Entropy Sentinel: Continuous LLM Accuracy Monitoring from Decoding Entropy Traces in STEM

Deploying LLMs raises two coupled challenges: (1) monitoring--estimating where a model underperforms as traffic and domains drift--and (2) improvement--prioritizing data acquisition to close the largest performance gaps. We test whether an inference-time signal can estimate slice-level accuracy under domain shift. For each response, we compute an output-entropy profile from final-layer next-token probabilities (from top-$k$ logprobs) and summarize it with different statistics. A lightweight classifier predicts instance correctness, and averaging predicted probabilities yields a domain-level accuracy estimate. We evaluate on ten STEM reasoning benchmarks with exhaustive train/test compositions ($k\in\{1,2,3,4\}$; all $\binom{10}{k}$ combinations), on different classifier models and features across nine LLMs from six families (3B--20B). Estimates often track held-out benchmark accuracy, and several models show near-monotonic ordering of domains, providing evidence for output-entropy profiles being an accessible signal for scalable monitoring and for targeted data acquisition.