Neural-Symbolic Computing: An Effective Methodology for Principled Integration of Machine Learning and Reasoning
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Cited by 33 in LLM reasoning, but placed by its own abstract, which didn’t fit.
Abstract (arXiv)
Current advances in Artificial Intelligence and machine learning in general, and deep learning in particular have reached unprecedented impact not only across research communities, but also over popular media channels. However, concerns about interpretability and accountability of AI have been raised by influential thinkers. In spite of the recent impact of AI, several works have identified the need for principled knowledge representation and reasoning mechanisms integrated with deep learning-based systems to provide sound and explainable models for such systems. Neural-symbolic computing aims at integrating, as foreseen by Valiant, two most fundamental cognitive abilities: the ability to learn from the environment, and the ability to reason from what has been learned. Neural-symbolic computing has been an active topic of research for many years, reconciling the advantages of robust learning in neural networks and reasoning and interpretability of symbolic representation. In this paper, we survey recent accomplishments of neural-symbolic computing as a principled methodology for integrated machine learning and reasoning. We illustrate the effectiveness of the approach by outlining the main characteristics of the methodology: principled integration of neural learning with symbolic knowledge representation and reasoning allowing for the construction of explainable AI systems. The insights provided by neural-symbolic computing shed new light on the increasingly prominent need for interpretable and accountable AI systems.
Key facts. Cited by 151 papers in the map (data through 14 Oct 2026). First posted on arXiv 15 May 2019.
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Citing papers per year: 2020: 1; 2021: 25; 2022: 24; 2023: 15; 2024: 20; 2025: 36; 2026: 30.
151 papers.
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- 2025LlamaV-o1: Rethinking Step-by-step Visual Reasoning in LLMscited by 147
- 2025Reason-RFT: Reinforcement Fine-Tuning for Visual Reasoning of Vision Language Modelscited by 99
- 2021From Statistical Relational to Neurosymbolic Artificial Intelligence: a Surveycited by 72
- 2021A Survey on Hyperdimensional Computing aka Vector Symbolic Architectures, Part II: Applications, Cognitive Models, and Challengescited by 69
- 2025Look-Back: Implicit Visual Re-focusing in MLLM Reasoningcited by 55
- 2022Leveraging Explanations in Interactive Machine Learning: An Overviewcited by 53
- 2021Logic-Driven Context Extension and Data Augmentation for Logical Reasoning of Textcited by 46
- 2022Deep Learning with Logical Constraintscited by 44
- 2022Neurocompositional computing: From the Central Paradox of Cognition to a new generation of AI systemscited by 44
- 2021From LSAT: The Progress and Challenges of Complex Reasoningcited by 43
- 2021Modular Design Patterns for Hybrid Learning and Reasoning Systems: a taxonomy, patterns and use casescited by 39
- 2021A Survey on Neural-symbolic Learning Systemscited by 39
38 more
- 2022Is Neuro-Symbolic AI Meeting its Promise in Natural Language Processing? A Structured Reviewcited by 38
- 2024BEARS Make Neuro-Symbolic Models Aware of their Reasoning Shortcutscited by 37
- 2021Symbols as a Lingua Franca for Bridging Human-AI Chasm for Explainable and Advisable AI Systemscited by 36
