arXiv:2603. 04852v2 Announce Type: replace Abstract: Multi-step theorem prediction is a central challenge in geometry problem solving.
By Junbo Zhao, Ting Zhang, Can Li, Wei He, Jingdong Wang, Hua Huang
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.
By Sahil Rajesh Dhayalkar
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.
By Zhaoyu Li, Hangrui Bi, Youyuan Zhang, Wenjie Ma, Zenan Li, Zhaolei Zhang, Xujie Si, Kaiyu Yang
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.
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.
By Qingde Li, Qingqi Hong, Jie Tian
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.
By Haizhao Fan, Yuchi Xiong, Jize Wang, Xinping Guan, Xinyi Le