Neuro-Symbolic Reasoning

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Neuro-symbolic reasoning studies how to combine neural models’ ability to learn from language, images, and other data with symbolic systems that represent facts, rules, and constraints explicitly. Common approaches use differentiable or probabilistic logic, learned rule induction, and knowledge graphs, or have language models translate problems into programs that solvers, planners, or verifiers can execute. These methods are applied to tasks such as mathematical proof, visual and temporal question answering, robotics, clinical decision support, and policy compliance, where traces and constraints can make decisions easier to check. A central challenge is reliably grounding neural outputs in symbols: translation errors, uncertain evidence, and irrelevant rules can undermine correctness, while stronger verification and structured search may add computational cost or limit flexibility.

Latest papers

279 papers17 papers in the last four weeks, down 35% on the four weeks before. 0.1% of all new papers.

Mar 6, 2026

The EpisTwin: A Knowledge Graph-Grounded Neuro-Symbolic Architecture for Personal AI

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

Giovanni Servedio, Potito Aghilar, Alessio Mattiace +6

Politecnico di Bari · Universit`a degli Studi della Tuscia

Personal AI Agents Neuro-Symbolic Reasoning Knowledge Graphs Multimodal KGs Question Answering Graph Retrieval-Augmented Generation

Mar 5, 2026

Distilling Formal Logic into Neural Spaces: A Kernel Alignment Approach for Signal Temporal Logic

We introduce a framework for learning continuous neural representations of formal specifications by distilling the geometry of their semantics into a latent space. Existing approaches rely either on symbolic kernels -- which preserve behavioural semantics but are computationally prohibitive, anchor-dependent, and non-invertible -- or on syntax-based neural embeddings that fail to capture underlying structures. Our method bridges this gap: using a teacher-student setup, we distill a symbolic robustness kernel into a Transformer encoder. Unlike standard contrastive methods, we supervise the model with a continuous, kernel-weighted geometric alignment objective that penalizes errors in proportion to their semantic discrepancies. Once trained, the encoder produces embeddings in a single forward pass, effectively mimicking the kernel's logic at a fraction of its computational cost. We apply our framework to Signal Temporal Logic (STL), demonstrating that the resulting neural representations faithfully preserve the semantic similarity of STL formulae, accurately predict robustness and constraint satisfaction, and remain intrinsically invertible. Our proposed approach enables highly efficient, scalable neuro-symbolic reasoning and formula reconstruction without repeated kernel computation at runtime.

Sara Candussio, Gabriele Sarti, Gaia Saveri +1

AILab, MIGe, University of Trieste, IT · Khoury College of Computing Sciences, Northeastern University, Boston, MA, USA

Neuro-Symbolic Reasoning Signal Temporal Logic

Mar 5, 2026

Logi-PAR: Logic-Infused Patient Activity Recognition via Differentiable Rule

Patient Activity Recognition (PAR) in clinical settings uses activity data to improve safety and quality of care. Although significant progress has been made, current models mainly identify which activity is occurring. They often spatially compose sub-sparse visual cues using global and local attention mechanisms, yet only learn logically implicit patterns due to their neural-pipeline. Advancing clinical safety requires methods that can infer why a set of visual cues implies a risk, and how these can be compositionally reasoned through explicit logic beyond mere classification. To address this, we proposed Logi-PAR, the first Logic-Infused Patient Activity Recognition Framework that integrates contextual fact fusion as a multi-view primitive extractor and injects neural-guided differentiable rules. Our method automatically learns rules from visual cues, optimizing them end-to-end while enabling the implicit emergence patterns to be explicitly labelled during training. To the best of our knowledge, Logi-PAR is the first framework to recognize patient activity by applying learnable logic rules to symbolic mappings. It produces auditable why explanations as rule traces and supports counterfactual interventions (e.g., risk would decrease by 65% if assistance were present). Extensive evaluation on clinical benchmarks (VAST and OmniFall) demonstrates state-of-the-art performance, significantly outperforming Vision-Language Models and transformer baselines. The code is available via: https://github.com/zararkhan985/Logi-PAR.git}

Muhammad Zarar, MingZheng Zhang, Xiaowang Zhang +3

School of Computer Software, Tianjin University, China

Human Activity Recognition Neuro-Symbolic Reasoning

Mar 4, 2026

Neuro-Symbolic Financial Reasoning via Deterministic Fact Ledgers and Adversarial Low-Latency Hallucination Detector

Standard Retrieval-Augmented Generation (RAG) architectures fail in high-stakes financial domains due to two fundamental limitations: the inherent arithmetic incompetence of Large Language Models (LLMs) and the distributional semantic conflation of dense vector retrieval (e.g., mapping "Net Income" to "Net Sales" due to contextual proximity). In deterministic domains, a 99% accuracy rate yields 0% operational trust. To achieve zero-hallucination financial reasoning, we introduce the Verifiable Numerical Reasoning Agent (VeNRA). VeNRA shifts the RAG paradigm from retrieving probabilistic text to retrieving deterministic variables via a strictly typed Universal Fact Ledger (UFL). We mathematically bound this ledger using a novel Double-Lock Grounding algorithm. Coupled with deterministic Python execution, this neuro-symbolic routing compresses systemic hallucination rates to a near-zero 1.2%. Recognising that upstream parsing anomalies inevitably occur, we introduce the VeNRA Sentinel: a 3-billion parameter SLM trained to forensically audit candidate using a single-token inference budget with optional post-hoc reasoning. To train the Sentinel, we steer away from traditional hallucination datasets in favour of Adversarial Simulation, programmatically sabotaging financial records to simulate Ecological Errors. The compact Sentinel consequently outperforms 70B+ frontier models in error detection. Through Loss Dilution phenomenon in Reverse-CoT training, we present a novel Micro-Chunking loss algorithm to stabilise gradients under extreme verdict penalisation, yielding a 28x latency speedup without sacrificing forensic rigor.

