Neuro-Symbolic Reasoning

Neuro-Symbolic (NeSy) predictors incorporate prior knowledge into the prediction process of neural networks, ensuring that outputs satisfy specified constraints, making them particularly suitable for high-stakes applications where compliance with domain knowledge is essential. A key bottleneck in this paradigm is the acquisition of symbolic constraints: encoding domain knowledge into logical formulas remains a manual and expert-intensive process. In this work, we investigate the extent to which auto-formalization via LLMs can systematically translate textual knowledge into symbolic knowledge that can be plugged into NeSy predictors. To this end, we introduce auto-nesy-bench, a new benchmark for evaluating constraint formalization and its impact on downstream accuracy of NeSy predictors. Through an extensive evaluation across several domains, we find that LLMs can formalize constraints to a meaningful extent, generating formulas that are often similar to those provided by human experts. Moreover, when the generated formulas are syntactically valid, they can lead to high-quality downstream predictions. The code and benchmark are available at https://unitn-sml.github.io/auto-nesy-bench/.

As robots are increasingly deployed in everyday environments, ensuring their safety has become a central challenge. Existing methods often encode safety requirements as opaque mathematical/logical formulations or dense cost functions. While effective in specific tasks, they remain difficult to interpret, tightly coupled to individual tasks, and offer limited insight into why a robot action is considered safe or unsafe. To address this limitation, we propose ``Neuro-Symbolic Predicate Learning for Semantic Safe Robot Control'' (NEUPRO), which leverages a differentiable reasoner that can learn reusable safety representations from human-specified safety knowledge. NEUPRO allows practitioners to express task-related safety requirements as transparent symbolic rules, while enabling gradients to propagate through these rules to a feature extractor that maps raw observations to safety-relevant concepts. As a result, the learned feature extractor is (softly) grounded in human-understandable semantics, supports transparent constraint evaluation, and is transferable across tasks. By coupling interpretability with differentiability, NEUPRO moves beyond opaque cost design toward reusable safety reasoning. To evaluate NEUPRO's capability, we collect and release REASON, the first real robot benchmark dataset for interpretable robot safety specification. Experiments on REASON show that NEUPRO learns safety-critical features that generalize across tasks, mitigate the interpretability limitations of conventional black-box cost formulations, and provide explicit explanations of safety violation.

Many computer tasks recur: the same workflow runs many times, with new inputs and from different starting states. Current computer-use agents re-plan every step of every run, which makes them costly and unreliable on such tasks. We introduce neuro-symbolic computer use, in which a recurring workflow is executed by a learned policy rather than re-derived by an agent on each run. The policy fixes the decisions that are stable across runs (ordering, variables, loops, and branches) in executable code, and delegates observation-dependent decisions, such as grounding and state checks, to neural models. We learn these policies with neuro-symbolic policy iteration: starting from one agent trajectory, it executes the policy, diagnoses failures with task-completion and step-level judges, and revises the code with a coding model informed by an agent's continuation from the point of failure, without access to the benchmark evaluator. Iterating on generated parameter and initial-state variants makes the policy reusable, and a pre-action verifier guards each state-mutating step at deployment. On OSWorld-Verified and ScienceBoard, the learned policies achieve the highest Pass^3 of all methods in all four settings, 3.6-15.8 points above the base agent, while cutting per-run cost by 15-217$\times$ and latency by 3.4-5.1$\times$. On OSWorld-Verified, policies built only on variants transfer to the held-out original tasks, exceeding AutoRPA by 8.6-17.5 points in Pass^3.

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.

Neurosymbolic research typically assumes a pre-existing symbolic specification, leaving the upstream challenge of acquiring and formalizing requirements and constraints largely unaddressed. We present an architecture that fills this gap by using an OWL configuration ontology to mediate between neural constraint sources and downstream consumers. In this framework, LLM assistants elicit soft stakeholder preferences, while hardware specifications define hard physical and engineering limits. The ontology unifies these heterogeneous inputs, leverages description logic to identify unsatisfiability, and generates symbolic explanations that enable LLMs to interactively renegotiate terms with users. Any remaining conflicts are resolved downstream via priority-based relaxation. We illustrate our approach on a microgrid use case from the FLEXI project and argue its generalizability to multi-stakeholder domains where constraint acquisition is distributed across human and automated sources of unequal authority.

