Constructing a Neuro-Symbolic Mathematician from First Principles
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866918268569124864 |
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| author | Xie, Keqin |
| author_facet | Xie, Keqin |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_00125 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Constructing a Neuro-Symbolic Mathematician from First Principles Xie, Keqin Artificial Intelligence 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. |
| title | Constructing a Neuro-Symbolic Mathematician from First Principles |
| topic | Artificial Intelligence |
| url | https://arxiv.org/abs/2601.00125 |