aiqbench analysis
This article is a primary AI/ML research paper on LLM decoding theory, so it passes the topic gate. It proposes a closed-form "tilted temperature" sampling rule derived from a pass@k maximization framework, along with two practical methods (J-EOS online, Calibrated Temperature Decoding offline) evaluated on code generation benchmarks. For readers, the key takeaway is a theoretical justification for why higher temperatures help when sample budgets grow, with the caveat that results are shown on HumanEval and MBPP and depend on verifier estimates or model calibration.
The Optimal Decoder is Tilted Temperature
arXiv:2610.15058v1 Announce Type: new Abstract: 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} $q^\star \propto \bigl(p e^{\eta V}\bigr)^{1/T}$. Here, the tilt comes from a verifier potential $V$ that quantifies how likely a partial generation is to eventually pass. Ordinary temperature sampling, verifier-greedy decoding, and reward-tilted policies represent special cases. We further show that, under a natural rule for scaling the diversity budget with sample size $k$, the resulting optimal temperature increases with $k$, turning empirical choice into a theorem. The optimum still needs the unknown verifier potential, which we estimate using two design approaches. In the online setting, our J-EOS algorithm jointly tracks the two constraint multipliers and learns the verifier potential from binary pass/ fail feedback alone. In the offline setting, we show that when the model is calibrated, its log-probability tracks correctness up to an affine map. Under this condition, the tilt collapses into the exponent and the optimum reduces to ordinary temperature sampling. Calibrated Temperature Decoding (CTD) then fits one scalar offline and samples with zero additional inference-time overhead relative to temperature sampling. Building on these decision rules, we design a practical decoding algorithm for code generation and evaluate it alongside CTD on benchmarks including HumanEval and MBPP, showing improvements over standard and adaptive decoding baselines.
Abstract: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} $q^\star \propto \bigl(p e^{\eta V}\bigr)^{1/T}$. Here, the tilt comes from a verifier potential $V$ that quantifies how likely a partial generation is to eventually pass. Ordinary temperature sampling, verifier-greedy decoding, and reward-tilted policies represent special cases. We further show that, under a natural rule for scaling the diversity budget with sample size $k$, the resulting optimal temperature increases with $k$, turning empirical choice into a theorem. The optimum still needs the unknown verifier potential, which we estimate using two design approaches. In the online setting, our J-EOS algorithm jointly tracks the two constraint multipliers and learns the verifier potential from binary pass/ fail feedback alone. In the offline setting, we show that when the model is calibrated, its log-probability tracks correctness up to an affine map. Under this condition, the tilt collapses into the exponent and the optimum reduces to ordinary temperature sampling. Calibrated Temperature Decoding (CTD) then fits one scalar offline and samples with zero additional inference-time overhead relative to temperature sampling. Building on these decision rules, we design a practical decoding algorithm for code generation and evaluate it alongside CTD on benchmarks including HumanEval and MBPP, showing improvements over standard and adaptive decoding baselines.
Machine Learning (cs.LG)
arXiv:2610.15058 [cs.LG]
(or arXiv:2610.15058v1 [cs.LG] for this version)
https://doi.org/10.48550/arXiv.2610.15058 Focus to learn more arXiv-issued DOI via DataCite (pending registration)
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Full text under the publisher's open licence · 364 words