Three-dimensional reconstruction from unorganized point clouds remains a challenging problem in computer vision, geometric modeling, and computer-aided design. While neural implicit methods achieve impressive reconstruction accuracy, geometry is typically encoded in latent representations that limit interpretability and reuse within engineering workflows. We present NeuSOGA3D (Neuro-Symbolic Geometric Abstraction in 3D), a hybrid framework that combines learned perceptual priors inherited from NeuSOGA with explicit symbolic geometric reasoning. The method projects point clouds onto principal orthographic planes, constructs symbolic implicit spline representations from the resulting observations, and fuses them through shape-preserving constructive solid geometry operations to generate a coarse visual hull. Additional geometric detail is recovered through cross-sectional decomposition and volumetric reconstruction using Partial Shape-Preserving Splines. Unlike conventional neural implicit approaches, NeuSOGA3D progressively transforms observations into explicit symbolic entities, including control polygons, implicit spline fields, cross-sections, and volumetric lofts. Experiments on all forty categories of the ModelNet40 benchmark demonstrate the ability of the framework to recover structurally meaningful and CAD-compatible geometric representations from diverse point-cloud observations. The results highlight the potential of combining learned perception with symbolic geometric reasoning for explainable geometric intelligence.

Networked low-altitude unmanned aerial vehicles (UAVs) need reliable and adaptive decision-making capabilities to operate under uncertain observations, dynamic environments, and intermittent connectivity, while many existing agentic systems remain limited by hallucination risks, data dependence, and weak generalization. This article investigates neuro-symbolic agentic AI (NSAAI) as a framework for combining neural grounding, symbolic reasoning, and closed-loop agentic interaction to support more reliable and adaptive UAV autonomy. We first examine its capability foundations in data efficiency, compositional generalization, continual learning, and zero-shot transfer, and then develop a reference architecture integrating task and goal management, neuro-symbolic planning, verification and metacognition, skill execution and network interaction, and shared knowledge and memory. An urban fire-inspection case implemented in LAESim illustrates how a UAV can coordinate sensing and cloud access under intermittent connectivity, reuse a verified image-delivery skill, and satisfy explicit evidence conditions before completing the mission. The results illustrate the potential of NSAAI to support reusable skills, evidence-grounded decision-making, and adaptive mission execution in networked UAV systems. We further discuss key research directions in uncertainty-aware reasoning, knowledge and skill expansion, adaptive self-monitoring, and standardized evaluation.

Personalized agents are required to reason over long-term history interactions to infer both explicit preferences and implicit behavioral evidence. While early flat retrieval methods score memory fragments independently and neglect the distributed information, current structured memory frameworks rely on query-agnostic static graphs that fail to capture the context-dependent relations. Crucially, raw textual memories are inherently entangled and noisy, making fine-grained personalization and cross-session reasoning computationally prohibitive. To this end, we present LGM, a novel neuro-symbolic framework that shifts long-term memory disentanglement into a continuous latent space. Specifically, (i) instead of persisting fixed graphs, we design a tailored latent graph construction with a sparse autoencoder. Subject to each query, it maps historical interactions into latent memory nodes and disentangles the memory traces into sparse concept activations, dynamically synthesizing query-aware relational edge weights. (ii) A graph encoder then treats the query embedding as a conditioning preference to direct non-linear message passing across the task-specific latent subgraph. This yields a highly expressive memory representation for effective activations. Extensive experiments on long-term personalization benchmarks demonstrate that LGM significantly outperforms state-of-the-art baselines in capturing both explicit and implicit preferences while enabling personalized responses.

