Constructing a Neuro-Symbolic Mathematician from First Principles

📝 Original Info

• Title: Constructing a Neuro-Symbolic Mathematician from First Principles
• ArXiv ID: 2601.00125
• Date: 2025-12-31
• Authors: Keqin Xie

📝 Abstract

Large Language Models (LLMs) exhibit persistent logical failures in complex reasoning due to the lack of an internal axiomatic framework [1] . We propose Mathesis, a neuro-symbolic architecture that encodes mathematical states as higher-order hypergraphs and uses a Symbolic Reasoning Kernel (SRK)-a differentiable logic engine that maps constraints to a continuous energy landscape. By defining a global energy function E(G), where zero energy implies logical consistency, the SRK yields gradient-based signals to train a Hypergraph Transformer Brain, turning proof search into energy minimization. Multi-step deduction is enabled via Monte Carlo Tree Search and Evolutionary Proof Search, guided by learned value functions and semantic unification.

📄 Full Content

...(본문 내용이 길어 생략되었습니다. 사이트에서 전문을 확인해 주세요.)