Entropy Regularization: A Free Correction to Cross-Entropy for Verified Demonstrations
Large language models are often post-trained on expert demonstrations using cross-entropy (CE), even when the downstream objective is not to imitate the demonstrated solution but to produce any output accepted by a verifier. This mismatch is seen in verifiable domains with multiple correct solutions, such as mathematical reasoning and code generation, where training data may contain only one expert solution per problem. We show that minimizing cross-entropy can be misaligned with minimizing verifier risk; two policies can assign identical likelihood to the observed demonstrations while placing different probability mass on incorrect outputs. This is formalized through a learning-theoretic...
| Authors | Mihir Dhanakshirur, Adam Ousherovitch, Ambuj Tewari |
|---|---|
| Primary category | cs.LG |
| Published | 24 September 2026 |
| Last updated at source | 24 September 2026 |
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