Assistive autonomous systems must anticipate human goals before an observed behavior is complete. This article formulates anticipation as goal inference from a partially observed multimodal episode together with structured prediction of the remaining behavior, rather than exact motor forecasting. A compact Hierarchical Planning Decoder (HPD) is attached to a frozen neuro-symbolic recognition encoder and predicts, at four ontological levels, the next actions, the remaining activities and low-level intentions, and the episode high-level intention(HLI). The decoder is trained with soft neuro-symbolic regularization combining transition-coherence and hierarchical continuity losses, and is decoded with hard reachability masks that enforce ontological validity at inference. On a compositional four-level benchmark of 15,002 multimodal episodes built over NTU RGB+D 120 features, three headline properties are observed together. The advantage over the strongest sequential baseline grows with the anticipation horizon, from +1.7 points at step 1 to +7.3 points at step 3 (top-5). Under compositional generalization, where one parent association per multi-parent low level intention is held out, this advantage widens to +4.9 points at step 1. At the episode level, 96.8% of anticipated trajectories satisfy the joint logic constraints, above the 88.1% strongest-baseline value and the 73.9% ground-truth floor; soft logic terms alone account for a 59.8 to 71.1% relative reduction of HLI-reachability violations, and the hard masks then eliminate them entirely. Neural generation supplies predictive ranking, symbolic constraints supply onto logical validity, and their combination yields coherent hierarchical anticipation while exposing remaining challenges in compositional goal generalization and unordered set prediction.

This paper introduces NeuroSymbEAD, a large-scale neuro-symbolic caption dataset featuring an ego-centric knowledge graph (KG) of static and dynamic objects annotated with classes, categories, heading directions, orientations, and distances from the ego-vehicle. These annotations are used on the KITTI-360 dataset to generate multilevel textual captions representing a lightweight version of an ego-centric scene map. Outdoor scene-map reconstruction, visual recognition, and object grounding establish baselines for driving common sense and traffic/scene understanding. For these purposes, natural language-based grounded captioning of objects and their complex relationships is a widely adopted contextual representation for indoor scene tasks. Neuro-symbolic representations have proven effective in handling structured information for various computer vision and language applications. Our data annotation pipeline allows the generation of varied map segments, populating simulated or real objects within the bounding boxes predicted by any 3D object detection network, and building hierarchical text captions. We benchmark our neuro-symbolic and ontological caption generation using pre-trained grounding and learned auto-regressive captioning networks. By converting 3D driving scenes into structured ego-centric language, NeuroSymbEAD provides a benchmark for vision-language and foundation models for traffic-scene explanation, 3D reasoning, and interpretable autonomous-driving perception.

Neuro-symbolic models are usually trained with supervision only on final labels, leaving the intermediate concepts unobserved. Since many concept assignments are consistent with a given label, training can predict labels correctly while recovering the wrong concepts, a failure known as a reasoning shortcut. Prototypical networks reduce shortcuts by anchoring each concept to a few labeled examples, but existing methods still couple perception and reasoning through a hand-crafted, task-specific differentiable loss that must be redesigned for every task. We introduce \textbf{Soft-PNet}, which removes this loss: it reframes concept grounding as a Metropolis walk over a precomputed cache of feasible symbolic solutions, guided by a prototype distribution built from a single labeled anchor per concept, and trains against one KL objective between the prototype-weighted cache and the network's concept predictions. The objective is identical across tasks and remains applicable when the solution space cannot be enumerated. On \texttt{MNIST-EvenOdd}, Visual Sudoku, and \texttt{Kand-Logic} under scarce supervision, Soft-PNet matches loss-engineered prototypical networks at the concept and label levels and recovers concepts that soft-grounding baselines miss, with no loss engineering and lower training time.

With the proliferation of LLM agents, the ability to understand and diagnose failures in agents is essential to achieving superior effectiveness and trustworthiness. As agent failures often manifest via long and complex trajectories, manually finding the needles in the haystack is untenable. However, traditional diagnosis techniques for software bugs can hardly address LLM agent failures, while completely relying on LLMs as the judge yields unreliable diagnosis results. To overcome these challenges, this paper presents AGENTSCOPE, a new neuro-symbolic approach for agent failure mode diagnosis. The key principle of AGENTSCOPE is to abstract agent behavior, based on its trajectories, into structured representations. Furthermore, AGENTSCOPE introduces the concept of neural invariants to specify agent behavior properties. AGENTSCOPE leverages LLM-guided reasoning atop the structured representation against neural invariants to pinpoint both the failure step and its type in the trajectory. We show the effectiveness of AGENTSCOPE on publicly available agent failure datasets (Who&When) and a more comprehensive dataset created by us (AgentErrata), where AGENTSCOPE significantly outperforms the current state of the art in fault localization and attribution accuracy. Our work shows that integrating structured abstractions with LLM-guided reasoning enables effective, reliable, and interpretable diagnosis for agent failures.

