Constructing a Neuro-Symbolic Mathematician from First Principles
This addresses the issue of logical inconsistencies in AI reasoning for mathematics and formal domains, representing a novel method rather than an incremental improvement.
The paper tackles the problem of persistent logical failures in Large Language Models (LLMs) during complex reasoning by proposing Mathesis, a neuro-symbolic architecture that encodes mathematical states as hypergraphs and uses a Symbolic Reasoning Kernel for gradient-based training, resulting in a system that turns proof search into energy minimization.
Large Language Models (LLMs) exhibit persistent logical failures in complex reasoning due to the lack of an internal axiomatic framework. 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.