A Reference-Free Score for Detecting Silent Reasoning Failures in Large Language Models

Large language models (LLMs) often use chain-of-thought (CoT) prompting to generate multi-step mathematical solutions. However, standard evaluation relies on exact-match accuracy, which ignores the quality of the derivation. This creates a "reasoning-answer consistency gap," where a model might arrive at the correct answer through flawed reasoning (a silent failure) or produce a valid derivation followed by a minor transcription error. The authors seek to develop a diagnostic tool that can identify these failures without requiring a gold-standard reference answer.

The authors introduce the Reasoning-Answer Faithfulness Score (RAFS), a composite metric that measures the credibility of a reasoning trace and its causal link to the final answer. RAFS is calculated through four primary components:

1. Step Validity: A verifier assesses the correctness of each atomic step in the derivation.
2. Reasoning-to-Answer Support: The system performs counterfactual interventions—modifying pivotal steps to see if the final answer changes in the expected direction—to confirm the trace actually justifies the answer.
3. Answer Consensus: The model samples multiple solutions to measure the stability of the final answer.
4. Conditional Reasoning Stability: The system compares the semantic content of reasoning traces that lead to the same answer to ensure consistency.

These components are combined using a non-compensatory geometric mean, ensuring that a failure in one critical area (like step validity) cannot be masked by high performance in another (like answer consensus).

RAFS provides an auditable warning signal for LLM deployment in high-stakes mathematical or logical tasks. By distinguishing between "faithful successes" (correct reasoning leading to a correct answer) and "silent failures" (incorrect reasoning leading to a correct answer), the framework allows developers to implement more nuanced deployment policies, such as triggering human review or model regeneration when reasoning is deemed untrustworthy, even if the final output appears correct.