linear text trajectories makes their reasoning difficult to audit. In particular, deterministic computations over raw data and semantic deductions over natural-language claims are often entangled in an unstructured stream, leaving numerical conclusions hard to reproduce and qualitative judgments hard to inspect. To address this, we propose VeriGraph, a traceable neuro-symbolic reasoning framework that enables agents to construct an explicit heterogeneous evidence directed acyclic graph (DAG) during execution. VeriGraph introduces three evidence-expansion primitives, namely computational, grounding, and derivational expansion, to connect raw data, interpreter variables, computed results, and natural-language claims in a unified graph. Under this formulation, structural traceability is reduced to graph reachability from raw data sources to terminal claims, while semantic support is measured by claim-level evidence evaluation. To improve graph construction, we further design a graph-based policy optimization strategy with a composite reward that jointly supervises answer correctness, computational integrity, and derivational coherence. Experiments on four benchmarks show that VeriGraph-8B achieves the highest overall score among all baselines. More importantly, VeriGraph produces auditable evidence graphs with substantially stronger claim grounding, achieving a 87.61% Grounding Rate under our claim-level evidence support evaluation. These results suggest that explicit evidence-graph construction is a promising path toward verifiable data-analytic agents. Our code is available at https://github.com/ignorejjj/VeriGraph.

Jiajie Jin, Zhao Yang, Wenle Liao +5

Gaoling School of Artificial Intelligence, Renmin University of China

Data Provenance Neuro-Symbolic Reasoning LLM Agent Reliability Data Analysis Agents

Jun 14, 2026cs.CV

NeRD: Neuro-Symbolic Rule Distillation for Efficient Ontology-Grounded Chain-of-Thought in Medical Image Diagnosis

Interpretability is essential for trustworthy medical image diagnosis. However, existing concept-driven interpretable methods have key limitations: Concept Bottleneck Models (CBMs) require scoring all predefined concepts at inference time and for manual intervention, imposing a substantial burden on clinicians, while rationale-based generative approaches often select concepts by class discriminability, which can drift from diagnostic ontologies. To address these issues, we propose Neuro-Symbolic Rule Distillation (NeRD), a framework that produces efficient, ontology-grounded reasoning chains that are sufficient yet non-redundant, without manually crafting diagnostic rules. Experiments on two skin datasets demonstrate strong diagnostic performance and interpretability, and blinded expert evaluation confirms the clinical plausibility of NeRD rationales. Our method further enables a first expert-in-the-loop study for Multimodal Chain-of-Thought-based diagnosis, achieving efficient and effective concept-level intervention.

Hongxi Yang, Yiwen Jiang, Siyuan Yan +8

Department of Data Science & AI, Faculty of Information Technology, Monash University, Melbourne, Australia · AIM for Health Lab, Faculty of Information Technology, Monash University, Melbourne, Australia · Faculty of Engineering, Monash University, Melbourne, Australia +2

Medical Image Classification Multimodal CoT Reasoning Neuro-Symbolic Reasoning Explainable Medical Image Analysis

Jun 13, 2026cs.RO

Driving, Fast or Slow? Neuro-Symbolic Guidance for Motion Prediction in Multi-Modal Ground Mobility

Accurate and interpretable motion prediction for heterogeneous traffic spaces, including pedestrians, bicycles, cars, and trucks, is essential for safe autonomous navigation. Nevertheless, state-of-the-art approaches remain predominantly black-box, lacking explicit encoding of the regulatory and behavioral constraints of real-world mobility. We propose Trajectory Compliance-Shaping (TraCS), a neuro-symbolic framework that augments existing black-box motion prediction backbones with interpretable and probabilistic first-order logic. To do so, TraCS employs an agentic code-generation pipeline to bridge the gap between natural-language descriptions of traffic regulations and probabilistic motion prediction. Furthermore, TraCS employs a reactive data-streaming inference engine that maintains and efficiently updates compliance landscapes as scenes evolve. To prevent TraCS from overconfidently steering the backbone's predictions in the wrong direction, we propose a neural confidence rating learned as a context-aware attenuation of the compliance signal. We demonstrate on the Argoverse 2 benchmark how TraCS consistently improves state-of-the-art prediction backbones, showing that probabilistic and symbolic compliance reasoning is a broadly applicable and computationally efficient complement to purely neural motion predictors.