Pedram Agand

FactAI Lab, Vancouver, BC, Canada.

Financial Reasoning in Language Models Neuro-Symbolic Reasoning Numerical Reasoning in Language Models LLM Hallucination Detection Language Model Auditing

Mar 4, 2026

Continuous Modal Logical Neural Networks: Modal Reasoning via Stochastic Accessibility

We propose Fluid Logic, a paradigm in which modal logical reasoning, temporal, epistemic, doxastic, deontic, is lifted from discrete Kripke structures to continuous manifolds via Neural Stochastic Differential Equations (Neural SDEs). Each type of modal operator is backed by a dedicated Neural SDE, and nested formulas compose these SDEs in a single differentiable graph. A key instantiation is Logic-Informed Neural Networks (LINNs): analogous to Physics-Informed Neural Networks (PINNs), LINNs embed modal logical formulas such as (

\Box

bounded) and (

\Diamond

visits_lobe) directly into the training loss, guiding neural networks to produce solutions that are structurally consistent with prescribed logical properties, without requiring knowledge of the governing equations. The resulting framework, Continuous Modal Logical Neural Networks (CMLNNs), yields several key properties: (i) stochastic diffusion prevents quantifier collapse (

\Box

and

\Diamond

differ), unlike deterministic ODEs; (ii) modal operators are entropic risk measures, sound with respect to risk-based semantics with explicit Monte Carlo concentration guarantees; (iii)SDE-induced accessibility provides structural correspondence with classical modal axioms; (iv) parameterizing accessibility through dynamics reduces memory from quadratic in world count to linear in parameters. Three case studies demonstrate that Fluid Logic and LINNs can guide neural networks to produce consistent solutions across diverse domains: epistemic/doxastic logic (multi-robot hallucination detection), temporal logic (recovering the Lorenz attractor geometry from logical constraints alone), and deontic logic (learning safe confinement dynamics from a logical specification).

Antonin Sulc

Lawrence Berkeley National Laboratory, Berkeley, CA, USA

Logical Reasoning Neuro-Symbolic Reasoning Neural Algorithmic Reasoning Epistemic Logic

Mar 4, 2026

Can LLM Aid in Solving Constraints with Inductive Definitions?

Solving constraints involving inductive (aka recursive) definitions is challenging. State-of-the-art SMT/CHC solvers and first-order logic provers provide only limited support for solving such constraints, especially when they involve, e.g., abstract data types. In this work, we leverage structured prompts to elicit Large Language Models (LLMs) to generate auxiliary lemmas that are necessary for reasoning about these inductive definitions. We further propose a neuro-symbolic approach, which synergistically integrates LLMs with constraint solvers: the LLM iteratively generates conjectures, while the solver checks their validity and usefulness for proving the goal. We evaluate our approach on a diverse benchmark suite comprising constraints originating from algebrai data types and recurrence relations. The experimental results show that our approach can improve the state-of-the-art SMT and CHC solvers, solving considerably more (around 25%) proof tasks involving inductive definitions, demonstrating its efficacy.

Weizhi Feng, Shidong Shen, Jiaxiang Liu +3

Key Laboratory of System Software (Chinese Academy of Sciences), Institute of Software, Chinese Academy of Sciences, Beijing, China · University of Chinese Academy of Sciences, Beijing, China · Birkbeck, University of London, United Kingdom +1

Automated Theorem Proving Neuro-Symbolic Reasoning Satisfiability Modulo Theories

Mar 3, 2026

Neuro-Symbolic Artificial Intelligence: A Task-Directed Survey in the Black-Box Models Era

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

Giovanni Pio Delvecchio, Lorenzo Molfetta, Gianluca Moro

Department of Computer Science and Engineering, University of Bologna, Cesena Campus Via dell’Universit`a 50, I-47522 Cesena, Italy

Neuro-Symbolic AI Neuro-Symbolic Reasoning Neurosymbolic Learning Explainable Artificial Intelligence

Mar 3, 2026

NeuroProlog: Multi-Task Fine-Tuning for Neurosymbolic Mathematical Reasoning via the Cocktail Effect

Large Language Models (LLMs) achieve strong performance on natural language tasks but remain unreliable in mathematical reasoning, frequently generating fluent yet logically inconsistent solutions. We present NeuroProlog, a neurosymbolic framework that ensures verifiable reasoning by compiling math word problems into executable Prolog programs with formal verification guarantees. We propose a multi-task Cocktail training strategy that jointly optimizes three synergistic objectives in a unified symbolic representation space: (i) mathematical formula-to-rule translation (KB), (ii) natural language-to-program synthesis (SOLVE), and (iii) program-answer alignment. This joint supervision enables positive transfer, where symbolic grounding in formula translation directly improves compositional reasoning capabilities. At inference, we introduce an execution-guided decoding pipeline with fine-grained error taxonomy that enables iterative program repair and quantifies model self-debugging capacity. Evaluation on GSM8K across multiple model scales demonstrates that cocktail training improves accuracy over single-task baselines, with statistically significant gains for most evaluated models. Error analysis reveals scale-associated differences in repair behavior: larger models exhibit more readily correctable errors, whereas smaller models show reduced syntactic errors but persistent semantic failures. These findings suggest that model capacity influences the acquisition of reliable symbolic reasoning and self-correction capabilities.

