Neurosymbolic Learning

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5 papers in the last four weeks, up 67% on the four weeks before. 0.0% of all new papers.

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Latest papers 37

Oct 5, 2026cs.AI

DPNL: A DPLL-based Algorithm for Probabilistic Neurosymbolic Learning

Probabilistic Neurosymbolic Learning (PNL) combines neural predictions with symbolic reasoning, enabling end-to-end learning from final-output supervision without labels for intermediate concepts. A central challenge is probabilistic inference: state-of-the-art approaches often rely on materializing the logical provenance of a query, which can itself become a major computational bottleneck. We introduce Dynamic Probabilistic Neurosymbolic Learning (DPNL), an oracle-guided framework that avoids requiring complete provenance materialization before inference. DPNL lazily explores the space of intermediate assignments, while oracles resolve entire regions that can already be certified to produce or exclude the target output. We establish conditions ensuring soundness and termination. ApproxDPNL extends the same search with early termination while maintaining certified bounds on the exact output probability, providing controlled approximation guarantees. The oracle interface decouples inference from the representation of the symbolic component, enabling problem-specific reasoning within the same framework. Experiments on several neurosymbolic tasks show that DPNL and ApproxDPNL substantially extend the range of problem instances tractable by probabilistic neurosymbolic inference.

Thomas Jean-Michel Valentin, Pierre Genev{è}s, Luisa Sophie Werner +3

ENS Paris Saclay,TYREX · LIG,TYREX · TYREX +1

Probabilistic Logic Neurosymbolic Learning

Sep 30, 2026cs.LG

Prototype-Rule Neurosymbolic Regularization for Rank-Constrained Tensor Neural Networks under Label Scarcity

Rank-constrained tensor neural networks reduce the parameterization of high-order inputs, but they do not explicitly constrain class geometry in the learned representation. This study investigates whether a differentiable prototype-rule can provide a complementary inductive bias for Rank-R tensor learning under limited supervision. The proposed framework augments the Rank-R objective with prototype-based regularization and optionally fuses prototype evidence with neural logits at inference. Four hyperspectral benchmarks are evaluated with four Rank-R configurations under both seven-fold stratification and spatially separated folds that mitigate leakage; a separate spatial study varies the class support budget from 2 to 20 samples. Under spatial evaluation, full neurosymbolic inference changes Macro-F1 score by +8.82 percentage points on Botswana, +5.49 on Indian Pines, +1.59 on Pavia University, and -0.62 on Salinas. Most of the benefit arises from training-time regularization, whereas inference fusion is small and dataset dependent.

Eftychios Protopapadakis, Konstantinos Makantasis, Konstantinos M. Giannoutakis

Department of Applied Informatics, University of Macedonia, 156 Egnatia Street, 54636 Thessaloniki, Greece · Department of Artificial Intelligence, Faculty of Information & Communication Technology, University of Malta, Msida, Malta

Tensor Networks Prototype Learning Few-Shot Learning Hyperspectral Image Classification Neurosymbolic Learning

Sep 30, 2026cs.LG

Candidate Retention for Abductive Learning

Abductive learning combines neural perception with symbolic reasoning, using explanations generated by abduction to supervise the perception model. Multiple valid explanations of the same symbolic target can assign conflicting labels to the same inputs. Common policies select a single candidate as a pseudo-label, which may reinforce mistaken assignments, or weight all candidates, which may spread supervision across competing labels. These risks motivate selecting a retained subset to balance supervision sharpness and model-mass coverage. To guide this choice, we bound the coordinate-level supervision error using retained uncertainty, discarded model mass, and model mismatch. For a fixed model and training pair, only the first two terms depend on the retained set. We propose Abductive Candidate Retention (ACR), which uses these terms to guide greedy additions, accepting a candidate when its recovered mass exceeds the increase in retained uncertainty. Experiments show that ACR improves concept accuracy over single-candidate baselines and A3BL in most evaluated aggregated mod-addition settings. Objective ablations support the joint use of uncertainty and posterior mass.

