AI Sampling Temperature Optimizes with Budget for Pass@k.

Changsu Jeong (Independent Researcher)· August 18, 2026 View original

Key takeaways

  • Optimal AI sampling temperature for pass@k often rises with larger budgets.
  • This pattern is explained by a monotone-likelihood-ratio power tilt towards lower-success tasks.
  • The paper provides formal conditions and a theoretical framework for this phenomenon.
  • Understanding this helps optimize LLM performance in multi-sample inference.

Who benefits

Software DevelopmentAI ResearchMachine Learning EngineeringCloud Computing

Summary

This theoretical paper provides formal conditions explaining why the optimal sampling temperature for maximizing pass@k often increases with larger sampling budgets in AI code generation. It identifies the mechanism as a monotone-likelihood-ratio power tilt towards lower-success tasks.

This theoretical study investigates an observed phenomenon in AI code generation: the optimal sampling temperature for maximizing pass@k (a metric for code generation success) tends to be low for small sampling budgets but rises with larger budgets. While previous work noted that for a fixed task, the optimal temperature is independent of k, this paper provides a formal, population-level sufficient condition for the aggregate pattern. The core mechanism identified is a "monotone-likelihood-ratio power tilt" that favors lower-success tasks. The research demonstrates that if the conditional log-success response is nonincreasing in current success probability, then the normalized temperature derivative of aggregate pass@k is nondecreasing in k. This implies that if each temperature-performance curve is strictly single-peaked, its unique maximizer will be nondecreasing in k. The paper also derives a closed-form two-stratum phase diagram and a Beta(2,k) kernel representation for the marginal temperature derivative, offering diagnostic shape restrictions and insights into task-level localization.

Why it matters

Understanding the theoretical underpinnings of sampling temperature optimization is crucial for AI engineers and researchers to fine-tune large language models more effectively, leading to improved code generation and other multi-sample inference tasks.

How to implement this in your domain

  1. 1Review current LLM sampling strategies in light of these theoretical findings.
  2. 2Experiment with dynamic temperature adjustments based on the available sampling budget for code generation tasks.
  3. 3Develop tools to analyze the "conditional log-success response" of models to predict optimal temperature shifts.
  4. 4Incorporate these insights into prompt engineering and model deployment guidelines for better performance.

Original post by Changsu Jeong (Independent Researcher)

"arXiv:2608.14665v1 Announce Type: new Abstract: The temperature that maximizes pass@$k$ is often low for a small sampling budget and higher for a large budget. This pattern has been reported from Codex through recent multi-sample inference studies. It is not an algebraic property…"

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Originally posted by Changsu Jeong (Independent Researcher) on X · view source

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