Simon Kohaut, Felix Divo, Julius Hahnewald +4

Artificial Intelligence and Machine Learning Lab, TU Darmstadt · Honda Research Institute · Hessian Center for AI (hessian.AI) +3

Multi-Agent Trajectory Prediction Autonomous Driving Neuro-Symbolic Reasoning Multimodal Trajectory Prediction Vehicle Trajectory Prediction

Jun 12, 2026cs.AI

PrologMCP: A Standardized Prolog Tool Interface for LLM Agents

Frontier reasoning-tuned language models still fail on deductive tasks at depth, and the cost of improved performance through extended internal reasoning scales poorly. Symbolic delegation offers a complementary route: a language model translates the problem, while a solver performs the inference. However, current autoformalization pipelines for logic programming are typically bespoke integrations tied to particular tasks or agents. We introduce PrologMCP, a task-agnostic, open-source server that exposes Prolog as a stateful tool through the Model Context Protocol (MCP). Its compact tool interface, structured error reporting, and per-session isolation make the translate-run-inspect-repair loop a reusable primitive for MCP-capable agents. We evaluate a formalizer agent enhanced with PrologMCP against standard and reasoning LLMs (Claude Sonnet 4.6, GPT-4.1, and o4-mini) on two subsets of PARARULE-Plus: a general-purpose sample and a more challenging one targeting a specific failure mode of natural-language reasoning. On the general sample, the formalizer matches or exceeds reasoning LLMs (accuracy 1.00 vs.\ 1.00 / 0.998), with the largest gains over standard models (0.762 for GPT-4.1). On the challenging subset, the formalizer remains near-perfect (1.00 / 0.99) while reasoning LLMs drop to 0.95 / 0.94. These results suggest that delegating inference to Prolog via MCP is a robust and inspectable alternative to extended natural-language reasoning.

Agnieszka Mensfelt, Adarsh Prabhakaran, Adrian Haret +2

Department of Computer Science, Royal Holloway, University of London, UK

Logic Programming Symbolic Reasoning Agentic Reasoning Neuro-Symbolic Reasoning Autoformalization LLM Reasoning

Jun 12, 2026cs.LG

EM-NeSy: Expectation Maximization for Neurosymbolic Learning

Neurosymbolic (NeSy) models integrate neural networks and symbolic reasoning for robust and interpretable AI. State-of-the-art NeSy models require that the symbolic component is expressed in a differentiable way, often complicating the use of approximate inference. We propose EM-NeSy which casts probabilistic NeSy learning as an instance of the Expectation-Maximization (EM) algorithm. In the expectation step, we compute the posterior over the neurally predicted symbols conditioned on the label via probabilistic inference. In the maximization step, we update the neural parameters based on this posterior using gradient descent only through the neural component. This formulation unlocks the full potential of the EM algorithm for NeSy learning. It allows NeSy to extend naturally to approximate reasoning without any additional modifications or differentiability requirements of the symbolic component. Furthermore, it recovers the standard end-to-end gradient-based NeSy setting under exact inference. Our experimental results demonstrate the scalability and computational efficiency of EM-NeSy.

