The Optimal Decoder is Tilted Temperature
Larger sample budgets benefit from higher sampling temperatures in LLMs, but what temperature tuning optimizes and why it works remain poorly understood. We seek to answer these questions: we pose decoding as pass@$k$ maximization subject to two constraints that encode critical decoding failure modes: an entropy floor preventing diversity collapse, and a cross-entropy ceiling preventing implausibility. We prove that this maximization takes the form of a single closed-form conditional sampling rule, the \emph{tilted temperature} $q^\star \propto \bigl(p e^{ηV}\bigr)^{1/T}$. Here, the tilt comes from a verifier potential $V$ that quantifies how likely a partial generation is to eventually p...
| Authors | Nikolaos Papagiannis, Ananth Grama, Wojciech Szpankowski |
|---|---|
| Primary category | cs.LG |
| Published | 10 October 2026 |
| Last updated at source | 10 October 2026 |
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