Pratibha Zunjare, Michael Hsiao

Electrical and Computer Engineering, Virginia Tech, Blacksburg, USA

LLM Mathematical Reasoning Neuro-Symbolic Reasoning Program Synthesis Multi-Task Learning

Mar 2, 2026

NeuroSymb-MRG: Differentiable Abductive Reasoning with Active Uncertainty Minimization for Radiology Report Generation

Automatic generation of radiology reports seeks to reduce clinician workload while improving documentation consistency. Existing methods that adopt encoder-decoder or retrieval-augmented pipelines achieve progress in fluency but remain vulnerable to visual-linguistic biases, factual inconsistency, and lack of explicit multi-hop clinical reasoning. We present NeuroSymb-MRG, a unified framework that integrates NeuroSymbolic abductive reasoning with active uncertainty minimization to produce structured, clinically grounded reports. The system maps image features to probabilistic clinical concepts, composes differentiable logic-based reasoning chains, decodes those chains into templated clauses, and refines the textual output via retrieval and constrained language-model editing. An active sampling loop driven by rule-level uncertainty and diversity guides clinician-in-the-loop adjudication and promptbook refinement. Experiments on standard benchmarks demonstrate consistent improvements in factual consistency and standard language metrics compared to representative baselines.

Rong Fu, Yiqing Lyu, Chunlei Meng +9

University of Macau · Tsinghua University · Fudan University +6

Radiology Report Generation Clinical Reasoning Neuro-Symbolic Reasoning Abductive Reasoning

Mar 1, 2026

Contextual Invertible World Models: A Neuro-Symbolic Agentic Framework for Colorectal Cancer Drug Response

Precision oncology is currently limited by the small-N, large-P paradox, where high-dimensional genomic data is abundant but pharmacological response samples are sparse. While deep learning achieves predictive accuracy, it frequently fails to provide the mechanistic clarity required for clinical adoption. We present the Contextual Invertible World Model (CIWM), a Neuro-Symbolic Agentic Framework that bridges this gap by integrating a quantitative machine learning emulator with a Large Language Model reasoning layer. Utilising a stringently curated, high-fidelity data engineering pipeline on the Sanger GDSC dataset (

N=83

), we isolate true biological signals from in vitro artifacts to establish a rigorous baseline predictive correlation for complex transcriptomics (

r=0.268

). Through Inverse Reasoning, we perform in silico CRISPR perturbations across the colorectal landscape. The framework autonomously overturns classical mechanistic assumptions, identifying a hierarchical dominance of mutant KRAS over the APC/Wnt-axis in driving 5-fluorouracil resistance (

Δ=-0.0469

) via a "KRAS Shield" mapped to MAPK/PI3K networks. Furthermore, the agentic layer identified a "PIK3CA Paradox", revealing that repairing PIK3CA inadvertently increases chemoresistance (

Δ=+0.0085

) by triggering a compensatory feedback loop that hyperactivates the dominant MAPK survival pathway.

Christopher Baker, Tianyu Ren, Karen Rafferty +1

School of Electronics, Electrical Engineering and Computer Science, Queen's University Belfast, Belfast, United Kingdom

Cancer Drug Response Prediction World Models Cancer Genomics Neuro-Symbolic Reasoning

Mar 1, 2026

BioProAgent: Neuro-Symbolic Grounding for Constrained Scientific Planning

Large language models (LLMs) have demonstrated significant reasoning capabilities in scientific discovery but struggle to bridge the gap to physical execution in wet-labs. In these irreversible environments, probabilistic hallucinations are not merely incorrect; they can cause equipment damage or experimental failure. We propose BioProAgent, a neuro-symbolic framework that anchors probabilistic planning in a deterministic Finite State Machine (FSM). We introduce a State-Augmented Planning mechanism that enforces a rigorous Design-Verify-Rectify workflow, ensuring hardware compliance before execution. Furthermore, we address the context bottleneck inherent in complex device schemas by Semantic Symbol Grounding, reducing token consumption by ~6* through symbolic abstraction. In the extended BioProBench benchmark, BioProAgent achieves 95.6% physical compliance (compared to 21.0% for ReAct), demonstrating that neuro-symbolic constraints are essential for reliable autonomy in irreversible physical environments. Code: https://github.com/YuyangSunshine/bioproagent | Website: https://yuyangsunshine.github.io/BioPro-Project.

