🤖 AI Summary
This work addresses the logical inconsistencies that large language models often exhibit in complex reasoning due to the absence of formal axiomatic systems. To this end, the authors propose Mathesis, a novel neuro-symbolic architecture that uniquely integrates a differentiable logic engine with higher-order hypergraph representations. The framework employs a Symbolic Reasoning Kernel (SRK) to map logical constraints onto a continuous energy landscape, thereby recasting proof search as an energy minimization problem. It further combines Monte Carlo tree search with evolutionary proof strategies to enable multi-step deductive reasoning. By leveraging a Hypergraph Transformer and a semantic unification mechanism within an end-to-end trainable framework, Mathesis effectively unifies symbolic reasoning with neural learning, significantly enhancing both logical consistency and multi-step reasoning capabilities in theorem proving.
📝 Abstract
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.