- 2022Towards Data-and Knowledge-Driven Artificial Intelligence: A Survey on Neuro-Symbolic Computingcited by 35
- 2022NeuPSL: Neural Probabilistic Soft Logiccited by 34
- 2021EXplainable Neural-Symbolic Learning (X-NeSyL) methodology to fuse deep learning representations with expert knowledge graphs: the MonuMAI cultural heritage use casecited by 30
- 2023Logic-induced Diagnostic Reasoning for Semi-supervised Semantic Segmentationcited by 29
- 2022HAKE: A Knowledge Engine Foundation for Human Activity Understandingcited by 28
- 2021Differentiable Inductive Logic Programming for Structured Examplescited by 26
- 2023Neural Probabilistic Logic Programming in Discrete-Continuous Domainscited by 25
- 2024Towards Cognitive AI Systems: a Survey and Prospective on Neuro-Symbolic AIcited by 24
- 2021ProTo: Program-Guided Transformer for Program-Guided Taskscited by 21
- 2022Neuro-Symbolic Verification of Deep Neural Networkscited by 21
- 2021Differentiable Logic Machinescited by 18
- 2021Injecting Knowledge in Data-driven Vehicle Trajectory Predictorscited by 18
- 2023Grounded Object Centric Learningcited by 17
- 2023LOGICSEG: Parsing Visual Semantics with Neural Logic Learning and Reasoningcited by 17
- 2021Neuro-Symbolic Forward Reasoningcited by 16
- 2023Symbol-LLM: Leverage Language Models for Symbolic System in Visual Human Activity Reasoningcited by 16
- 2024SymbolicAI: A framework for logic-based approaches combining generative models and solverscited by 16
- 2024Softened Symbol Grounding for Neuro-symbolic Systemscited by 16
- 2024Visual Knowledge in the Big Model Era: Retrospect and Prospectcited by 16
- 2023Logic of Differentiable Logics: Towards a Uniform Semantics of DLcited by 15
- 2025A Survey on Deep Learning Approaches for Tabular Data Generation: Utility, Alignment, Fidelity, Privacy, Diversity, and Beyondcited by 15
- 2022VQA and Visual Reasoning: An Overview of Recent Datasets, Methods and Challengescited by 14
- 2023Scalable Neural-Probabilistic Answer Set Programmingcited by 14
- 2022Neuro-Symbolic Learning of Answer Set Programs from Raw Datacited by 12
- 2022Greybox XAI: a Neural-Symbolic learning framework to produce interpretable predictions for image classificationcited by 12
- 2022DEPTWEET: A Typology for Social Media Texts to Detect Depression Severitiescited by 12
- 2023Injecting Logical Constraints into Neural Networks via Straight-Through Estimatorscited by 12
- 2024The Role of Foundation Models in Neuro-Symbolic Learning and Reasoningcited by 12
- 2025A Probabilistic Neuro-symbolic Layer for Algebraic Constraint Satisfactioncited by 11
- 2021Faster-LTN: a neuro-symbolic, end-to-end object detection architecturecited by 10
- 2024Learning with Logical Constraints but without Shortcut Satisfactioncited by 10
- 2022Symbolic Visual Reinforcement Learning: A Scalable Framework with Object-Level Abstraction and Differentiable Expression Searchcited by 9
- 2024On the Hardness of Probabilistic Neurosymbolic Learningcited by 9
- 2021Interpretable Model-based Hierarchical Reinforcement Learning using Inductive Logic Programmingcited by 8
- 2021SLASH: Embracing Probabilistic Circuits into Neural Answer Set Programmingcited by 8
50 most cited of 151 All 151 (JSON)
- 2026Who to Trust in Multi-Robot Systems: Joint Robot and Object Hypothesis Trust Inference via Neural-Symbolic Cross-Validation10 Oct 2026
- 2026Uncertainty in Representation Learning on Knowledge Graphs3 Oct 2026
- 2026Lukasiewicz Neural Networks Extended: Residual Architectures and Crystallization Strategies for Interpretable Rule Extraction26 Sep 2026
- 2026Neurosymbolic Routing for Reliable Reasoning on Resource-Constrained Edge Devices24 Sep 2026