Yuyang Liu, Jingya Wang, Liuzhenghao Lv +1

School of AI for Science, Peking University · School of Electronic and Computer Engineering, Peking University · School of Computer Science, Peking University

Autonomous Experimentation Neuro-Symbolic Planning Laboratory Automation Symbolic Planning Neuro-Symbolic Reasoning AI Agent Safety Benchmarks

Feb 26, 2026

RT-NeuS: Towards Real-Time Neuro-Symbolic Video Understanding via Adaptive Temporal Verification

Long-form video question answering (LVQA) requires answering natural-language queries about videos spanning minutes to hours, demanding temporal reasoning across thousands of frames. Standard vision-language models (VLMs) struggle with this task: their fixed frame budgets force aggressive downsampling that misses the temporal structure that complex queries depend on. Neuro-symbolic approaches address this by decomposing queries into atomic propositions, translating them into temporal logic specifications, and applying formal model checking to retrieve segments satisfying the specification. This yields up to 10% higher accuracy on temporally complex benchmarks, with interpretability and formal guarantees. However, constructing the video automaton requires grounding every proposition at every frame window via VLM calls, resulting in up to 130x slower inference than standard VLM prompting. We present RT-NeuS, a framework that preserves the accuracy and formal guarantees of temporal-logic-guided LVQA while closing this latency gap. RT-NeuS introduces coarse-to-fine adaptive sampling to identify the small set of query-relevant, visually distinct frames, and batched proposition detection with KV-cache reuse to evaluate all propositions per window in a single forward pass. We derive latency upper bounds as a function of video length, proposition count, and sampling density. Experiments on LongVideoBench, Video-MME, and MLVU reduce inference latency by up to 13x on a single NVIDIA H200 GPU, while matching or exceeding prior neuro-symbolic accuracy.

Shawn Liang, Sahil Shah, Chengwei Zhou +5

Case Western Reserve University · The University of Texas at Austin

Long-Video QA Temporal Video Understanding Neuro-Symbolic Reasoning Efficient VLM Inference Query-Aware Video Frame Selection

Feb 26, 2026

WaterVideoQA: ASV-Centric Perception and Rule-Compliant Reasoning via Multi-Modal Agents

While autonomous navigation has achieved remarkable success in passive perception (e.g., object detection and segmentation), it remains fundamentally constrained by a void in knowledge-driven, interactive environmental cognition. In the high-stakes domain of maritime navigation, the ability to bridge the gap between raw visual perception and complex cognitive reasoning is not merely an enhancement but a critical prerequisite for Autonomous Surface Vessels to execute safe and precise maneuvers. To this end, we present WaterVideoQA, the first large-scale, comprehensive Video Question Answering benchmark specifically engineered for all-waterway environments. This benchmark encompasses 3,029 video clips across six distinct waterway categories, integrating multifaceted variables such as volatile lighting and dynamic weather to rigorously stress-test ASV capabilities across a five-tier hierarchical cognitive framework. Furthermore, we introduce NaviMind, a pioneering multi-agent neuro-symbolic system designed for open-ended maritime reasoning. By synergizing Adaptive Semantic Routing, Situation-Aware Hierarchical Reasoning, and Autonomous Self-Reflective Verification, NaviMind transitions ASVs from superficial pattern matching to regulation-compliant, interpretable decision-making. Experimental results demonstrate that our framework significantly transcends existing baselines, establishing a new paradigm for intelligent, trustworthy interaction in dynamic maritime environments.

Runwei Guan, Shaofeng Liang, Ningwei Ouyang +9

Thrust of Artificial Intelligence, The Hong Kong University of Science and Technology (Guangzhou), Guangzhou, China. · Hubei Key Laboratory of Inland Shipping Technology (Wuhan University of Technology), Wuhan, China · School of Advanced Technology, Xi’an Jiaotong-Liverpool University, Suzhou, China. +5

Video QA Video Reasoning Unmanned Surface Vehicle Multimodal Agents Neuro-Symbolic Reasoning

Feb 25, 2026

Neural-Symbolic Logic Query Answering in Non-Euclidean Space

Answering complex first-order logic (FOL) queries on knowledge graphs is essential for reasoning. Symbolic methods offer interpretability but struggle with incomplete graphs, while neural approaches generalize better but lack transparency. Neural-symbolic models aim to integrate both strengths but often fail to capture the hierarchical structure of logical queries, limiting their effectiveness. We propose HYQNET, a neural-symbolic model for logic query reasoning that fully leverages hyperbolic space. HYQNET decomposes FOL queries into relation projections and logical operations over fuzzy sets, enhancing interpretability. To address missing links, it employs a hyperbolic GNN-based approach for knowledge graph completion in hyperbolic space, effectively embedding the recursive query tree while preserving structural dependencies. By utilizing hyperbolic representations, HYQNET captures the hierarchical nature of logical projection reasoning more effectively than Euclidean-based approaches. Experiments on three benchmark datasets demonstrate that HYQNET achieves strong performance, highlighting the advantages of reasoning in hyperbolic space.