Hao-Yuan He, Yu Liu, Ming Li

School of Artificial Intelligence, Nanjing University · National Key Laboratory for Novel Software Technology, Nanjing University

Abductive Reasoning Pseudo-Labeling Neurosymbolic Learning

Sep 24, 2026cs.AI

Neuro-symbolic AI for Industrial Configuration

Large Language Models (LLMs) have shown impressive performance on a wide range of generative tasks. Yet their probabilistic nature makes them, in isolation, fundamentally unsuited for industrial product configuration, where outputs must be syntactically valid, semantically consistent with a knowledge base of hundreds of features and rules, and producible by an existing manufacturing chain. We argue that Neuro-symbolic (NeSy) AI methods lay out a promising path towards industrial-grade configurators that are reliable by design, explainable, and trustworthy. This paper describes a taxonomy of three NeSy integration strategies, namely hybrid inference, hybrid fine-tuning, and hybrid training, exploring their usage in the configuration domain. We report our effort to operationalize NeSy concepts in an industrial configuration copilot and derive a set of practical design choices for deploying trustworthy AI in engineering environments. We close with a discussion of open research challenges we consider most pressing, in particular how to scale NeSy methods from small academic demonstrators to the size of industrial configurators.

Danilo Valerio, Philipp Kogler, Stefan Bischof +2

Siemens AG Österreich · Siemens AG

Manufacturing Neuro-Symbolic Reasoning Neuro-Symbolic AI Neurosymbolic Learning

Sep 22, 2026cs.AI

Neurosymbolic Action Model Learning under Partial Observability

AI planning studies how an agent can reach a goal by executing a sequence of actions. To plan correctly, the agent needs an action model describing when each action can be executed and how it changes the world. Constructing such models by hand requires domain expertise, and can be costly and error-prone. Action models can instead be learned from available data using existing neurosymbolic approaches, but they currently assume access to complete traces of fully observable images . These approaches fail to learn action models under partial observability where some of the images might not be present or are not fully informative of the current state of the world. Hence, this paper proposes NeSyAM, a novel neurosymbolic modeling paradigm for action model learning under partial observability. In addition, the paper presents a unified variational framework for theoretically analysing the limitations of existing methods compared to our proposed approach. NeSyAM is then tested extensively on six visual planning domains and three observation regimes to show it consistently recovers relevant parts of the true action model under partial observability.

Adem Kikaj, Lennert De Smet, Giuseppe Marra +1

KU Leuven, Belgium

Symbolic Planning Neurosymbolic Learning

Sep 14, 2026cs.AI

Learning Symbolic Constraint Representations from Examples: A Neuro-Symbolic Approach

Learning user-defined concepts as constraint networks has been extensively studied in the constraint acquisition (CA) literature. However, existing approaches typically rely on intensive interactions with a human oracle, making the learning process costly in terms of time and number of queries. In this paper, we propose a neuro-symbolic framework for automatic CA that significantly reduces user involvement by introducing neural Oracle Transformer models which learn to emulate user responses and to generalize conceptual knowledge. Trained on previously available examples, the learned oracle interacts with a dedicated CA engine, FastCA, which systematically refines the oracle's responses into a sound, consistent, and interpretable constraint network. This neuro-symbolic interaction enables the recovery of structured symbolic models from data without prior domain knowledge. Our results demonstrate that this neuro-symbolic interplay effectively aligns data-driven pattern recognition with symbolic reasoning, offering a robust approach to automating model construction in combinatorial domains.

Nassim Belmecheri, Arnaud Gotlieb, Nadjib Lazaar +1

Simula Research Laboratory, Oslo, Norway · Microsoft, Norway · LISN, CNRS, Paris-Saclay University, France

Symbolic Reasoning Neurosymbolic Learning Constraint Programming

Sep 1, 2026cs.LG

Neural Symbollic Regression Using Deep Learning and Sparse Modelling

Symbolic Regression (SR) seeks to find succinct mathematical expressions that represent the fundamental relationships within data, providing interpretability and scientific understanding that exceeds that of black-box models. Nevertheless, traditional methods like Genetic Programming face challenges with scalability and are highly sensitive to noise, while sparse regression techniques such as SINDy rely significantly on predetermined feature libraries. In this work, we present a Neural Symbolic Regression (NSR) framework that treats neural networks as functional preconditioners for symbolic discovery. Our approach uses a decoupled pipeline: a neural network first learns a smooth, noise-robust approximation of the target function in an interaction- aware nonlinear feature space. LASSO is then applied to extract sparse, interpretable closed-form expressions. To improve predictive accuracy and symbolic fidelity by integrating distributed hyperparameter optimization with Ray Tune and ASHA scheduling. Experiments on the Nguyen benchmark suite show that our approach consistently outperforms SINDy and non-tuned neural baselines in RMSE, noise robustness, and out-of-distribution generalization. Ablation studies confirm the significance of feature interactions, neural depth, and tuning strategies. In general, this study presents a scalable and understandable neural-symbolic framework, creating a solid link between neural approximation and the discovery of sparse equations for scientific machine learning.