Neuro-Symbolic (NeSy) AI has recently emerged as a novel paradigm to enable trustworthy AI, aiming at integrating sub-symbolic neural perception with grounded symbolic reasoning. The neuro-symbolic integration process that characterizes these models has been proven beneficial to achieve more transparent, explainable and efficient AI systems. Meanwhile, their properties under adversarial settings have been overlooked being frequently deemed robust-by-design. However, the neural-symbolic integration process they leverage constitutes an additional layer of complexity that may provide an attack entry-point. Therefore, in this paper, we claim that an in-depth investigation of the adversarial robustness of NeSy models is necessary and provide the first systematic evaluation of backdoor attacks against NeSy. To this end, we compare the most popular NeSy framework, namely DeepProbLog, against baseline neural networks across a total of eight backdoor settings and four reasoning tasks. Our experimental results show that while NeSy models are indeed more robust than their neural counterpart on average, their robustness vastly depend on the strictness of the reasoning process being enforced and its compatibility with the chosen adversarial target. The source code to reproduce our experiments is made available at https://github.com/marcoantoniocorallo/NeSy-Backdoor.

Neurosymbolic reasoning has shown promising success in addressing complex reasoning tasks by combining large language models (LLMs) and symbolic solvers. While this approach shows promise, a fundamental challenge remains: improving the accuracy of translations from natural language to logical formulas. Current methods predominantly rely on prompt engineering, which is difficult to scale across different domains and input formats. Drawing inspiration from the success of fine-tuning in other model adaptation and alignment applications, we propose a fine-tuning-based Stratified Consistency Distillation approach: (1) We generate K logical translations per input using a frontier LLM and cluster them by semantic equivalence (2) Based on the entropy level, we apply majority voting (low entropy), LLM-as-a-Judge (medium entropy), or unification/abstention (high entropy), and (3) fine-tune a smaller model using the selected pseudo-labels. Our experiments show significant and consistent improvements in both Pass@K and our novel Equivalent Logical Similarity metrics, demonstrating the potential of advancing logical translation through consistency distillation.

In many practical applications of generative AI systems, from tax rules to airline baggage allowance, responses to natural language queries must respect written policies or rules. We present a hybrid symbolic approach that expresses policies in formal logic and at inference time exploits the representation power of language models for fact extraction to ground predicates, and an answer set solver for reasoning such that responses are interpretable, auditable, and as we show, accurate and robust under input perturbations. Specifically, we show this separation of extraction and reasoning steps outperforms policy-as-prompt and policy-as-code methods in most cases with ~10x reduction in token usage. The results point to the value of structured reasoning and symbolic solvers in conjunction with generative models to make robust decisions involving objective criteria.

Logic Tensor Networks (LTN) provide a neurosymbolic framework in which first-order logic is interpreted through tensor operations, enabling logical constraints to be integrated with differentiable learning. However, the original formulation of LTN is primarily suited to data represented as flat collections of individuals, and does not explicitly capture structural organization such as temporal order, sequential position, or graph connectivity. We introduce sLTN, an extension of LTN that makes structural dimensions first-class elements of the language. Structural dimensions represent named tensor axes associated with domain-specific organization, such as time steps, sequence positions, or graph nodes. They can be quantified explicitly, related through structural relations, and used to express temporal, sequential, and relational constraints directly at the logical level. We formalize the syntax and fuzzy tensor semantics of sLTN and show that, in the absence of structural dimensions, the framework recovers the original LTN semantics as a special case. We further describe a PyTorch implementation based on a declarative signature, formula parsing, and tensorial interpretation. The framework is illustrated on representative temporal and sequential reasoning examples. This paper serves as a companion to the sltn library, available at https://github.com/logictensornetworks/sltn.

