AXIOM: A Trust-First Neuro-Symbolic Execution Architecture for Verifiable Mathematical Reasoning
arXiv:2606.00671v1 Announce Type: cross Abstract: We present AXIOM, a trust-first neuro-symbolic execution architecture for natural-language mathematical reasoning. In AXIOM, the language model functions strictly as a canonicalizer: it rewrites informal problem text into a narrow schema consumed by a deterministic Computer-Algebra-System (CAS) pipeline, which derives and verifies the answer or abstains as a first-class output. Routing follows a 1:1:1 alignment between problem-shape regex, schema-specific prompt, and closed-form CAS handler, with 3,100+ such routes shipped and zero LOST_CORRECT
The increasing complexity of mathematical reasoning required for advanced AI systems and the growing demand for verifiable, trust-first AI solutions necessitate architectures like AXIOM.
This development addresses a core limitation of current large language models in mathematical reasoning by introducing a verifiable, deterministic approach, enhancing their reliability and trustworthiness for critical applications.
The role of language models shifts from primary reasoners to canonicalizers, allowing for a more robust and verifiable mathematical problem-solving pipeline in AI.
- · AI developers
- · Computer Algebra Systems (CAS) providers
- · High-assurance AI sectors
- · Mathematics education technology
- · Purely stochastic LLM mathematical reasoning approaches
- · Sectors reliant on non-verifiable AI mathematical outputs
AXIOM's architecture provides a new paradigm for integrating symbolic reasoning with neural networks, enhancing accuracy and trustworthiness.
This framework could lead to a broader adoption of neuro-symbolic AI in fields requiring high precision and verifiability, such as engineering and scientific research.
The success of AXIOM might inspire similar trust-first architectures for other complex cognitive tasks currently handled by black-box AI models.
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