Ravi Kumar U, Sumitra S

Department of Mathematics Indian Institute of Space Science and Technology Thiruvananthapuram, India

Scientific ML Neurosymbolic Learning Symbolic Regression

Aug 31, 2026cs.LG

Reinforcement Learning for Symbolic Equation Solving

We present a reinforcement-learning agent that solves symbolic equations step by step, covering both nonlinear closed equations (radicals, exponentials, trigonometric) and a controlled class of restricted-open families requiring a change of variables (CoV) such as completing the square. We cast algebra as an MDP with a dynamic action space and a tree-structured policy (TreeMLP). The main policy learns from reward alone with no supervised solution traces; the CoV substitution comes from a supervised generator interchangeable with a CAS call. On closed equations the agent matches the prior best on CommonCore (0.93 greedy vs. ConPoLe's 0.925) under a single policy. On four hand-designed restricted-open families (quadratic, cubic, quartic, exponential) it reaches 0.79 beam / 0.67 greedy, exceeding the strongest non-learned search (A-star, 0.64). Learned CoV timing has content only on the exponential family, the one requiring a nested CoV, where a natural rule solves none of the held-out equations while the policy solves 75% from reward alone. At 10x scale a sharp seed-level bimodality emerges; a UCB learning-progress curriculum shows a non-significant positive trend toward mitigating it. We do not claim general open-equation solving: every open-equation result is confined to these four controlled families.

Kevin P O Keeffe

Starling Research Institute

Reinforcement Learning Neurosymbolic Learning

Aug 13, 2026cs.AI

Moose: Latent concept learning with reasoning-shortcut awareness in $\mathcal{EL}^{++}$

The OWL 2 EL profile is used in some of the largest production ontologies, including the Gene Ontology and SNOMED CT. Existing neuro-symbolic (NeSy) learning methods accept propositional theories or Datalog, and reasoning-shortcut (RS) awareness has not been investigated in ontology settings. We present Moose, a method that compiles an

\mathcal{EL}^{++}

TBox and finite ABox to a Sentential Decision Diagram (SDD). The SDD acts as a differentiable weighted-model-counting layer, and we add closure clauses outside the

\mathcal{EL}^{++}

profile on declared exhaustive families to overcome the limited expressivity of

\mathcal{EL}^{++}

under partial supervision. We show termination, soundness, completeness, and polynomial intermediate sizes, and validate the proofs in Lean. We then define the first formal partial-supervision latent-concept-learning task over an OWL EL ontology, i.e., learning per-individual classifiers for latent concepts from observed ABox literals, and evaluate Moose on MNIST-with-ontology and Pizzaïolo. Moose improves over propositional-NeSy, fuzzy-logic, and ontology embedding baselines, and presents the first reasoning-shortcut analysis in an OWL EL setting.

Olga Mashkova, Asaad Mohammedsaleh, Fernando Zhapa-Camacho +1

Computer Science Program, Computer, Electrical, and Mathematical Sciences & Engineering Division, King Abdullah University of Science and Technology, Thuwal 23955, Saudi Arabia

Neurosymbolic Learning Description Logic

Aug 4, 2026cs.AI

The RAIL Principles for Neurosymbolic AI: Reasoning, Assurances, Interfacing and Learning

Neurosymbolic AI systems that integrate machine learning and symbolic reasoning are rapidly gaining attention. They complement the data-intensive statistical approaches of neural networks and language models with symbolic reasoning algorithms to function in high-stakes domains or in low-data regimes that characterize many real-world applications. We argue that the neurosymbolic combination of machine learning and formal reasoning is not a niche approach within AI, but rather includes many already successful techniques that are of crucial importance to the development of reliable, efficient and, ultimately, trustworthy systems. This perspective prompts a re-examination of the design of current AI systems. We show that many leading AI systems, including some that are not traditionally considered as neurosymbolic, can be analysed from the perspective of four principles of neurosymbolic AI design: Reasoning, Assurances, Interfacing and Learning (RAIL). Applying the RAIL framework offers a unified view of seemingly disparate AI systems, ranging from physics-aware machine learning to neuro-guided search (such as Google DeepMind's Alpha-* suite), causal learning and tool-augmented Large Language Models. Importantly, the RAIL principles will enable engineers to make better-informed and more principled decisions about the design and deployment of production-level AI systems. In this article, we introduce the RAIL principles, examine how they can be applied across major areas of AI, and illustrate how they may guide practitioners to integrate neurosymbolic methods into next-generation AI technologies.

