arXiv AI
Jun 10
Non-Parametric Structural Priors for Geometry Theorem Prediction
arXiv:2603. 04852v2 Announce Type: replace Abstract: Multi-step theorem prediction is a central challenge in geometry problem solving.
The Topological Dual of a Dataset: A Logic-to-Topology Encoding for AlphaGeometry-Style Data
arXiv:2604. 18050v2 Announce Type: replace Abstract: AlphaGeometry represents a milestone in neuro-symbolic reasoning, yet its architecture faces a log-linear scaling bottleneck within its symbolic deduction engine that limits its efficiency as problem complexity increases.
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arXiv AI
Jun 16
Overcoming the Impedance Mismatch: A Theoretical Roadmap for Fusing Foundation Models and Knowledge Graphs
arXiv:2606. 15656v1 Announce Type: new Abstract: Modern artificial intelligence remains fundamentally divided between the continuous, probabilistic spaces of Foundation Models and the discrete, deterministic structures of Knowledge Graphs.
arXiv AI
Aug 18
Euclid-Omni : A Unified Neuro-Symbolic Framework for Plane Geometry
Euclid-Omni is a unified neuro‑symbolic framework that integrates a formal geometry system with Large Language Models and Vision‑Language Models to solve both calculation and proving problems in Euclidean geometry up to Olympiad level. Its core component, Euclidea, automatically generates deductive reasoning steps and algebraic computations, while a data‑generation pipeline creates synthetic symbolic problems, diagrams, and natural‑language translations for training. Experiments show that VLMs trained on this synthetic data outperform on calculation tasks, and LLMs paired with Euclidea match state‑of‑the‑art proving systems using far less compute and data.
Hugging Face Trending Papers
Aug 27
SymbolLKG: Towards Verifiable Logical Reasoning via Logical Knowledge Graph and Symbolic Solvers
The paper introduces SymbolLKG, a neuro-symbolic framework that combines a Logical Knowledge Graph (LKG) with dynamic solver routing to improve logical reasoning in large language models. The LKG represents logical rules and constraints as topological nodes, allowing explicit modeling of dependencies extracted from text. A Logic Router dispatches tasks to the most suitable symbolic engine, supported by a topology-aware hybrid retrieval mechanism, and the approach outperforms existing prompting and RAG baselines on logical reasoning benchmarks.
arXiv AI
Sep 2
Neuro-Symbolic Geometric Abstraction (NeuSOGA): From Observations to Symbolic Mathematical Representations
Neuro‑Symbolic Geometric Abstraction (NeuSOGA) is a framework that converts raw observations into explicit symbolic mathematical representations. It achieves this by sequentially generating topological and geometric abstractions, using tools such as Euclidean Distance Transforms, Segment Anything, and Implicit Area Splines. The resulting analytical implicit models are interpretable, editable, and support arbitrary‑order smoothness, additive composition, and closed‑form evaluation across diverse sensing modalities.
arXiv AI
Aug 28
SymbolLKG: Towards Verifiable Logical Reasoning via Logical Knowledge Graph and Symbolic Solvers
The paper introduces SymbolLKG, a neuro-symbolic framework that combines a Logical Knowledge Graph (LKG) with dynamic solver routing to improve logical reasoning in large language models. The LKG represents logical rules and constraints as topological nodes, enabling explicit modeling of dependencies extracted from text. A Logic Router dispatches tasks to the most suitable symbolic engine, supported by a topology-aware hybrid retrieval mechanism, and the approach outperforms existing prompting and RAG baselines on logical reasoning benchmarks.
arXiv Machine Learning
Aug 3
Persistent Convolution: A Topological Framework for AI Alignment Testing and Semantic Space Characterization
arXiv:2607. 29008v1 Announce Type: cross Abstract: Modern opaque AI models prize performance over interpretability, which makes testing difficult.
arXiv AI
Aug 26
ReactBench: A Benchmark for Topological Reasoning in MLLMs on Chemical Reaction Diagrams
ReactBench is a benchmark designed to evaluate the structural reasoning abilities of multimodal large language models (MLLMs) using chemical reaction diagrams. The dataset contains 1,618 expert‑annotated question‑answer pairs that test reasoning across four hierarchical task dimensions, from simple endpoint counting to complex topological analysis. Evaluation of 24 MLLMs shows a performance gap of more than 30% between anchor‑based tasks and holistic structural reasoning tasks, indicating that current models struggle with reasoning over branching, converging, and cyclic structures.
arXiv AI
Sep 15
Circuit-MLLM: Topological Logic-Guided Latent-Space Visual Reasoning for Circuit Schematic Understanding
arXiv:2609.15668v1 Announce Type: cross Abstract: Through pre-training on extensive text and image datasets, current multi-modal large language models (MLLMs) achieve strong performance on general ta...
arXiv AI
Aug 6
The RAIL Principles for Neurosymbolic AI: Reasoning, Assurances, Interfacing and Learning
arXiv:2608. 04285v1 Announce Type: new Abstract: Neurosymbolic AI systems that integrate machine learning and symbolic reasoning are rapidly gaining attention.
arXiv AI
Sep 3
When Evidence Shapes Collaboration: Knowledge-Conditioned Topology Generation for Multi-Agent Systems
The paper introduces K‑GAT, a neuro‑symbolic framework that generates multi‑agent collaboration topologies conditioned on external evidence, treating the design as a knowledge‑conditioned structure learning problem. Unlike prior methods that rely mainly on large language model parameters, K‑GAT integrates external evidence directly into autoregressive graph generation, reducing redundant interactions and improving verification in knowledge‑intensive tasks. Experiments on benchmarks such as the expert‑level GPQA dataset show K‑GAT achieving a +15.7% accuracy gain over the LLM‑Debate baseline while using fewer computational tokens.
arXiv AI
Jul 24
Knowledge Graph Re-engineering Along the Ontological Continuum (extended version)
arXiv:2605. 22093v3 Announce Type: replace Abstract: Knowledge graphs have become the primary vehicle for data integration and are critical to the success of modern AI, but the diversity of KG modelling practices, from lightweight vocabularies to richly axiomatised ontologies, makes integration and reuse expensive and brittle.