First-order concept synthesis asks a system to infer one formula that classifies labeled objects consistently across several finite relational structures. Every candidate can be evaluated exactly, but quantified first-order formulas form a vast search space, and LLM outputs are often semantically promising without being fully correct. We introduce Hypothesis Frontier, a verifier-guided neurosymbolic framework that evaluates each LLM formula on every training object, retains the strongest verified hypothesis across rounds, and uses its remaining errors to guide subsequent generation. Symbolic processing repairs invalid formulas while remaining anchored to the LLM-generated hypothesis, and simplifies train-valid formulas without changing any training prediction. Under matched models, problem sets, and LLM-round budgets, Hypothesis Frontier solves substantially more problems than repeated original-prompt generation. After the final formulas are selected, exact simplification shortens many train-valid formulas while preserving every training prediction. Exact symbolic reasoning therefore helps both to solve more induction problems and to compress many of the resulting formulas.

Reasoning shortcuts are solutions of a neurosymbolic system's rules that produce correct predictions through unintended concepts. A recent framework of Takemura, Inoue, and Nishino analyzes them through an automorphism group of value relabelings and asks, as its central open question, when rules pin concepts down. We first show that the framework's key definition, one shared permutation applied at every position, does not apply as stated to any of the four heterogeneous benchmarks it was evaluated on, and that the most direct embedding, padding domains to a common size, produces confident false pathology: 90.91% of solution pairs reported unexplained on CLE4EVR, where every well-defined member of the hierarchy we introduce reports 0%, and the padded verdict's content rotates with configuration-file ordering. Re-measuring eleven rule families under fifteen pre-specified predictions (thirteen confirmed), unexplained-pair rates span 0% to 99.9999% and track provable structure: six theorems give sufficient conditions for transitivity and its failure, including a Free Slot Lemma certifying Kandinsky's pathology from syntax alone. For circuit-given rules, deciding symmetry-inertness of a coordinate is coNP-complete; nontrivial-automorphism existence is coNP-hard under randomized reductions, lies in $Σ_2^p$, is not $Σ_2^p$-complete unless PH collapses, and on monotone circuits is coNP-complete outright. In the Boolean case transitivity is classified exactly: automorphisms explain everything iff the solution set is an affine coset. Weakly supervised models place all 94 observed shortcuts at the one level the componentwise theory flags and none at the 48 it certifies transitive; twelve typed-ambiguous levels produce none, separating what symmetry permits from what optimization selects, and a dual-head control replicates the geography. All numbers trace to released artifacts.

Large language models (LLMs) increasingly serve as data-driven reasoners, yet their chains-of-thought (CoT) can be unfaithful even when final answers are correct. Most existing verification'' signals are not diagnostic: answer matching observes only the outcome, LLM-as-judge provides subjective and non-verifiable critiques, and scalar rewards (e.g., PRMs/RMs) offer little insight into where a multi-step derivation fails.We propose \textbf{SymDiag}, a neuro-symbolic framework that \textbf{reframes reasoning verification as structured failure diagnosis}. SymDiag translates natural-language CoT into symbolic constraints and performs step-level satisfiability/entailment checks to (i) localize failing steps and (ii) produce verifiable diagnostic evidence, including counterexamples, inconsistency witnesses, and missing-premise indicators. A central challenge is that apparent logic violations'' can be caused either by genuine reasoning defects or by neural-to-symbolic translation noise. SymDiag therefore incorporates a Self-Auditor that disentangles TranslationError from ReasoningError via dual symbolic encodings consistency checks, enabling robust diagnosis under partial observability. Across diverse mathematical, logical, scientific, and general reasoning benchmarks, SymDiag improves detection of unfaithful reasoning and provides substantially more effective feedback for multi-round reasoning repair than outcome-only verification and LLM-based judging, offering a principled foundation for trustworthy and scalable reasoning diagnosis.