Agnese Chiatti, Michael Cochez, Cristina Cornelio +14

Politecnico di Milano · ELLIS Institute Finland & Abo Akademi University · Samsung AI +12

Symbolic Reasoning Neuro-Symbolic Reasoning Neuro-Symbolic AI Neurosymbolic Learning

Aug 4, 2026cs.LG

SJEPA: Learning Elegant Latent Dynamics with Hybrid Symbolic-Neural Predictors

Joint-embedding predictive architectures learn abstract states by predicting target embeddings from context embeddings, but their transition models are typically opaque neural maps. We introduce SJEPA, a reconstruction-free JEPA framework that learns predictive representations whose induced dynamics admit compact symbolic descriptions. Its hybrid transition combines a symbolic law with a regularised neural correction for dynamics outside the selected grammar. The central principle is to learn the simplest adequate dynamics: representation constraints preserve informative, non-collapsed predictive coordinates, while operator compression favours low-complexity symbolic-neural transitions that remain predictively adequate. We formalise this principle through induced-dynamics complexity, analyse predictive-coordinate non-identifiability, and show that unconstrained operator compression creates a direct shortcut to representation collapse. The framework supports both alternating representation-equation learning and symbolic dynamics fitted to fixed representations. In controlled pendulum experiments, joint learning discovers substantially simpler symbolic dynamics with lower long-horizon rollout error and divergence than post-hoc fitting, while an unconstrained one-step diagnostic realises the predicted collapse shortcut. Under grammar misspecification, correction regularisation preserves the representable symbolic mechanism and directs the neural component towards residual dynamics. The results expose a controllable trade-off among predictive fidelity, representation quality, symbolic parsimony, and symbolic-neural allocation.

Yongchao Huang

Latent Dynamics Modeling Joint-Embedding Predictive Architecture Predictive Representation Learning Neurosymbolic Learning

Jul 21, 2026cs.NI

NSMA: Neuro-Symbolic Manifold Alignment for Generalizable Adaptive Bitrate Streaming under Texture Shift

For decades, ABR has kept two kinds of intelligence apart. Neural policies learn rich behaviors yet forget them the moment the environment changes; rules never learn, and never forget. Every prior attempt to combine them has kept this separation, letting rules supervise, constrain, or override the network from outside. We dissolve the boundary itself. But no union can be trusted before it can be tested, and ABR has never known how to measure what its policies learn or forget. The field's yardstick is bandwidth statistics, and we show it misleads. Identical statistics can hide entirely different outcomes, while wildly different statistics can hide similar ones. We replace the yardstick before building the bridge, with Texture-Aware Generalization Evaluation, a protocol that judges a policy by its whole training journey across traces whose temporal nature is laid bare. What truly breaks a policy is invisible. No statistic reveals it, no feature extracts it, yet rules walk through it untouched, for they reason from physics and owe the data nothing. So we build the bridge. Neuro-Symbolic Manifold Alignment (NSMA) embeds rule decisions as anchors inside the latent space of the neural policy, so that it keeps learning where learning pays, and can no longer forget what rules have always known. Generalization cannot be argued, only survived. We raise NSMA on 3G traces alone and release it, without fine-tuning, into eight unseen datasets spanning 4G, 5G, and WiFi, and onto a real-world player. It outperforms every state-of-the-art baseline. And when we open its latent space to ask why, probing and visualization return the same answer the design promised. https://tinyzqh.github.io/NSMA/

Zhiqiang He, Zhi Liu

The University of Electro-Communications Tokyo, Japan

Neural Network Generalization Domain Generalization Neurosymbolic Learning

Jul 9, 2026cs.AI

Answer Set Programming Energised! End-to-End Neurosymbolic Reasoning and Learning with ASP and Energy Based Models

We present a general neurosymbolic reasoning and learning methodology based on a modular integration of answer set programming with an energy based model substrate. Key contributions are: (1) supporting joint optimisation in the continuous latent space through explicit ASP-based declarative semantics fully incorporating background knowledge, constraints, non-monotonic inference; and (2) advancing recent works at the interface of answer sets, probabilistic logic, and answer set modulo theories by providing a generalised model and practical platform for ASP-centric robust, end-to-end training for applications in dynamic domains (e.g., involving perception and interaction). We provide a practical implementation, and demonstrate basic use and application (with MNIST), and evaluate with the visual question-answering benchmark Clevr and the multi-object tracking benchmark MOT.