Annegret Seibt, Luc De Raedt, Giuseppe Marra

Department of Computer Science KU Leuven

Symbolic Reasoning Expectation-Maximization Neuro-Symbolic Reasoning Neurosymbolic Learning

Jun 10, 2026cs.DB

Neuro-Relational Programs: Unifying Queries and Neural Computation over Structured Data

The conventional approach to deep learning over relational databases applies neural models, such as Graph Neural Networks (GNNs), to a graph representation of the database. Recent approaches instead operate on databases directly, associating tuples with embeddings and extending query mechanisms to jointly process embeddings and relational content. Inspired by these developments, we introduce Neuro-Relational Programs (NRPs), a declarative query language for relational databases whose facts carry numeric vector embeddings. NRPs extend Datalog-style rules with operations that combine, aggregate, and transform embeddings, thereby interleaving relational reasoning and learnable neural components within a single formalism. This yields a general approach to neural computation over relational data: an NRP can be read both as a query plan with trainable components and as a neural architecture with relational structure built in. Natural syntactic fragments of NRPs recover existing architectures and query formalisms. Zero-ary NRPs correspond to non-adaptive query algorithms; monadic NRPs generalize GNN-style message passing and precisely capture Deep Homomorphism Networks, a connection that we extend to frontier-guarded NRPs over databases with row-ids. We characterize the expressive power of unrestricted NRPs with ReLU-FFN transformations by FOCQ, an extension of first-order logic with counting interpreted over real-weighted structures, yielding a precise connection with uniform TC

^0

over ordered databases. Together, these results establish NRPs as a broad declarative framework for querying and neural computation over relational data.

Arie Soeteman, Balder ten Cate, Maurice Funk +3

ILLC, University of Amsterdam, Amsterdam, Netherlands · Leipzig University, Leipzig, Germany · ScaDS.AI Center Dresden/Leipzig, Germany +2

Graph Neural Networks Relational Reasoning Neuro-Symbolic Reasoning Relational Deep Learning Neural Network Expressivity Relational Databases

Jun 9, 2026cs.RO

Bridging Semantics and Physical Execution: A Neuro-Symbolic Framework for Multi-Pair Robotic Assembly

Multi-pair robotic assembly in unstructured environments faces spatial interference and contact uncertainties. Existing paradigms fail to bridge cognitive decision-making and physical execution, as they either encounter state-space explosion and knowledge bottlenecks or suffer from logical hallucinations and topological conflicts. We propose an end-to-end neuro-symbolic framework that solves the challenge hierarchically: generating optimal subgraphs for each pair, decoupling generality from edge cases, and then resolving cross-pair interferences. Given an eye-on-hand RGB-D assembly scene, the framework extracts semantic instance identity and state while quantifying the scene for divergence calculation. For each pair, optimal subgraph is generated via LLM using barely basic actions to mitigate hallucinations. Supportive actions for edge cases are reasoned and inserted with a lightweight discriminator. Driven by the divergence between the quantified baseline and current scene, it is easily extensible at low cost. Augmented subgraphs are topologically coordinated into global sequences while preserving internal behavioral coherence. Dynamic behavior trees embedding atomic skills close the force-aware execution loop. Offline evaluation on 100 real-world scenes achieves 97.00% global executability, outperforming classical and state-of-the-art planners. Real-robot deployment on a UR3 arm attains 90% success rate with 0.5 mm tolerance under strong interference, demonstrating a unified and verifiable solution for complex autonomous assembly.

Xinyi Li, Aiguo Song, Linhu Wei +1

School of Instrument Science and Engineering, Southeast University, Nanjing 210096, China.

Large Language Model-Based Robot Planning Robotic Manipulation Neuro-Symbolic Reasoning Robotic Assembly

Jun 9, 2026cs.AI

Accelerating NeurASP with vectorization and caching

Neurosymbolic AI combines neural networks with symbolic programs to create robust and explainable predictions. One such framework is NeurASP, which trains a neural network to predict concepts and reasons over them using rules written in answer set programming (ASP) to solve downstream tasks. Crucially, labels are only provided for the downstream prediction produced by the symbolic rules, not for the latent concepts themselves. Backpropagation through the non-differentiable ASP component requires expensive probability and gradient calculations, which has hindered scalability to more sophisticated tasks. In this paper, we address the current limitations of NeurASP by improving its computational performance through vectorization, batch processing and caching of intermediate computations during training. We compare computation speeds between the original and our new implementation of NeurASP and report speedups of multiple orders of magnitude for larger tasks. To this end, we propose a new dataset of difficult tasks involving playing cards, which we use to test the capabilities of NeurASP's enhanced learning function.