Lihui Liu

Wayne State University, Detroit, Michigan, USA

Neuro-Symbolic Reasoning Knowledge Graph Question Answering Multi-Hop Reasoning

Feb 25, 2026

Knowledge, Rules and Their Embeddings: Two Paths towards Neuro-Symbolic JEPA

Modern self-supervised predictive architectures excel at capturing complex statistical correlations from high-dimensional data but lack mechanisms to internalize verifiable human logic, leaving them susceptible to spurious correlations and shortcut learning. Conversely, traditional rule-based inference systems offer rigorous, interpretable logic but suffer from discrete boundaries and NP-hard combinatorial explosion. To bridge this divide, we propose a bidirectional neuro-symbolic framework centered around Rule-informed Joint-Embedding Predictive Architectures (RiJEPA). In the first direction, we inject structured inductive biases into JEPA training via Energy-Based Constraints (EBC) and a multi-modal dual-encoder architecture. This fundamentally reshapes the representation manifold, replacing arbitrary statistical correlations with geometrically sound logical basins. In the second direction, we demonstrate that by relaxing rigid, discrete symbolic rules into a continuous, differentiable logic, we can bypass traditional combinatorial search for new rule generation. By leveraging gradient-guided Langevin diffusion within the rule energy landscape, we introduce novel paradigms for continuous rule discovery, which enable unconditional joint generation, conditional forward and abductive inference, and marginal predictive translation. Empirical evaluations on both synthetic topological simulations and a high-stakes clinical use case confirm the efficacy of our approach. Ultimately, this framework establishes a powerful foundation for robust, generative, and interpretable neuro-symbolic representation learning.

Yongchao Huang, Hassan Raza

Differentiable Logic Neuro-Symbolic Reasoning Joint-Embedding Predictive Architecture

Feb 25, 2026

NGDB-Zoo: Towards Efficient and Scalable Neural Graph Databases Training

Neural Graph Databases (NGDBs) facilitate complex logical reasoning over incomplete knowledge structures, yet their training efficiency and expressivity are constrained by rigid query-level batching and structure-exclusive embeddings. We present NGDB-Zoo, a unified framework that resolves these bottlenecks by synergizing operator-level training with semantic augmentation. By decoupling logical operators from query topologies, NGDB-Zoo transforms the training loop into a dynamically scheduled data-flow execution, enabling multi-stream parallelism and achieving a

1.8\times

-

6.8\times

throughput compared to baselines. Furthermore, we formalize a decoupled architecture to integrate high-dimensional semantic priors from Pre-trained Text Encoders (PTEs) without triggering I/O stalls or memory overflows. Extensive evaluations on six benchmarks, including massive graphs like ogbl-wikikg2 and ATLAS-Wiki, demonstrate that NGDB-Zoo maintains high GPU utilization across diverse logical patterns and significantly mitigates representation friction in hybrid neuro-symbolic reasoning.

Zhongwei Xie, Jiaxin Bai, Shujie Liu +5

The Hong Kong University of Science and Technology · Microsoft Research Asia

Graph Reasoning Neuro-Symbolic Reasoning Graph Neural Networks

Feb 22, 2026

Neuro-Symbolic Decoding of Neural Activity

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

Yanchen Wang, Joy Hsu, Ehsan Adeli +1

Columbia University · Stanford University

Neural Decoding fMRI-Based Visual Decoding Neuro-Symbolic Reasoning Multimodal Grounding Compositional Generalization

Feb 20, 2026

Neurosymbolic Language Reasoning as Satisfiability Modulo Theory

Natural language understanding requires interleaving textual and logical reasoning, yet large language models often fail to perform such reasoning reliably. Existing neurosymbolic systems combine LLMs with solvers but remain limited to fully formalizable tasks such as math or program synthesis, leaving natural documents with only partial logical structure unaddressed. We introduce Logitext, a neurosymbolic language that represents documents as natural language text constraints (NLTCs), making partial logical structure explicit. We develop an algorithm that integrates LLM-based constraint evaluation with satisfiability modulo theory (SMT) solving, enabling joint textual-logical reasoning. Experiments on a new content moderation benchmark, together with LegalBench and Super-Natural Instructions, show that Logitext improves both accuracy and coverage. This work is the first that treats LLM-based reasoning as an SMT theory, extending neurosymbolic methods beyond fully formalizable domains.

Hyunseok Oh, Sam Stern, Youngki Lee +1

Seoul National University · U. Mass. Amherst · Microsoft

Constraint-Guided Reasoning in Language Models Neuro-Symbolic Reasoning Symbolic Reasoning in Language Models Satisfiability Modulo Theories

Feb 19, 2026

Ontology-Guided Neuro-Symbolic Inference: Grounding Language Models with Mathematical Domain Knowledge

Language models exhibit fundamental limitations -- hallucination, brittleness, and lack of formal grounding -- that are particularly problematic in high-stakes specialist fields requiring verifiable reasoning. I investigate whether formal domain ontologies can enhance language model reliability through retrieval-augmented generation. Using mathematics as proof of concept, I implement a neuro-symbolic pipeline leveraging the OpenMath ontology with hybrid retrieval and cross-encoder reranking to inject relevant definitions into model prompts. Evaluation on the MATH benchmark with three open-source models reveals that ontology-guided context improves performance when retrieval quality is high, but irrelevant context actively degrades it -- highlighting both the promise and challenges of neuro-symbolic approaches.

