Proof of Coherence: An Observatory for Reasoning Consistency of Large Language Models

This article introduces the Proof of Coherence project, an open-source observatory for systematically measuring the reasoning consistency of large language models (LLMs). The project focuses on the self-contradiction phenomenon of LLMs, and through an auditable experimental framework, formal consistency metrics, and open methodologies, it provides a scientific foundation for understanding and improving AI reasoning consistency, helping to enhance AI reliability.

LLMs exhibit self-contradictory characteristics; the same model may give contradictory answers to the same question, impairing user experience and raising reliability concerns. Logical consistency is the cornerstone of rationality, a prerequisite for credibility, an indicator of knowledge representation, and an error detection mechanism, which is crucial for high-risk scenarios such as healthcare and law.

The project adopts a rigorous experimental framework: 1. Build an open-ended question bank (covering ethics, probability, causality, etc.); 2. Repeat queries to detect temporal inconsistency; 3. Conditional testing to verify logical inference consistency; 4. Adversarial probing to actively induce contradictions; 5. Formal checks (convert natural language to logical expressions and use theorem provers to verify satisfiability).

Preliminary experiments reveal: High consistency in simple logical problems; Probability/statistical reasoning is a major area of inconsistency; Ethical answers depend on wording; Self-correction abilities vary widely; Temperature parameters significantly affect consistency (high temperature reduces consistency, low temperature improves it but sacrifices creativity).

Project applications include: Assisting model selection (high-consistency models are suitable for scenarios like law); Optimizing prompt engineering (designing more stable templates); Guiding training feedback (using weaknesses for fine-tuning); Risk grading (marking high-risk areas for manual review); Supplementing benchmark tests (focusing on the lower limit of reliability).

Limitations: Errors exist in converting natural language to logic, limited coverage of open domains, insufficient causal modeling, insufficient exploration of dynamic consistency, and lack of human baselines. Future directions: Develop inconsistency repair tools, build interactive debugging systems, integrate neuro-symbolic AI, and study multi-agent consistency protocols.

The Proof of Coherence project shifts focus from the upper limit of capability to the lower limit of reliability, reminding us that LLMs still have significant flaws in logical consistency. This project provides a tool framework for the trustworthy AI ecosystem, and it is expected to become an industry standard in the future, promoting the development of more robust and trustworthy AI systems.