Alexander Philipp Rader, Alessandra Russo

Imperial College London

Answer Set Programming Neuro-Symbolic Reasoning Neuro-Symbolic AI Neurosymbolic Learning

Jun 7, 2026cs.AI

Artificial Intelligence for Mathematical Reasoning: An Integrated Survey of Language Models, Neuro-symbolic Systems, and Verified Discovery

Mathematical reasoning has long served as a stringent test of machine intelligence; over the past decade, it has moved from a niche problem within NLP to one of the most consequential AI frontiers. This survey provides a unified account of the field's evolution, from early rule-based math word problem (MWP) solvers and template-driven geometry systems, through neural expression generation and LLM prompting, to contemporary reasoning models, multi-agent systems, neuro-symbolic theorem provers, and verified discovery workflows. We organize the landscape along four axes: (i) informal reasoning over text and diagrams, spanning MWP solving, multimodal geometry, and VLMs; (ii) formal reasoning in proof assistants, including autoformalization, tactic prediction, compiler-guided repair, and proof search; (iii) mathematical discovery, where systems propose constructions, improve bounds, or assist attacks on open problems; and (iv) the inference and training-time techniques, including CoT prompting, tool use, process reward models, and RLVR, that increasingly connect generation with verification. We catalog major benchmarks across grade-school arithmetic, competition mathematics, geometry, formal proving, multimodal and multilingual reasoning, and expert evaluation, and we examine benchmark saturation, contamination, reporting mismatches, and the distinction between pass@1, majority voting, and verifier-assisted pass@

k

. We critically assess failure modes: brittleness under perturbation, reward hacking, multimodal grounding failures, fragile formalization, and the energy cost of reasoning-scale inference. Drawing on recent perspectives from working mathematicians, we identify future directions centered on verified-discovery workflows, reasoning efficiency, and infrastructure to make AI-assisted formalization broadly usable. Companion materials: https://github.com/Starscream-11813/awesome-AI4Math.

Syed Rifat Raiyan, Mohsinul Kabir, Hasan Mahmud +2

Systems and Software Lab (SSL), Department of Computer Science and Engineering, Islamic University of Technology, Gazipur, Bangladesh · Department of Computer Science, University of Manchester, Manchester, United Kingdom

Mathematical Reasoning Benchmarks Automated Theorem Proving Symbolic Reasoning Mathematical Reasoning Neuro-Symbolic Reasoning LLM Mathematical Reasoning

Jun 7, 2026cs.AI

Extending Ontologies: From Dense Embeddings to Hybrid Quantum-Fuzzy Systems

LLMs have revolutionized knowledge representation and retrieval, but lack the explicit modeling that knowledge ontologies possess. This paper surveys the ways that ontologies and knowledge graphs have been integrated with dense embedding algorithms. All hitherto attempts involve a trade-off between probabilistic and crisp inference. This paper proposes a novel frontier for devising knowledge representation systems that can simultaneously accommodate probabilistic and crisp inference in the same representation. To this effect, the paper proposes neuro-quantum-fuzzy systems as knowledge representation systems that accommodate both classical and contextual inference implemented through quantum-neural networks (QNN).

Angjelin Hila

KG Embedding Knowledge Representation Neuro-Symbolic Reasoning

Jun 3, 2026cs.AI

BiNSGPS: Geometry Problem Solving via Bidirectional Neuro-Symbolic Interaction

Geometry problem solving poses distinct challenges in artificial intelligence. Existing approaches typically fall into two paradigms: symbolic methods, which exhibit limited adaptability, and neural methods, which are prone to hallucinations. Recent neuro-symbolic hybrids predominantly rely on a unidirectional pipeline where neural outputs are fed into solvers without feedback, making system brittle to early-stage errors. To break this unidirectional bottleneck, we propose BiNSGPS, a framework that establishes Bidirectional Neuro-Symbolic Interaction (BiNS) between a MLLM Adviser and a Symbolic Solver. MLLM Adviser actively incorporates feedback from the symbolic solver to dynamically rectify inconsistent formal representations or propose auxiliary hypotheses, resolving symbolic conflicts and facilitating complex deductions.