Jakob Suchan, Julius Monsen, Salim Baloch +1

Constructor University Bremen, Bremen, Germany · CoDesign Lab > Cognitive Vision · Örebro University, Örebro, Sweden

Energy-Based Models Answer Set Programming Neuro-Symbolic Reasoning Neurosymbolic Learning

Jul 3, 2026cs.LG

Differentiate the Evaluator, Not the Program: An Efficient Runtime Representation for Neuro-Symbolic Learning

AI systems increasingly propose executable scientific models whose value depends on both their symbolic structure and their fitted continuous parameters. This makes parameter calibration the bottleneck of program-and-parameter co-search: an outer loop can generate thousands of candidate programs, but each needs an inner gradient-based optimization before it can be assessed. Staging each candidate into its own differentiable graph makes individual models fast but sacrifices the program-as-data property that keeps search fluid; interpreter-based approaches preserve programs as runtime data but pay interpreter overhead that dominates the numerical work. We present the Native Differentiable Virtual Machine (NDVM), a runtime representation that differentiates executable programs without compiling each candidate into a separate graph. NDVM separates symbolic structure from differentiable numeric state: tags, symbols, environments, and control remain native runtime data, while numeric payloads live in dense batched buffers with exact reverse-mode gradients recorded along the realized execution trace, so one evaluator walk is amortized across large populations of parameter vectors. A locked cost model of a real differentiable self-hosted Scheme interpreter motivates the design. We realize NDVM as a native runtime with forward and gradient equivalence to the reference backend, about 60x per-lane batch amortization, near-linear multicore scaling, and two independent front ends. In fixed-budget co-search over LLM-proposed programs, NDVM reaches high-quality solutions about 24x sooner in wall-clock time, suggesting runtime differentiation as a practical systems foundation for scientific discovery workflows.

Lucas Sheneman

Institute for Interdisciplinary Data Sciences University of Idaho

Automatic Differentiation Differentiable Programming Differentiable Optimization Neurosymbolic Learning

Jun 24, 2026cs.LG

KG-TRACE: A Neuro-Symbolic Framework for Mechanistic Grounding in Antimicrobial Resistance Prediction

While WGS-based AMR prediction has reached high accuracy, existing models lack a mechanism to ground neural attributions in established biological pathways. We present KG-TRACE, a novel neuro-symbolic framework that integrates the WHO mutation knowledge graph (KG) as a structured biological constraint on a neural genomic model. Unlike existing methods that learn statistical patterns in isolation, KG-TRACE fuses genomic features and RotatE-based KG embeddings through a learned epistemic trust gate, dynamically weighting neural evidence against symbolic biological knowledge. Evaluated on the CRyPTIC M. tuberculosis cohort, KG-TRACE achieves an AUROC of 0.9760 for isoniazid, achieving competitive accuracy while its primary value lies in symbolic grounding, not predictive uplift. More importantly, we introduce the Biological Grounding Ratio (BGR), a dataset-level metric that quantifies alignment between neural attributions and established biology. Our framework achieves a 92.5% symbolic coverage of isoniazid-resistant predictions and effectively identifies MDR co-occurrence artifacts by issuing laboratory follow-up flags for 'UNCERTAIN' cases. We demonstrate that neuro-symbolic grounding provides a verifiable audit trail for clinicians, bridging the gap between predictive accuracy and clinical trust.

Naman Garg, Sarika Jain, Sourav Yadav +4

National Institute of Technology Kurukshetra, Kurukshetra, India · Indian Institute of Information Technology Manipur, Manipur, India · Purdue University, West Lafayette, IN, USA +1

Genomics Neurosymbolic Learning

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 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 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 5, 2026cs.RO

Neuro-Symbolic Learning for Long-Horizon Task Planning Under Complex Logical Constraints

Task planning often suffers from severe efficiency bottlenecks when robots must reason over long-horizon action sequences under complex logical constraints, including object affordances, spatial relationships, and sequential action dependencies. Recent neuro-symbolic methods improve planning efficiency by learning object-importance scores to prune task-irrelevant objects, but they typically rely on fixed offline supervision generated from full search spaces. This creates a train-test mismatch: at deployment, the planner operates in pruned search spaces induced by the model's own imperfect predictions, leading to exposure bias and degraded planning performance. To address this challenge, we formulate object-importance learning for task planning as an imperative learning-based bilevel optimization problem. The upper level optimizes a neural scorer, while the lower level solves a symbolic planning problem in the score-pruned search space. To stabilize this learning process, we introduce a 3R strategy into the lower-level planning, using parallel Repair, Restart, and Rollback recovery to provide reliable and adaptive feedback for upper-level learning. Experiments on three challenging benchmarks demonstrate state-of-the-art performance, including an 80.04% reduction in failure rate and a 57.14% reduction in planning time. We further validate the framework on a quadruped-based mobile manipulator in simulation and the real world, demonstrating its potential for efficient and deployable neuro-symbolic task planning.