In medical applications, raw data is frequently associated with significant privacy concerns, lending particular importance to the encoding of summary statistics from the literature. On the other hand, deep learning has become an invaluable tool for assessing symptoms based on visual or auditory sensor data. DeepProbLog allows for an extensible neuro-symbolic approach that accommodates connectionist components to analyse patient images within a transparent and rigorous probabilistic framework, namely probabilistic logic programming under the distribution semantics. Framed as a case study in stroke detection from multimodal data, this contribution explores the pathway from summary statistics available in the literature to a DeepProbLog-based diagnostic system. It suggests a workflow using established maximum entropy techniques to complete available probabilistic information and the probabilistic logic programming system ProbLog 2 to move from the entropy-maximising causal model to a discriminative neuro-symbolic model expressible within DeepProbLog. The relative performance of models derived from less complete data is analysed alongside the potential of the probabilistic inductive logic programming system ProbFOIL 2 for compressing large discriminative models, and the perspectives and implications of using DeepProbLog for diagnostic reasoning are discussed.

There are several methods for searching for graphs with prescribed properties, such as SAT solvers and specialized generators. These methods return the result as raw data: an adjacency matrix or a string encoding. The raw data certifies that the graph exists, but it does not reveal any structural properties of the graph. We ask whether one can automatically discover a short algebraic description if only this raw data is provided. We look for a description such as a Cayley graph $\mathrm{Cay}(Γ, S)$ or a lexicographic product $C_5[K_3]$. We address this question with a neurosymbolic approach. We propose an agent that runs on a general-purpose large language model with no fine-tuning or per-target training. The model interleaves reasoning with calls to the computer algebra system SageMath: it analyzes the target graph, proposes and tests candidate constructions, and revises them until the output matches the target. The agent communicates with SageMath through a Model Context Protocol (MCP) server, which we release as a general-purpose bridge. Whether a construction matches the target is checked by a single exact isomorphism test, and therefore rests on the symbolic side and not on the model. We test the approach on a benchmark of 100 highly symmetric graphs, namely two-orbit graphs on up to 25 vertices; the benchmark was fixed in advance. Our agent could find verified algebraic constructions for all of them, without falling back to raw encodings. A strong template-enumeration baseline reaches only about $20\%$, and a catalog lookup could not identify any of these graphs. However, construction quality declines when symmetry is removed. As a concrete application, we identify the smallest known counterexample to the Bernhart-Kainen dispersability conjecture, a $16$-vertex graph that enumeration found as raw data. For this graph, our agent found an explicit algebraic construction.

Large vision-language models have achieved strong performance in multimodal reasoning, but they remain unreliable on fine-grained spatial tasks that demand both precise spatial perception and fine-grained geometric computation beyond end-to-end generation. Tool augmentation offers a natural solution, while existing methods either plan tool calls from scratch without explicit dependency constraints or rely on fixed pipelines that are redundant and generalize poorly across spatial tasks. An effective spatial reasoning agent should instead accumulate reusable experience and adaptively compose it for new problems. To this end, we propose NeSy-Spatial, a neuro-symbolic framework for self-evolving spatial skills. NeSy-Spatial abstracts tool interactions and geometric operations into typed executable atomic instructions and composes them into two complementary skill types: Tool-Use Skills for organizing tool execution and Geometry Skills for structured geometric reasoning. During inference, NeSy-Spatial retrieves and executes relevant skills in a closed-loop process. During evolution, it analyzes buffered successful and failed trajectories to refine skill structures and prune unreliable or inactive entries. Experiments on three spatial reasoning benchmarks show that NeSy-Spatial consistently improves reasoning accuracy with more precise tool utilization.