Qi Wang, Peijie Wang, Fei Yin +1

1MAIS, Institute of Automation of Chinese Academy of Sciences · School of Artificial Intelligence, University of Chinese Academy of Sciences

Mathematical Reasoning Neuro-Symbolic Reasoning

Jun 3, 2026cs.AI

Simulate, Reason, Decide: Scientific Reasoning with LLMs for Simulation-Driven Decision Making

Scientific simulators are increasingly being integrated into LLM-driven systems for high-stakes simulation-driven decision-making. However, existing frameworks primarily use LLMs to generate, calibrate, or execute simulators, treating them as black-box interfaces rather than as structured mechanistic systems that can be reasoned about. As a result, current approaches lack the ability to identify, represent, and reason about the assumptions and mechanisms underlying simulator behavior, limiting transparency, auditability, and decision justification. We introduce MechSim, a mechanism-grounded neuro-symbolic reasoning framework for executable scientific simulators. Unlike prior neuro-symbolic approaches that primarily reason over static symbolic structures, MechSim enables LLM agents to reason about the mechanisms, assumptions, and execution behavior of scientific simulators. Our framework represents simulators through a shared structured schema capturing assumptions, variables, mechanism dependencies, and execution traces. On top of this representation, LLM agents operate as constrained reasoning engines that generate structured, evidence-grounded explanations linking simulator outcomes to their underlying mechanisms. We evaluate our approach across multiple high-stakes domains and show that it improves mechanism-level explanation quality, simulator analysis, and downstream decision-making reliability.

Yuhan Yang, Ruipu Li, Alexander Rodríguez

Computer Science and Engineering University of Michigan

AI for Science Neuro-Symbolic Reasoning LLM Reasoning

Jun 1, 2026cs.SE

The Biomimetic Architecture of Software 4.0

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

Philip Sheldrake, Dirk Scheffler

Unnamed Labs Amsterdam

Neuro-Symbolic Reasoning

May 31, 2026cs.CV

Distilling Neuro-Symbolic Programs into 3D Multi-modal LLMs

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.

Wentao Mo, Yang Liu

Wangxuan Institute of Computer Technology, Peking University

CoT Distillation 3D Spatial Reasoning Multimodal CoT Reasoning Neuro-Symbolic Reasoning 3D VLMs

May 30, 2026cs.AI

AXIOM: A Trust-First Neuro-Symbolic Execution Architecture for Verifiable Mathematical Reasoning

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.

Alessio Bruno

Independent researcher

LLM Answer Verification Symbolic Reasoning Neuro-Symbolic Reasoning LLM Mathematical Reasoning

May 29, 2026cs.CL

Neuro-symbolic Syntactic Parsing: Shaping a Neural Network with the CYK Algorithm

In this paper, we show the possibility of a direct injection of algorithms into neural network architecture. We focus on a complex algorithm, that is, Cocke-Youger-Kasami (CYK) for parsing context-free grammars in Chomsky Normal Form and we propose CYKNN, a simple recurrent neural network architecture for encoding the CYK algorithm in trainable matrix-vector multiplications.We experimented with a very simple grammar with 4 variations showing that our approach outperforms existing LLMs with more than 20B parameters with an in-context learning setting and smaller LLMs of the Qwen family fine-tuned with LoRA. Our attempt paves the way to a different approach to neuro-symbolic methodologies.