Qiwei Du, Zitong Zhan, Shaoshu Su +7

Spatial AI & Robotics (SAIR) Lab, University at Buffalo, NY 14260 · Robotics Institute, Carnegie Mellon University, PA 15213

Symbolic Planning Robot Task Planning Neuro-Symbolic AI Neurosymbolic Learning

May 28, 2026cs.LG

DisjunctiveNet: Neural Symbolic Learning via Differentiable Convexified Optimization Layers

Many learning tasks in science and engineering are characterized by sparse datasets, which limits the effectiveness of purely data-driven approaches. At the same time, these problems are often accompanied by rich domain knowledge derived from physical laws, operational requirements, and expert heuristics. Such knowledge is frequently expressed as rules involving logical propositions and linear inequalities. Existing neuro-symbolic methods typically enforce these rules approximately through soft penalties, assume input-independent rules when designing specialized architectures, or rely on non-differentiable post-processing at inference time to achieve hard constraint satisfaction. While recent advances in differentiable optimization layers enable end-to-end feasibility enforcement within neural networks, extending these approaches to logical or mixed-integer rules remains challenging due to inherent nonconvexity. In this work, we propose a unified end-to-end framework for enforcing hard, input-dependent mixed integer linear constraints within neural networks. Our approach represents rules as disjunctive constraints and applies hierarchical convex relaxations to obtain convex hull formulations. These relaxations yield tractable linear constraints that can be embedded as differentiable optimization layers while enabling exact rule satisfaction. We demonstrate the effectiveness of the proposed framework on real-world datasets, achieving perfect rule satisfaction and strong predictive performance.

Shraman Pal, Can Li

Davidson School of Chemical Engineering, Purdue University, West Lafayette, USA.

Differentiable Optimization Neurosymbolic Learning

May 19, 2026cs.AI

Neurosymbolic Learning for Inference-Time Argumentation

Claim verification is an important problem in high-stakes settings, including health and finance. When information underpinning claims is incomplete or conflicting, uncertain answers may be more appropriate than binary true or false classifications. In all cases, faithful explanations of the considerations determining the final verdict are crucial. We introduce inference-time argumentation (ITA), a trainable neurosymbolic framework for ternary claim verification in which a formal argumentation semantics giving the strength of claims is used both (i) to guide LLM training as models learn to generate arguments and assign them base scores (representing intrinsic strengths) and (ii) to compute ternary (true/false/uncertain) predictions from generated, scored arguments. As a result, at training time, argument generation and scoring can be optimised according to the quality of the induced argumentative predictions. Moreover, at inference time, the final prediction is faithful, by construction, to the arguments and scores determining the verdict, rather than being justified by a potentially unfaithful post-hoc reasoning trace as in conventional reasoning models. We finally show that, on two datasets for ternary claim verification, ITA improves upon argumentative baselines and can perform competitively against non-argumentative direct-prediction baselines, while providing verdicts that are computed deterministically from explicit, inspectable argumentative structures.

Gabriel Freedman, Adam Dejl, Adam Gould +4

Department of Computing, Imperial College London

Claim Verification Computational Argumentation Neurosymbolic Learning

May 15, 2026cs.LG

Learning How to Cube

Despite the effectiveness of Cube-and-Conquer (C&C) for solving challenging Boolean Satisfiability (SAT) problems, no prior work has shown that transformer-based models can learn effective cubing heuristics. We introduce a neuro-symbolic post-training framework for this task. We design an MCTS-based data curation pipeline that uses symbolic heuristics to explore splitting decisions over SAT competition formulas, producing preference data grounded in solver statistics and augmented with reasoning traces from a teacher model. Our two-stage post-training, supervised fine-tuning (SFT) followed by direct preference optimization (DPO), enables a 4B-parameter model to achieve a pass@5 score of 53 on 100 SAT competition benchmarks, surpassing frontier LLMs such as Claude-Sonnet-4 (50) and matching the best symbolic heuristic (53). Ablations show that SFT alone improves pass@5 from 46 to 51, with DPO adding 2 additional benchmarks; an entropy/agreement ablation on realized first-cube decisions further shows that SFT, not DPO, accounts for the root-level decision diversity that produces complementary per-run coverage over deterministic symbolic methods. This demonstrates that transformers can be trained to make effective cubing decisions in a domain traditionally dominated by symbolic methods.