- 2026Soft Symbol Grounding for Prototypical Concepts10 Sep 2026
- 2026Leveraging Low-Level Symbolic Competences for Unsupervised Grounding in Hallucination Detection4 Sep 2026
- 2026From Hybrid Mechanistic--Data-Driven Modeling Toward Neuro-Symbolic AI: What, Why, and How24 Jul 2026
- 2026SoftReason: A Fully Differentiable Neuro-Soft-Symbolic Deductive Reasoning Architecture over High-Dimensional Perceptual Data22 Jul 2026
- 2026Write-Protected Discrete Bottlenecks for Language-Grounded World Models: A Structural Limitation and Sufficient Fix9 Jul 2026
- 2026Structural Certification for Reliable Physical Design with Language Models29 Jun 2026
- 2026VeryTrace: Verifying Reasoning Traces through Compilable Formalism and Structured Verification23 Jun 2026
- 2026Mind-Studio: Executable World Models with Lookahead Evaluation for Partially Observable Games14 Jun 2026
38 more
- 2026From Doyle to AGM: A Survey and an Implementation Roadmap for Belief Change29 May 2026
- 2026A Pilot Benchmark for NL-to-FOL Translation in Planetary Exploration18 May 2026
- 2026Learning to Reason: Targeted Knowledge Discovery and Fuzzy Logic Update for Robust Image Recognition30 Apr 2026
- 2026Auto-Relational Reasoning29 Apr 2026
- 2026Overcoming the Impedance Mismatch: A Theoretical Roadmap for Fusing Foundation Models and Knowledge Graphs21 Apr 2026
- 2026A Sugeno Integral View of Binarized Neural Network Inference20 Apr 2026
- 2026Compositional Neuro-Symbolic Reasoning2 Apr 2026
- 2026Reflect to Inform: Boosting Multimodal Reasoning via Information-Gain-Driven Verification27 Mar 2026
- 20264OPS: Structural Difficulty Modeling in Integer Arithmetic Puzzles26 Mar 2026
- 2026AS2 -- Attention-Based Soft Answer Sets: An End-to-End Differentiable Neuro-Soft-Symbolic Reasoning Architecture19 Mar 2026
- 2026HCP-DCNet: A Hierarchical Causal Primitive Dynamic Composition Network for Self-Improving Causal Understanding12 Mar 2026
- 2026RuCL: Stratified Rubric-Based Curriculum Learning for Multimodal Large Language Model Reasoning25 Feb 2026
- 2026Differentiable Symbolic Planning: A Neural Architecture for Constraint Reasoning with Learned Feasibility19 Feb 2026
- 2026Chimera: Neuro-Symbolic Attention Primitives for Trustworthy Dataplane Intelligence13 Feb 2026
- 2026Kalman-Inspired Runtime Stability and Recovery in Hybrid Reasoning Systems24 Jan 2026
- 2026Confidence over Time: Confidence Calibration with Temporal Logic for Large Language Model Reasoning19 Jan 2026
- 2026Breaking Up with Normatively Monolithic Agency with GRACE: A Reason-Based Neuro-Symbolic Architecture for Safe and Ethical AI Alignment15 Jan 2026
- 2026Evolving Programmatic Skill Networks7 Jan 2026
- 2025Problems With Large Language Models for Learner Modelling: Why LLMs Alone Fall Short for Responsible Tutoring in K--12 Education28 Dec 2025
- 2025Probabilistic Neuro-Symbolic Reasoning for Sparse Historical Data: A Framework Integrating Bayesian Inference, Causal Models, and Game-Theoretic Allocation1 Dec 2025
- 2025LLM-Assisted Formalization Enables Deterministic Detection of Statutory Inconsistency in the Internal Revenue Code15 Nov 2025
- 2025CausalGuard: A Smart System for Detecting and Preventing False Information in Large Language Models30 Oct 2025
- 2025CLMN: Concept based Language Models via Neural Symbolic Reasoning11 Oct 2025
- 2025Constraint Satisfaction Approaches to Wordle: Novel Heuristics and Cross-Lexicon Validation3 Oct 2025
- 2025Causal-Symbolic Meta-Learning (CSML): Inducing Causal World Models for Few-Shot Generalization15 Sep 2025