Marcelo Labre

Advanced Institute for Artificial Intelligence (AI2)

Retrieval-Augmented Generation LLM Grounding Knowledge Augmentation for Language Models LLM Reliability Neuro-Symbolic Reasoning LLM Mathematical Reasoning

Feb 19, 2026

Differentiable Symbolic Planning: A Neural Architecture for Constraint Reasoning with Learned Feasibility

Neural networks excel at pattern recognition but struggle with constraint reasoning -- determining whether configurations satisfy logical or physical constraints. We introduce Differentiable Symbolic Planning (DSP), a neural architecture that performs discrete symbolic reasoning while remaining fully differentiable. DSP maintains a feasibility channel (phi) that tracks constraint satisfaction evidence at each node, aggregates this into a global feasibility signal (Phi) through learned rule-weighted combination, and uses sparsemax attention to achieve exact-zero discrete rule selection. We integrate DSP into a Universal Cognitive Kernel (UCK) that combines graph attention with iterative constraint propagation. Evaluated on three constraint reasoning benchmarks -- graph reachability, Boolean satisfiability, and planning feasibility -- UCK+DSP achieves 97.4% accuracy on planning under 4x size generalization (vs. 59.7% for ablated baselines), 96.4% on SAT under 2x generalization, and maintains balanced performance on both positive and negative classes where standard neural approaches collapse. Ablation studies reveal that global phi aggregation is critical: removing it causes accuracy to drop from 98% to 64%. The learned phi signal exhibits interpretable semantics, with values of +18 for feasible cases and -13 for infeasible cases emerging without supervision.

Venkatakrishna Reddy Oruganti

Sithara Inc., Plano, Texas, USA

Neuro-Symbolic Planning Neuro-Symbolic Reasoning Symbolic Planning Constraint Satisfaction

Feb 18, 2026

Neuro-Symbolic Strong-AI Robots with Closed Knowledge Assumption: Learning and Deductions

Knowledge representation formalisms are aimed to represent general conceptual information and are typically used in the construction of the knowledge base of reasoning agent. A knowledge base can be thought of as representing the beliefs of such an agent. Like a child, a strong-AI (AGI) robot would have to learn through input and experiences, constantly progressing and advancing its abilities over time. Both with statistical AI generated by neural networks we need also the concept of causality of events traduced into directionality of logic entailments and deductions in order to give to robots the emulation of human intelligence. Moreover, by using the axioms we can guarantee the controlled security about robot's actions based on logic inferences. For AGI robots we consider the 4-valued Belnap's bilattice of truth-values with knowledge ordering as well, where the value "unknown" is the bottom value, the sentences with this value are indeed unknown facts, that is, the missed knowledge in the AGI robots. Thus, these unknown facts are not part of the robot's knowledge database, and by learn through input and experiences, the robot's knowledge would be naturally expanded over time. Consequently, this phenomena can be represented by the Closed Knowledge Assumption and Logic Inference provided by this paper. Moreover, the truth-value "inconsistent", which is the top value in the knowledge ordering of Belnap's bilattice, is necessary for strong-AI robots to be able to support such inconsistent information and paradoxes, like Liar paradox, during deduction processes.

Zoran Majkic

ISRST, Tallahassee, FL, USA

Logical Reasoning Knowledge Representation Neuro-Symbolic Reasoning

Feb 17, 2026

NeuroSymActive: Differentiable Neural-Symbolic Reasoning with Active Exploration for Knowledge Graph Question Answering

Large pretrained language models and neural reasoning systems have advanced many natural language tasks, yet they remain challenged by knowledge-intensive queries that require precise, structured multi-hop inference. Knowledge graphs provide a compact symbolic substrate for factual grounding, but integrating graph structure with neural models is nontrivial: naively embedding graph facts into prompts leads to inefficiency and fragility, while purely symbolic or search-heavy approaches can be costly in retrievals and lack gradient-based refinement. We introduce NeuroSymActive, a modular framework that combines a differentiable neural-symbolic reasoning layer with an active, value-guided exploration controller for Knowledge Graph Question Answering. The method couples soft-unification style symbolic modules with a neural path evaluator and a Monte-Carlo style exploration policy that prioritizes high-value path expansions. Empirical results on standard KGQA benchmarks show that NeuroSymActive attains strong answer accuracy while reducing the number of expensive graph lookups and model calls compared to common retrieval-augmented baselines.

Rong Fu, Yang Li, Zeyu Zhang +7

Independent Researcher

Knowledge Graph Question Answering Multi-Hop QA Neuro-Symbolic Reasoning

Feb 11, 2026

Neuro-Symbolic Synergy for World Modeling

Large language models (LLMs) exhibit strong general-purpose reasoning capabilities, yet they frequently hallucinate when used as world models (WMs), where strict compliance with deterministic transition rules--particularly in corner cases--is essential. In contrast, Symbolic WMs provide logical consistency but lack semantic expressivity. To bridge this gap, we propose Neuro-Symbolic Synergy (NeSyS), a framework that integrates the probabilistic semantic priors of LLMs with executable symbolic rules to achieve both expressivity and robustness. NeSyS alternates training between the two models using trajectories inadequately explained by the other. Unlike rule-based prompting, the symbolic WM contributes candidate-level scores through log-linear reranking, without requiring the LLM to interpret rule text. Rule-guided sampling prioritizes transitions that are weakly covered by symbolic rules, using 35--60% of the training pairs while outperforming full-data supervised fine-tuning in five of six settings. Experiments on ScienceWorld, WebShop, and PlanCraft demonstrate consistent gains in WM prediction accuracy and data efficiency; one-step lookahead on open-ended WebShop also improves agent reward. Our models, rules, and code are available at https://github.com/tianyi-lab/NeSyS.

