Probabilistic Soundness Guarantees in LLM Reasoning Chains

In reasoning chains generated by large language models (LLMs), initial errors often propagate and undermine the reliability of the final conclusion. Current LLM-based error detection methods often fail to detect propagated errors because earlier errors can corrupt judgments of downstream reasoning. To better detect such errors, we introduce Autoregressive Reasoning Entailment Stability (ARES), a probabilistic framework that evaluates each reasoning step based solely on previously-verified premises. This inductive method yields a nuanced score for each step and provides certified statistical guarantees of its soundness, rather than a brittle binary label. ARES achieves state-of-the-art performance across four benchmarks (72.1% Macro-F1, +8.2 points) and demonstrates superior robustness on very long synthetic reasoning chains, where it excels at detecting propagated errors (90.3% F1, +27.6 points). 1 Correct Reasoning Chain Claim 1: Let the numerator be x. Claim 2: The denominator is 3x-7. Claim 3: We know that x/(3x-7) = 2/5. Claim 4: Therefore, 5x = 6x-14. Claim 5: Finally, we get x = 14. (Correct) Unsound Steps Claim 1: Let the numerator be x. Claim 2: The denominator is 3x-7. Claim 3: We know that x/(3x-7) = 3/5.