Fabio Massimo Zanzotto, Federico Ranaldi, Giorgio Satta

Human-centric ART, University of Rome Tor Vergata, Italy · DEI, University of Padua, Italy

Neural Algorithmic Reasoning Recurrent Neural Networks Neuro-Symbolic Reasoning Algorithmic Reasoning

May 27, 2026cs.LG

BIRDNet: Mining and Encoding Boolean Implication Knowledge Graphs as Interpretable Deep Neural Networks

Tabular data in knowledge-rich domains often carries a latent prior in the form of Boolean implication relationships (BIRs) between pairs of features. We mine such relationships with a sparse-exception binomial test. The mined implications form a typed directed graph, equivalent to a propositional rule base of 2-literal clauses. We encode this graph as the connectivity of a layered neural network, called BIRDNet, in which each hidden unit corresponds to one mined rule and binds only to its two features. We show two consequences of this design: First, the architecture is sparse by construction: at most

2/d

of the weights in each BIR layer are active, where

d

is the input dimension. Second, the model is interpretable: every trained unit keeps a stable symbolic identity, so rules can be read off the network without surrogate models. Unlike most neurosymbolic models, BIRDNet does not consume an external rule base; its structural prior is mined from the data. We evaluate BIRDNet on six transcriptomic and proteomic benchmarks. Our results show that BIRDNet stays within 0.02 AUROC of the strongest dense baseline, at a small accuracy cost, while using up to

96\times

fewer active parameters than an architecture-matched dense MLP. First-layer rules recover known biological signatures across multiple cancer subtypes and tissue types, including canonical amplicons, lineage-defining co-expression modules, and immune-infiltration markers. Data and code are available at: https://github.com/MAHI-Group/BIRDNet.

Tirtharaj Dash

BITS Pilani, K K Birla Goa Campus Zuarinagar, Goa 403726, India

Neural Network Interpretability Neuro-Symbolic Reasoning Sparse Neural Networks

May 27, 2026cs.LG

SYNAPSE: Neuro-Symbolic Visual Thought-to-Text Decoding via Topological Semantic Denoising

Recent advances in large language models have accelerated open-vocabulary EEG-to-imagined-text decoding, where non-invasive neural activity recorded during visual perception is translated into coherent natural language descriptions of viewed stimuli. However, existing systems remain highly vulnerable to biological noise, where corrupted neural projections induce hallucinated or semantically unstable generation in frozen language models. We introduce SYNAPSE (Symbolic Neural Alignment for Precise Semantic Extraction), a lightweight neuro-symbolic framework that stabilizes neural text generation through inference-time symbolic regularization. By purifying EEG-derived semantic candidates using commonsense graph structure and latent exemplars, SYNAPSE improves semantic stability without end-to-end LLM fine-tuning. Experiments across popular EEG decoding benchmarks and multiple frozen LLM backends demonstrate consistent gains over unconstrained prompting baselines, robustness under object-label ablation, and performance commensurate with substantially more resource-intensive fine-tuned systems, while preserving biometric privacy by localizing raw EEG processing entirely within the encoder stack.

Akshaj Murhekar, Abhijit Mishra

School of Information University of Texas at Austin

Language Model Decoding EEG Decoding EEG-Based Visual Decoding Neuro-Symbolic Reasoning

May 26, 2026cs.AI

Neuro-Symbolic Verification of LLM Outputs for Data-Sensitive Domains (extended preprint)

LLMs deployed in high-stakes domains face fundamental reliability challenges: hallucinations, inconsistencies, and privacy vulnerabilities introduce unacceptable risks where errors carry legal, financial, or safety consequences. This paper presents a hybrid verification architecture combining formal symbolic methods with neural semantic analysis to provide complementary guarantees for LLM-generated content. This architecture employs logical reasoning for input verification, leveraging completeness properties to provide decidable guarantees on structured requirements. For output validation, embedding-based semantic similarity detects contextual hallucinations where formal methods lack expressiveness. This separation is realized in a parallel, actor-based pipeline, addressing limitations of prompt-based self-verification approaches, which inherit the distributional biases that produce hallucinations. The proposed architecture and type-aware verification method are validated with HAIMEDA, a real-world medical device damage assessment reporting system developed through Action Design Research. Evaluation shows hallucination detection rates of over 83% for structured entities and 72% for semantic fabrications, with a 30% reduction in report creation time, demonstrating that neuro-symbolic architectures can provide principled safeguards for LLM deployment in data-sensitive domains.