Hongyu Zhao, Siyu Zhou, Haolin Yang +2

Department of Computer Science University of Maryland College Park, MD 20742, USA · Faculty of Engineering and IT Australian AI Institute University of Technology Sydney Sydney, Australia · Department of Statistics University of Chicago Chicago, IL 60637, USA +2

LLM World Models World Model Learning World Models Symbolic Reasoning Neuro-Symbolic Reasoning Symbolic Reasoning in Language Models

Jan 27, 2026

VERGE: Formal Refinement and Guidance Engine for Verifiable LLM Reasoning

Despite the syntactic fluency of Large Language Models (LLMs), ensuring their logical correctness in high-stakes domains remains a fundamental challenge. We present a neurosymbolic framework that combines LLMs with SMT solvers to produce verification-guided answers through iterative refinement. Our approach decomposes LLM outputs into atomic claims, autoformalizes them into first-order logic, and verifies their logical consistency using automated theorem proving. We introduce three key innovations: (1) multi-model consensus via formal semantic equivalence checking to ensure logic-level alignment between candidates, eliminating the syntactic bias of surface-form metrics, (2) semantic routing that directs different claim types to appropriate verification strategies: symbolic solvers for logical claims and LLM ensembles for commonsense reasoning, and (3) precise logical error localization via Minimal Correction Subsets (MCS), which pinpoint the exact subset of claims to revise, transforming binary failure signals into actionable feedback. Our framework classifies claims by their logical status and aggregates multiple verification signals into a unified score with variance-based penalty. The system iteratively refines answers using structured feedback until acceptance criteria are met or convergence is achieved. This hybrid approach delivers formal guarantees where possible and consensus verification elsewhere, advancing trustworthy AI. With the GPT-OSS-120B model, VERGE demonstrates an average performance uplift of 18.7% at convergence across a set of reasoning benchmarks compared to single-pass approaches.

Vikash Singh, Darion Cassel, Nathaniel Weir +2

Case Western Reserve University · Amazon Web Services

LLM Answer Verification Reasoning Consistency in Language Models Neuro-Symbolic Reasoning

Dec 11, 2025

Achieving Olympiad-Level Geometry Large Language Model Agent via Complexity Boosting Reinforcement Learning

Large language model (LLM) agents exhibit strong mathematical problem-solving abilities and can even solve International Mathematical Olympiad (IMO) level problems with the assistance of formal proof systems. However, due to weak heuristics for auxiliary constructions, AI for geometry problem solving remains dominated by expert models such as AlphaGeometry 2, which rely heavily on large-scale data synthesis and search for both training and evaluation. In this work, we make the first attempt to build a medalist-level LLM agent for geometry and present InternGeometry. InternGeometry overcomes the heuristic limitations in geometry by iteratively proposing propositions and auxiliary constructions, verifying them with a symbolic engine, and reflecting on the engine's feedback to guide subsequent proposals. A dynamic memory mechanism enables InternGeometry to conduct more than two hundred interactions with the symbolic engine per problem. To further accelerate learning, we introduce Complexity-Boosting Reinforcement Learning (CBRL), which gradually increases the complexity of synthesized problems across training stages. Built on InternThinker-32B, InternGeometry solves 44 of 50 IMO geometry problems (2000-2024), exceeding the average gold medalist score (40.9), using only 13K training examples, just 0.004% of the data used by AlphaGeometry 2, demonstrating the potential of LLM agents on expert-level geometry tasks. InternGeometry can also propose novel auxiliary constructions for IMO problems that do not appear in human solutions.

Haiteng Zhao, Junhao Shen, Yiming Zhang +7

1Shanghai AI Laboratory · 2Shanghai Jiao Tong University · 3Peking University +2

LLM Agents Reinforcement Learning Neuro-Symbolic Reasoning

Dec 3, 2025

CRAFT-E: An Interpretable and Editable Neuro-Symbolic Framework for Affordance-Grounded Active Object Retrieval

Assistive robots operating in unstructured environments must reason not only about what objects are, but how they can be used, including non-canonical and improvised uses. This requires grounding language-based action queries to objects that afford the requested function, are visually present, and can be physically retrieved. Existing approaches often rely on black-box models, fixed affordance labels, or direct object predictions, limiting transparency and controllability. We introduce CRAFT-E, a modular neuro-symbolic framework that composes an LLM-derived verb-property-object knowledge graph with CLIP-based visual alignment and energy-based grasp reasoning. The system exposes interpretable grounding paths, incorporates grasp feasibility into affordance inference, and supports targeted graph edits without retraining. We also construct a benchmark dataset with unified annotations for verb-object compatibility, segmentation, and grasp candidates, and deploy the full pipeline on a physical robot. Across static scenes, real-world trials involving 20 verbs and 39 objects, ImageNet-based functional retrieval, and COCO-Tasks transfer, CRAFT-E provides a competitive training-free prior for affordance-grounded retrieval while exposing component-level diagnostics and graph-level interventions. Under staged and full-pipeline perception, CRAFT-E matches strong flat LLM priors in several settings while adding failure attribution and editable reasoning paths. By coupling symbolic reasoning with embodied perception, CRAFT-E offers an inspectable and customizable framework for affordance-grounded object retrieval.

Zhou Chen, Joe Lin, Carson Bulgin +1

CSSE Department, Auburn University, Auburn, 36849, AL, USA.

