Proof-of-Coherence: A New Method to Quantify Reasoning Consistency of Large Language Models

This article introduces an open-source framework called Proof-of-Coherence, which aims to systematically observe and quantify the reasoning consistency of large language models (LLMs). By detecting self-contradictions of models on the same problem, it provides an auditable evaluation tool for AI safety research, filling the gap in traditional LLM evaluations that lack consistency measurement.

LLMs perform well in various tasks, but the problem of self-contradiction has long plagued researchers: the same problem may yield inconsistent answers at different times or in different contexts. As LLMs are increasingly applied in high-risk scenarios such as medical diagnosis and legal consultation, such inconsistencies not only erode user trust but may also lead to serious consequences, making reliability a core concern.

Proof-of-Coherence is an open-source LLM reasoning observatory, whose core objective is to quantify and prove model 'incoherence'. It provides a complete toolchain (auditable test artifacts, formal coherence metrics, public evaluation methods) to address the problem that traditional evaluations focus on accuracy while ignoring internal logical consistency.

1. Repetitive Query Mechanism: Isolate context and query the same problem multiple times to simulate real scenarios;
2. Semantic Comparison: Identify opposing positions through semantic analysis rather than just string matching;
3. Contradiction Classification: Divided into four categories: position reversal, confidence drift, condition-dependent contradiction, time-sensitive contradiction;
4. Coherence Score: A 0-1 score to quantify model consistency, where 1 means fully coherent and 0 means completely contradictory.

• AI Safety Research: Locate training data biases, model architecture flaws, and evaluate the effectiveness of fine-tuning and alignment techniques;
• Model Developers: Detect unstable areas before deployment to avoid contradictions in production environments;
• End Users: Need to confirm key issues multiple times, cross-verify, and maintain a skeptical attitude towards decisions.

Technical Highlights: Auditability (detailed logs can be independently verified), modular architecture (easy to extend algorithms/problem types), public transparency (open-source methodology); Limitations: Semantic understanding has boundaries, some answers depend on unclear contexts, and current focus is on English model evaluation.

Future Directions: Multilingual detection, introducing human judgment as a gold standard, real-time consistency monitoring, combining with model uncertainty quantification; Summary: This project marks a shift in LLM evaluation towards focusing on internal consistency, which is an essential path to building reliable AI systems. It reminds researchers to stay clear-headed about the limitations while marveling at the models' capabilities.