Ferhat Erata, Sam Kouteili, Thanos Typaldos +4

Yale University · AWS Agentic AI

Transformer Constraint Satisfaction Neurosymbolic Learning

May 13, 2026cs.LO

Quantitative Linear Logic for Neuro-Symbolic Learning and Verification

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

Thomas Flinkow, Ekaterina Komendantskaya, Matteo Capucci +1

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

Neural Network Verification Neuro-Symbolic Reasoning Neurosymbolic Learning

May 13, 2026cs.AI

Differentiable Learning of Lifted Action Schemas for Classical Planning

Classical planners can effectively solve very large deterministic MDPs represented in STRIPS or PDDL where states are sets of atoms over objects and relations, and lifted action schemas add or delete these atoms. This compact representation yields strong search heuristics and provides an ideal setting for structural generalization, since lifted relations and action schemas give rise to infinitely many domain instances. A central challenge is to learn these relations and action schemas from data, and recent approaches have addressed this problem using different types of observations. In this work, we develop a novel neural network architecture for learning action schemas from traces where states are fully observed but action arguments are unobserved. The problem is a simplification but an important step towards learning planning domains from sequences of images and action labels, and we aim to solve this simplification in a nearly perfect manner. The challenge lies in learning the action schemas while simultaneously identifying the action arguments from observed state changes. Our approach yields a robust differentiable component that can then be integrated into larger neuro-symbolic models. We evaluate the architecture on various planning domains, where the learned lifted action schemas must recover the ground-truth structure. Additionally, we report experiments on robustness to observation noise and on a variation related to slot-based dynamics models.

Jonas Reiter, Jakob Elias Gebler, Hector Geffner

RWTH Aachen University

Symbolic Planning Differentiable Programming Neurosymbolic Learning

May 11, 2026cs.LG

DeepLog: A Software Framework for Modular Neurosymbolic AI

DeepLog is an operational neurosymbolic framework that unifies logic and deep learning within standard PyTorch workflows. While existing neurosymbolic systems focus on a particular paradigm and semantics, DeepLog serves as a universal backend that can emulate many systems in the neurosymbolic alphabet soup. By treating diverse neurosymbolic languages as high-level specifications, the DeepLog software automatically compiles them into optimized arithmetic circuits. This design lowers the barrier for machine learning practitioners by treating logic as composable modules, while providing neurosymbolic developers with a shared, high-performance basis for prototyping new integration strategies. The code is available here: https://github.com/ML-KULeuven/deeplog

Robin Manhaeve, Stefano Colamonaco, Vincent Derkinderen +4

Department of Computer Science and Leuven.AI KU Leuven, Belgium

Neuro-Symbolic AI Neurosymbolic Learning

May 10, 2026cs.AI

From Passive Reuse to Active Reasoning: Grounding Large Language Models for Neuro-Symbolic Experience Replay

While experience replay is essential for data efficiency in reinforcement learning (RL), standard methods treat the replay buffer as a passive memory system, prioritizing samples based on numerical prediction errors rather than their semantic significance. This approach stands in contrast to human learning, which accelerates mastery by actively abstracting fragmented experiences into behavioral rules. To bridge this gap, we propose Neuro-Symbolic Experience Replay (NSER), a framework that transforms experience replay from a passive sample reuse mechanism into an active engine for knowledge construction. Specifically, NSER addresses the incompatibility between linguistic reasoning and numerical optimization through a novel neuro-symbolic grounding pipeline. It leverages Large Language Models (LLMs) in a zero-shot manner to induce candidate behavioral rules from accumulated trajectories, grounds these insights into differentiable first-order logic representations, and utilizes the resulting symbolic structures to dynamically reweight the replay distribution. By allowing abstract knowledge to directly shape policy optimization, NSER achieves consistent superior sample efficiency and convergence speed across reactive, rule-based, and procedural benchmarks.

