Frontier LLMs are updated frequently and typically outperform their predecessors in aggregate. But aggregate gains say little about individual samples: an update can still cause sample-level regression, where a response correct under the old model becomes incorrect under the new one.

This paper studies how to predict such regressions from signals available at inference time. We compare single-model signals (confidence, logit margin, attention entropy) against cross-version signals (output KL divergence, likelihood drift, token-level KL, representation drift) under a unified added-value test that isolates each signal's gain over a confidence baseline.

Across six benchmarks in three task families (multiple-choice question answering, or MCQ; math reasoning; code generation) and six model update pairs, we find that (1) signal effectiveness is task-dependent: confidence is strongest on MCQ and simpler math, while likelihood/KL signals give the most frequent gains on harder math and code; (2) no signal is universally best across model updates either; and (3) some cross-version signals stay informative even when confidence fails, including without labels, which supports a proof-of-concept selective fallback that routes high-risk samples back to the old model. Practitioners can use these task-level patterns to choose which regression signal to trust for a given update.

Code is available at https://github.com/jiashengsally/llm-regression-signals.