"I May Not Have Articulated Myself Clearly": Diagnosing Dynamic Instability in LLM Reasoning at Inference Time

TL;DR

This paper introduces a method to diagnose reasoning failures in large language models during inference by analyzing token log probabilities, revealing that early instability can sometimes lead to correct answers, while late instability often indicates failure.

Contribution

The study presents a simple, training-free instability signal based on distributional shift and entropy that predicts reasoning failures in LLMs at inference time, distinguishing between corrective and destructive instability.

Findings

Instability strength predicts wrong answers with above-chance AUC.

Early instability can lead to correct answers (corrective instability).

Late instability often results in failure (destructive instability).

Abstract

Reasoning failures in large language models (LLMs) are typically measured only at the end of a generation, yet many failures manifest as a process-level breakdown: the model "loses the thread" mid-reasoning. We study whether such breakdowns are detectable from inference-time observables available in standard APIs (token log probabilities), without any training or fine-tuning. We define a simple instability signal that combines consecutive-step distributional shift (JSD) and uncertainty (entropy), summarize each trace by its peak instability strength, and show that this signal reliably predicts failure. Across GSM8K and HotpotQA, instability strength predicts wrong answers with above-chance AUC and yields monotonic bucket-level accuracy decline at scale across model sizes. Crucially, we show that instability is not uniformly harmful: early instability can reflect subsequent stabilization and a correct final answer (\emph{corrective instability}), whereas late instability is more often followed by failure (\emph{destructive instability}), even at comparable peak magnitudes, indicating that recoverability depends not only on how strongly the distribution changes but also on when such changes occur relative to the remaining decoding horizon. The method is model-agnostic, training-free, and reproducible, and is presented as a diagnostic lens rather than a corrective or control mechanism.