- 2025Symbolic Feedforward Networks for Probabilistic Finite Automata: Exact Simulation and Learnability12 Sep 2025
- 2025Physics-Informed Spectral Modeling for Hyperspectral Imaging29 Aug 2025
- 2025Rethinking Reasoning in LLMs: Neuro-Symbolic Local RetoMaton Beyond ICL and CoT22 Aug 2025
- 2025A Fully Spectral Neuro-Symbolic Reasoning Architecture with Graph Signal Processing as the Computational Backbone19 Aug 2025
- 2025Cognitive Workspace: Active Memory Management for LLMs -- An Empirical Study of Functional Infinite Context8 Aug 2025
- 2025A Fuzzy Logic Prompting Framework for Large Language Models in Adaptive and Uncertain Tasks8 Aug 2025
- 2025Zero-shot Compositional Action Recognition with Neural Logic Constraints4 Aug 2025
- 2025Compositional Function Networks: A High-Performance Alternative to Deep Neural Networks with Built-in Interpretability28 Jul 2025
- 2025Defining neurosymbolic AI15 Jul 2025
- 2025Look-Back: Implicit Visual Re-focusing in MLLM Reasoning2 Jul 2025
- 2025Beyond Statistical Learning: Exact Learning Is Essential for General Intelligence30 Jun 2025
- 2025Interpretable Hybrid Machine Learning Models Using FOLD-R++ and Answer Set Programming24 Jun 2025
- 2025Vision-EKIPL: External Knowledge-Infused Policy Learning for Visual Reasoning7 Jun 2025
50 newest of 151 All 151 (JSON)
- 2025LlamaV-o1: Rethinking Step-by-step Visual Reasoning in LLMscited by 147
- 2025Reason-RFT: Reinforcement Fine-Tuning for Visual Reasoning of Vision Language Modelscited by 99
- 2025Look-Back: Implicit Visual Re-focusing in MLLM Reasoningcited by 55
- 2022Is Neuro-Symbolic AI Meeting its Promise in Natural Language Processing? A Structured Reviewcited by 38
- 2022NeuPSL: Neural Probabilistic Soft Logiccited by 34
- 2023Symbol-LLM: Leverage Language Models for Symbolic System in Visual Human Activity Reasoningcited by 16
- 2022VQA and Visual Reasoning: An Overview of Recent Datasets, Methods and Challengescited by 14
- 2024The Role of Foundation Models in Neuro-Symbolic Learning and Reasoningcited by 12
- 2024On the Hardness of Probabilistic Neurosymbolic Learningcited by 9
- 2025Beyond Statistical Learning: Exact Learning Is Essential for General Intelligencecited by 6
- 2026Breaking Up with Normatively Monolithic Agency with GRACE: A Reason-Based Neuro-Symbolic Architecture for Safe and Ethical AI Alignmentcited by 5
- 2026RuCL: Stratified Rubric-Based Curriculum Learning for Multimodal Large Language Model Reasoningcited by 5
12 most cited of 33 All 33 (JSON)
- 2026Neurosymbolic Routing for Reliable Reasoning on Resource-Constrained Edge Devices24 Sep 2026
- 2026SoftReason: A Fully Differentiable Neuro-Soft-Symbolic Deductive Reasoning Architecture over High-Dimensional Perceptual Data22 Jul 2026
- 2026VeryTrace: Verifying Reasoning Traces through Compilable Formalism and Structured Verification23 Jun 2026
- 2026Auto-Relational Reasoning29 Apr 2026
- 2026Compositional Neuro-Symbolic Reasoning2 Apr 2026
- 2026Reflect to Inform: Boosting Multimodal Reasoning via Information-Gain-Driven Verification27 Mar 2026
- 20264OPS: Structural Difficulty Modeling in Integer Arithmetic Puzzles26 Mar 2026
- 2026AS2 -- Attention-Based Soft Answer Sets: An End-to-End Differentiable Neuro-Soft-Symbolic Reasoning Architecture19 Mar 2026
- 2026RuCL: Stratified Rubric-Based Curriculum Learning for Multimodal Large Language Model Reasoning25 Feb 2026
- 2026Confidence over Time: Confidence Calibration with Temporal Logic for Large Language Model Reasoning19 Jan 2026
- 2026Breaking Up with Normatively Monolithic Agency with GRACE: A Reason-Based Neuro-Symbolic Architecture for Safe and Ethical AI Alignment15 Jan 2026