Robotic Affordance Inference Robotic Object Search Assistive Robotics Neuro-Symbolic Reasoning

Dec 3, 2025

Modal Logic Neural Networks

Neural Networks are indispensable to natural sciences and society. Their impact extends from applications in public health to workforce productivity. Here, we introduce Modal Logic Neural Networks (MLNNs) -- an end-to-end differentiable logical neural network realisation of modal logic which evaluates a learnable truth function across possible-world semantics. This neural architecture handles para-consistency and inconsistency via a learnable world accessibility relation and valuation function. Because the modality is fixed by which frame axioms the relation satisfies rather than by the operator, one differentiable engine covers the epistemic, doxastic, deontic and temporal readings, with applications from verification of reactive and distributed systems to legal discourse and microeconomic utility models. In this paper, we introduce a model of differentiable Kripke semantics, and establish their soundness, convergence, and structural guarantees. We show four applications, in which the learned relation reads as a trust matrix, an operating-regime embedding with safety bounds, a temporal precedence order, and a recovered constraint graph.

Antonin Sulc, Noor Naddour

Lawrence Berkeley National Laboratory, Berkeley, CA, USA · The University of Queensland, Brisbane, QLD, Australia

Logical Reasoning Differentiable Logic Neuro-Symbolic Reasoning

Nov 21, 2025

Bridging Symbolic Control and Neural Reasoning in LLM Agents -- The Structured Cognitive Loop

Large language model agents suffer from architectural fragilities such as entangled reasoning and execution, memory volatility, and uncontrolled action sequences. We introduce Structured Cognitive Loop (SCL), a modular agent architecture that separates cognition into Retrieval, Cognition, Control, Action, and Memory (R-CCAM). SCL introduces Regulation as a dedicated governance layer through which Soft Symbolic Control applies symbolic constraints to probabilistic inference, while Control remains a distinct deterministic runtime engine for duplicate-call prevention, error limits, and termination judgment. Through multi-step conditional reasoning experiments, we show that SCL achieves zero policy violations, prevents redundant tool calls, and maintains complete decision traceability. We position SCL within hybrid intelligence, distinguish it from prompt-centric, memory-only, and neuro-symbolic approaches, and derive three design principles for trustworthy agents: modular decomposition, adaptive symbolic governance, and transparent state management. With an open-source implementation and a live GPT-4o-powered travel planning agent, this work offers a practical path toward reliable, explainable, and governable LLM agents.

Myung Ho Kim

JEI University

Neuro-Symbolic Reasoning AI Agent Governance LLM Agent Reliability

Oct 23, 2025

Neurosymbolic Characterization for Reliable Access Control Policy Analysis

Access control policies are reliability-critical configuration artifacts in cloud systems, yet administrators frequently struggle to verify that a policy permits exactly what they intend. This verification gap cannot be remedied by using LLMs to synthesize policies: we find that reasoning and non-reasoning LLMs fluently explain policy behavior but cannot reason about policy semantics with reliability-grade precision, even when the specification is the LLM's own explanation. We formulate this impasse as the Verifiable Synthesis Paradox: the verification gap persists regardless of how the policy was authored. To remedy this, we introduce PolicySummarizer, a neurosymbolic tool that pairs finite-state automata with an LLM-based simplification to generate precise human-readable characterizations of requests allowed by a policy. PolicySummarizer uses model counting to guarantee the fidelity of the generated characterization by rejecting characterizations that fall below a user-configured threshold in favor of the formally derived one. On 546 AWS, 100 Microsoft Azure, and 100 Google Cloud Platform policies, PolicySummarizer achieves a mean similarity score of 0.93 and a 2.7x improvement over an SMT-based baseline. In a user study, PolicySummarizer raised policy-change-review accuracy from 39% to 93% on the hardest sub-task while reducing self-reported mental demand. We release PolicySummarizer as an open-source tool.

Adarsh Vatsa, Bethel Hall, William Eiers

Stevens Institute of Technology

Neuro-Symbolic Reasoning Access Control

Oct 22, 2025

RLIE: Rule Generation with Logistic Regression, Iterative Refinement, and Evaluation for Large Language Models

Large Language Models (LLMs) can propose rules in natural language, sidestepping the need for a predefined predicate space in traditional rule learning. Yet many LLM-based approaches ignore interactions among rules, and the opportunity to couple LLMs with probabilistic rule learning for robust inference remains underexplored. We present RLIE, a unified framework that integrates LLMs with probabilistic modeling to learn a set of weighted rules. RLIE has four stages: (1) Rule generation, where an LLM proposes and filters candidates; (2) Logistic regression, which learns probabilistic weights for global selection and calibration; (3) Iterative refinement, which updates the rule set using prediction errors; and (4) Evaluation, which compares the weighted rule set as a direct classifier with methods that inject rules into an LLM. We evaluate multiple inference strategies on real-world datasets. Applying rules directly with their learned weights yields superior performance, whereas prompting LLMs with the rules, weights, and logistic-model outputs surprisingly degrades accuracy. This supports the view that LLMs excel at semantic generation and interpretation but are less reliable for precise probabilistic integration. RLIE clarifies the potential and limitations of LLMs for inductive reasoning and couples them with classic probabilistic rule combination methods to enable more reliable neuro-symbolic reasoning.

Yang Yang, Hua XU, Zhangyi Hu +1

The Hong Kong University of Science and Technology (Guangzhou), Guangzhou 511400, China · Institute of Deep Perception Technology, JITRI, Wuxi 214000, China

Logistic Regression Neuro-Symbolic Reasoning LLM Reasoning Rule-Based Classification