Paul Sigloch, Christoph Benzmüller

University of Bamberg, Bamberg, Germany · Free University of Berlin, Berlin, Germany

LLM Answer Verification LLM Hallucination Detection Neuro-Symbolic Reasoning

May 25, 2026cs.AI

Neural Scalable Symbolic Search Framework for Complex Logical Queries with Multiple Free Variables

Complex Query Answering (CQA) is a fundamental knowledge representation and reasoning task over incomplete knowledge graphs (KGs). Answering existential first-order queries with

k

free variables (i.e.,

\text{EFO}_k

queries) is a crucial yet challenging problem, as it requires ranking answer tuples in

\mathcal{E}^k

, where

\mathcal{E}

denotes the entity set of a KG. This quickly becomes intractable as

k

grows. Consequently, existing benchmarks and methods rely on marginal rankings over individual variables; however, marginal rankings are a poor proxy for the true joint ranking of tuples. Building on neural symbolic search for

\text{EFO}_1

queries, we propose Neural Scalable Symbolic Search (NS3), a budgeted framework that approximates joint ranking without enumerating

\mathcal{E}^k

. NS3 (i) answers marginalized sub-queries to obtain necessary candidate sets, (ii) merges multiple free variables into hypernodes whose domains are pruned and controlled by a dynamic budget

B

, and (iii) progressively reduces an

\text{EFO}_k

query to an

\text{EFO}_{k-1}

query over a budgeted reduced domain. Across three standard KG datasets, NS3 substantially improves joint ranking performance while retaining strong marginal accuracy. We further release a joint-ranking benchmark that extends existing

\text{EFO}_1

datasets to

k=3

, enabling systematic evaluation of multi-variable queries. Our code is provided in https://github.com/HKUST-KnowComp/NS3_KDD2026.

Weizhi Fei, Hang Yin, Zihao Wang +3

Department of Mathematical Sciences, Tsinghua University Beijing, China · Squarepoint Capital Singapore, Singapore · Department of Computer Science and Engineering, Hong Kong University of Science and Technology Hong Kong, Hong Kong +1

Learning to Rank Neuro-Symbolic Reasoning Knowledge Graphs

May 25, 2026cs.AI

Uncertainty Reasoning with Large Language Models for Explainable Disease Diagnosis

Clinical decision-making requires reasoning over incomplete, imprecise, and linguistically expressed patient narratives. While large language models (LLMs) excel at extracting latent information from natural language, they lack the verifiability and interpretability essential for trustworthy medical AI. We propose a neuro-symbolic reasoning framework that aligns LLMs with formal logic to enable explainable and formally verifiable medical diagnosis. Patient descriptions and clinical guidelines are embedded into a neural knowledge base, where LLMs extract structured medical entities, temporal relations, and fuzzy symptom patterns, which are decoded into a symbolic knowledge base expressed in fuzzy logic and declarative rules. We perform two-stage reasoning: (1) inductive symbolic generalization to capture diagnostic patterns from encoded narratives, and (2) inference verification via a logic programming engine to derive and validate diagnoses consistent with clinical standards. Each symptom is treated as a fuzzy predicate with probabilistic weights, and inference paths are auditable, adjustable, and compatible with physician feedback. Unlike purely statistical methods, our system supports iterative refinement: misalignment between LLM-generated diagnoses and ground truth can be traced, explained, and corrected through formal rules. By combining logic-based transparency, LLM adaptability, and probabilistic robustness, the framework enables human-aligned healthcare inference with strong generalization and verifiable, step-by-step reasoning chains. We validate our framework on public benchmarks, demonstrating effective reconciliation of symbolic reasoning and LLMs with real-world clinical narratives. Results show performance comparable to state-of-the-art LLMs, while additionally providing interpretable reasoning paths and formally verifiable diagnostic conclusions.

Xiaoyang Fan, Yufan Cai, Zhe Hou +1

National University of Singapore · Griffith University

Clinical Decision Support Clinical Reasoning Neuro-Symbolic Reasoning Medical LLMs