Why Pass@k Optimization Can Degrade Pass@1: Prompt Interference in LLM Post-training

TL;DR

This paper investigates why optimizing for pass@k in large language models can negatively impact pass@1, revealing that gradient conflicts caused by prompt interference lead to this degradation.

Contribution

It provides a theoretical analysis of the gradient conflict mechanism behind pass@k optimization degrading pass@1, supported by experiments on mathematical reasoning tasks.

Findings

Pass@k optimization can conflict with pass@1 due to gradient interference.

Prompt reweighting toward low-success prompts causes negative interference.

Theoretical characterization explains the trade-off observed in practice.

Abstract

Pass@k is a widely used performance metric for verifiable large language model tasks, including mathematical reasoning, code generation, and short-answer reasoning. It defines success if any of $k$ independently sampled solutions passes a verifier. This multi-sample inference metric has motivated inference-aware fine-tuning methods that directly optimize pass@$k$. However, prior work reports a recurring trade-off: pass@k improves while pass@1 degrades under such methods. This trade-off is practically important because pass@1 often remains a hard operational constraint due to latency and cost budgets, imperfect verifier coverage, and the need for a reliable single-shot fallback. We study the origin of this trade-off and provide a theoretical characterization of when pass@k policy optimization can reduce pass@1 through gradient conflict induced by prompt interference. We show that pass@$k$ policy gradients can conflict with pass@1 gradients because pass@$k$ optimization implicitly reweights prompts toward low-success prompts; when these prompts are what we term negatively interfering, their upweighting can rotate the pass@k update direction away from the pass@1 direction. We illustrate our theoretical findings with large language model experiments on verifiable mathematical reasoning tasks.