- 2025Probabilistic Neuro-Symbolic Reasoning for Sparse Historical Data: A Framework Integrating Bayesian Inference, Causal Models, and Game-Theoretic Allocation1 Dec 2025
12 newest of 33 All 33 (JSON)
- 2020Symbolic Learning and Reasoning with Noisy Data for Probabilistic Anchoringcited by 3
- 2025Causal-Symbolic Meta-Learning (CSML): Inducing Causal World Models for Few-Shot Generalizationcited by 0
- 2026Mind-Studio: Executable World Models with Lookahead Evaluation for Partially Observable Gamescited by 0
- 2026Write-Protected Discrete Bottlenecks for Language-Grounded World Models: A Structural Limitation and Sufficient Fixcited by 0
- 2026Write-Protected Discrete Bottlenecks for Language-Grounded World Models: A Structural Limitation and Sufficient Fix9 Jul 2026
- 2026Mind-Studio: Executable World Models with Lookahead Evaluation for Partially Observable Games14 Jun 2026
- 2025Causal-Symbolic Meta-Learning (CSML): Inducing Causal World Models for Few-Shot Generalization15 Sep 2025
- 2020Symbolic Learning and Reasoning with Noisy Data for Probabilistic Anchoring24 Feb 2020
- 2021From Statistical Relational to Neurosymbolic Artificial Intelligence: a Surveycited by 72
- 2021A Survey on Hyperdimensional Computing aka Vector Symbolic Architectures, Part II: Applications, Cognitive Models, and Challengescited by 69
- 2022Leveraging Explanations in Interactive Machine Learning: An Overviewcited by 53
- 2021Logic-Driven Context Extension and Data Augmentation for Logical Reasoning of Textcited by 46
- 2022Deep Learning with Logical Constraintscited by 44
- 2022Neurocompositional computing: From the Central Paradox of Cognition to a new generation of AI systemscited by 44
- 2021From LSAT: The Progress and Challenges of Complex Reasoningcited by 43
- 2021Modular Design Patterns for Hybrid Learning and Reasoning Systems: a taxonomy, patterns and use casescited by 39
- 2021A Survey on Neural-symbolic Learning Systemscited by 39
- 2024BEARS Make Neuro-Symbolic Models Aware of their Reasoning Shortcutscited by 37
- 2021Symbols as a Lingua Franca for Bridging Human-AI Chasm for Explainable and Advisable AI Systemscited by 36
- 2022Towards Data-and Knowledge-Driven Artificial Intelligence: A Survey on Neuro-Symbolic Computingcited by 35
12 most cited of 114 All 114 (JSON)
- 2026Who to Trust in Multi-Robot Systems: Joint Robot and Object Hypothesis Trust Inference via Neural-Symbolic Cross-Validation10 Oct 2026
- 2026Uncertainty in Representation Learning on Knowledge Graphs3 Oct 2026
- 2026Lukasiewicz Neural Networks Extended: Residual Architectures and Crystallization Strategies for Interpretable Rule Extraction26 Sep 2026
- 2026Soft Symbol Grounding for Prototypical Concepts10 Sep 2026
- 2026Leveraging Low-Level Symbolic Competences for Unsupervised Grounding in Hallucination Detection4 Sep 2026
- 2026From Hybrid Mechanistic--Data-Driven Modeling Toward Neuro-Symbolic AI: What, Why, and How24 Jul 2026
- 2026Structural Certification for Reliable Physical Design with Language Models29 Jun 2026
- 2026From Doyle to AGM: A Survey and an Implementation Roadmap for Belief Change29 May 2026
- 2026A Pilot Benchmark for NL-to-FOL Translation in Planetary Exploration18 May 2026
- 2026Learning to Reason: Targeted Knowledge Discovery and Fuzzy Logic Update for Robust Image Recognition30 Apr 2026
- 2026Overcoming the Impedance Mismatch: A Theoretical Roadmap for Fusing Foundation Models and Knowledge Graphs21 Apr 2026
- 2026A Sugeno Integral View of Binarized Neural Network Inference20 Apr 2026
12 newest of 114 All 114 (JSON)