From natural-language query interfaces to automated report generation, data analysis tools need a description of the data: the real-world entities it contains, which columns function as measures or identifiers, and how tables connect into units of analysis. Today, this semantic layer is usually written by hand. This is a knowledge-acquisition bottleneck that limits the scalability of analytic systems, keeps non-technical users dependent on experts, and is itself error-prone. We present TYTAN, a system for automatically constructing an analytic semantic schema from a relational database and, when available, a short user-provided description. TYTAN combines symbolic analysis of the database with LLM-based semantic inference for entity proposal, role assignment, and naming. When the evidence leaves a decision ambiguous, TYTAN asks the user a targeted natural-language question. We evaluate TYTAN on eight databases spanning real-world and benchmark domains along the three axes that define a schema's functional utility: (i) coverage, are all important entities and features captured?; (ii) retrieval correctness, do the schema's instructions actually reach the data; and (iii) characterization accuracy, are semantic types correct? Across the seven reference domains, TYTAN reaches every entity, attribute, and aggregable feature of the expert-corrected reference schemas (100% coverage). Additionally, 100% of its retrieval instructions execute correctly (1,678 of 1,678 self-generated claims), and semantic roles agree with the reference on 92-100% of matched attributes. Checking the underlying data showed the small disagreement is in the reference, not in TYTAN. On a held-out blind test (a live, ten-table database with no declared keys), TYTAN recovers the full entity structure with verified keys and satisfies 100% of the satisfiable expectations of five independent blind annotators.

Retrieval-augmented generation (RAG) improves question answering by grounding large language models (LLMs) in external knowledge such as text corpora. However, its reasoning process remains largely opaque: intermediate reasoning steps are difficult to verify and cannot be reliably attributed to specific evidence. Moreover, missing user-specific context is rarely detected systematically, often leading to incomplete or incorrect output. We propose NeSy-RAG, a modular neuro-symbolic RAG framework that synthesizes attributable Prolog modules from retrieved text chunks. For each chunk, the system generates semantically meaningful predicates that encode Boolean claims, which may depend on user facts. Using joint natural language-code embeddings, predicates are retrieved and composed into Prolog queries. To address incomplete user context, we introduce a symbolic knowledge-gap detection mechanism that identifies missing user facts whose truth values affect the query outcome and automatically triggers follow-up interactions. Executing the resulting Prolog queries yields deterministic answers together with transparent execution traces that link each reasoning step to its originating source. On the ShARC benchmark, without domain-specific training, NeSy-RAG achieves 61.1% accuracy, outperforming a same-model RAG baseline that achieves 42.8% accuracy.

A geometry-conditioned, neuro-symbolic closed-loop architecture is proposed for laser powder bed fusion, in which a standards-aligned ontology operates inside the control loop and couples symbolic reasoning with statistical learning to set the targets of a constraint-aware predictive controller. The ontology links the process objectives and constraints to the signals a controller can observe, and a description-logic reasoner converts them into the references and bounds enforced on each scan. The demonstrated case is overhang dross, a quality limit on the melt pool depth, which governs quality yet cannot be measured during the build, is mapped through a geometry- and power-dependent depth-to-width ratio onto a bound on the observable width, with the ratio and its calibrated uncertainty supplied by a Gaussian process. The reasoner classifies each upcoming feature and selects the active constraints-adding a lack-of-fusion floor at overhangs, a monotone guard beyond the calibrated range, and an energy-density cap where a process window is declared while running only on changes of geometric context and otherwise leaving a single small quadratic program on the per-scan path. In an Eagar-Tsai surrogate calibrated to the NIST AM-Bench benchmark for IN625, the architecture eliminates the dross produced by a geometry-blind controller, holds dross at zero with only a small residual lack-of-fusion under dual scoring, degrades gracefully under deliberate plant mismatch, and retargets to new alloys and constraints by editing ontology data rather than code. The results establish architectural feasibility, experimental calibration of the ratio is the principal next step.

Long-horizon embodied task requires agents to act under partial observability while preserving both scene belief and execution progress. Flat histories or implicit policy states may contain past observations, but they do not provide an explicit interface for deciding which world facts support the currently active goal. We introduce Mimir, a neuro-symbolic memory that separates world memory from task memory and dynamically grounds them before each action. World memory maintains object locations, object states, and perceptual evidence, while task memory maintains an ordered goal agenda, progress state, hand state, failures, and execution constraints. A grounding module binds the active goal to recalled world candidates, fills missing source locations, and attaches evidence before planning and embodiment-specific execution. Across tested backbones, Mimir consistently improves on different EB-ALFRED and EB-Habitat tasks, with maximum gains of 42.5% and average gains of 23.0%, respectively. Compared with the best results among prior agent and memory systems evaluated under the same backbone, Mimir improves the overall average success rate by 8.5%. Finally, on the EB-Habitat Long-horizon subset, Mimir achieves 86.0% success rate, substantially outperforming current closed-source models. Our code will be released soon.