Yanan Xiao, Yixiang Tang, Zechen Feng +3

1Affiliation 1 · 2Affiliation 2 · 3Affiliation 3

Reinforcement Learning Experience Replay LLM-Guided RL Neurosymbolic Learning Sample-Efficient RL

May 8, 2026cs.LG

Neurosymbolic Imitation Learning with Human Guidance: A Privileged Information Approach

Imitation learning is widely used for learning to act in complex environments. While pure neural-based methods handle high dimensional data effectively, they suffer from the requirement of large number of samples and are prone to overfitting. Pure symbolic approaches, while generalize well, do not handle high-dimensional data effectively. We propose a neurosymbolic approach that achieves the best of both worlds, i.e, handling high-dimensional data while achieving generalization. The key advantage of our approach is that it can effectively exploit additional privileged information that is available only during training (in our case, gaze data). Our empirical evaluations demonstrate the effectiveness, efficiency and the generalization capability of our proposed approach.

Nikhilesh Prabhakar, Varun Balaji, Athresh Karanam +2

Department of Computer Science, The University of Texas at Dallas, Richardson TX 75080, USA · Computer Science Department and Centre for Cognitive Science, TU Darmstadt, Germany

Imitation Learning Neurosymbolic Learning Learning Using Privileged Information

May 6, 2026cs.AI

LANTERN: LLM-Augmented Neurosymbolic Transfer with Experience-Gated Reasoning Networks

Transfer learning in reinforcement learning (RL) seeks to accelerate learning in new tasks by leveraging knowledge from related sources. Existing neurosymbolic transfer methods, however, typically rely on manually specified task automata, assume a single source task, and use fixed knowledge-integration mechanisms that cannot adapt to varying source relevance. We propose LANTERN, a unified framework for multi-source neurosymbolic transfer that addresses these limitations through three components: (i) deterministic finite automata generated from natural language task descriptions using large language models, (ii) semantic embedding-based aggregation of multiple source policies weighted by cross-task similarity, and (iii) adaptive teacher-student gating based on temporal-difference error and semantic uncertainty. Across domains spanning resource management, navigation, and control, LANTERN achieves 40-60% improvements in sample efficiency over existing baselines while remaining robust to poorly aligned sources. These results demonstrate that multi-source, adaptively weighted neurosymbolic transfer can improve scalability and robustness in symbolic RL settings.

Mahyar Alinejad, Yue Wang, Amrit Singh Bedi +1

Department of Electrical and Computer Engineering, University of Central Florida, Orlando, Florida, USA · Department of Computer Science, University of Central Florida, Orlando, Florida, USA

Reinforcement Learning LLM-Guided RL Neurosymbolic Learning Policy Learning

May 5, 2026cs.LG

Learning to Theorize the World from Observation

What does it mean to understand the world? Contemporary world models often operationalize understanding as accurate future prediction in latent or observation space. Developmental cognitive science, however, suggests a different view: human understanding emerges through the construction of internal theories of how the world works, even before mature language is acquired. Inspired by this theory-building view of cognition, we introduce Learning-to-Theorize, a learning paradigm for inferring explicit explanatory theories of the world from raw, non-textual observations. We instantiate this paradigm with the Neural Theorizer (NEO), a World Theory Model, that induces latent programs as a learned Language of Thought and executes them through a shared transition model. In NEO, a theory is represented as an executable, compositional program whose learned primitives can be systematically recombined to explain novel phenomena. Experiments show that this formulation enables explanation-driven generalization, allowing observations to be understood in terms of the programs that generate them.

Doojin Baek, Gyubin Lee, Junyeob Baek +2

KAIST

Computational Cognitive Modeling World Model Learning Program Synthesis Neurosymbolic Learning

May 3, 2026cs.AI

Neural Decision-Propagation for Answer Set Programming

Integration of Answer Set Programming (ASP) with neural networks has emerged as a promising tool in Neuro-symbolic AI. While existing approaches extend the capabilities of ASP to real world domains, their reasoning pipelines depend on classical solvers, which is a bottleneck for scalability. To tackle this problem, we propose a new method to compute stable models, called decision-propagation (DProp), which alternates falsity decisions and truth propagations. Successful DProp computations are shown to capture the stable model semantics. We then develop Neural DProp (NDProp), a differentiable extension of DProp with neural computation for decisions and fuzzy evaluation for propagations. We evaluate the capabilities of NDProp for learning decision heuristics as well as neuro-symbolic integration, and compare it with existing neuro-symbolic approaches. The results show that NDProp can learn to efficiently compute stable models, and it improves accuracy and scalability on neuro-symbolic benchmarks.

Thomas Eiter, Katsumi Inoue, Sota Moriyama

1Vienna University of Technology (TU Wien), Austria · 2National Institute of Informatics, Japan · 3The Graduate University for Advanced Studies, SOKENDAI, Japan

Answer Set Programming Neuro-Symbolic Reasoning Neurosymbolic Learning