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.

Biomedical relation extraction (BioRE) extracts structured knowledge from biomedical literature for applications such as knowledge base construction and hypothesis generation. Traditional symbolic systems such as SemRep provide high precision but limited recall, while large language models (LLMs) offer stronger contextual reasoning but remain prone to false-positive predictions. We developed ANCHOR-RE, a framework that integrates ontology-guided reasoning, external knowledge grounding, and data-driven verification rules into LLM inference. We evaluated it on three BioRE benchmarks (SemRepGS, DDI, and ChemProt) using both proprietary and open-weight LLMs. To assess generalizability beyond benchmark datasets while reducing potential evaluation bias from LLM pretraining contamination, we conducted a temporal evaluation using 100 biomedical articles published in 2026. With the proprietary backbone, ANCHOR-RE outperformed direct LLM prompting, improving micro-F1 from 0.654 to 0.676 on SemRepGS, from 0.769 to 0.872 on DDI, and from 0.939 to 0.941 on ChemProt. On DDI and ChemProt, it also outperformed previously reported inference-only methods and approached fine-tuned or instruction-tuned systems without parameter updates. Similar performance gains observed with open-weight LLMs indicate that the benefits were not limited to the proprietary backbone. On the post-cutoff set, manual assessment of 500 randomly sampled predictions yielded a precision of 69%, maintaining consistent precision on previously unseen biomedical literature. Neuro-symbolic reasoning can improve the reliability of LLM-based BioRE without fine-tuning. Results across multiple benchmarks, model families, and post-cutoff literature support ANCHOR-RE as a practical training-free approach to biomedical literature mining.

(Flat) Reinforcement Learning (RL) agents face significant challenges in environments with sparse rewards that require long-horizon reasoning. A compelling approach to improve sample efficiency is to incorporate knowledge into learning and decision-making. In standard Hierarchical RL (HRL), knowledge is encoded in a fixed, non-updatable form, such as architectural choices, and remains unchanged throughout learning. With fixed HRL, reasoning with incremental knowledge learned during exploration is impractical before sufficient environmental knowledge is acquired, leading to poor sample efficiency. In this work, we propose neurosymbolic HRL with {\em Incremental Knowledge (InK)}: symbolic high-level components perform {\em symbolic planning} (e.g. using $D^*$) on an updatable representation of current InK, while low-level goal-conditioned neural modules learn motion primitives through experience using reward shaping. Experiments on navigation tasks demonstrate that incorporating InK substantially improves sample efficiency. Additionally, to perform {\em optimal} symbolic planning given {\em prior} knowledge about the world, we develop Belief World Tree Search. The code is available at https://github.com/CPS-research-group/ink_bwts.

Vector symbolic architectures (VSA) are widely used for reasoning in neuro-symbolic (NeSy) AI, yet high-dimensional codebooks often create severe memory bottlenecks that limit scalability and deployment. In this paper, we propose Gram-Space, a compression framework that applies Gram-Schmidt orthogonalization to represent codebook vectors in a compact orthonormal coordinate system. Gram-Space preserves the dot-product structure required by matrix-based VSA operators, which supports numerically equivalent execution of matrix similarity, probability vectorization, and attention score computations. We provide a correctness analysis showing that inner products are preserved under the orthonormal basis representation. Using modern GPU hardware, we benchmark the Gram-Space framework on standard neuro-symbolic reasoning datasets. Experimental evaluations across state-of-the-art VSA models show that Gram-Space reduces model-level GPU memory usage by up to 15.75x and improves inference latency by up to 3.62x. Profiling results further indicate that Gram-Space reduces allocation-heavy overhead in codebook-associated stages and improves hardware utilization for NeSy workloads.