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

Anas Barakat, Souradip Chakraborty, Khushbu Pahwa, Amrit Singh Bedi · Feb 24, 2026 · Citations: 0

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Data freshness

Extraction: Fresh

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Feb 26, 2026, 6:11 PM

Stale

Extraction refreshed

Apr 13, 2026, 6:43 AM

Fresh

Extraction source

Persisted extraction

Confidence 0.35

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.

Low-signal caution for protocol decisions

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  • Extraction flags indicate low-signal or possible false-positive protocol mapping.
  • Extraction confidence is 0.35 (below strong-reference threshold).
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HFEPX Relevance Assessment

This paper is adjacent to HFEPX scope and is best used for background context, not as a primary protocol reference.

Best use

Background context only

Use if you need

A secondary eval reference to pair with stronger protocol papers.

Main weakness

Extraction flags indicate low-signal or possible false-positive protocol mapping.

Trust level

Low

Eval-Fit Score

0/100 • Low

Treat as adjacent context, not a core eval-method reference.

Human Feedback Signal

Not explicit in abstract metadata

Evaluation Signal

Detected

HFEPX Fit

Adjacent candidate

Extraction confidence: Low

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Field Provenance & Confidence

Each key protocol field shows extraction state, confidence band, and data source so you can decide whether to trust it directly or validate from full text.

Human Feedback Types

missing

None explicit

Confidence: Low Source: Persisted extraction missing

No explicit feedback protocol extracted.

Evidence snippet: Pass@k is a widely used performance metric for verifiable large language model tasks, including mathematical reasoning, code generation, and short-answer reasoning.

Evaluation Modes

partial

Automatic Metrics

Confidence: Low Source: Persisted extraction evidenced

Includes extracted eval setup.

Evidence snippet: Pass@k is a widely used performance metric for verifiable large language model tasks, including mathematical reasoning, code generation, and short-answer reasoning.

Quality Controls

missing

Not reported

Confidence: Low Source: Persisted extraction missing

No explicit QC controls found.

Evidence snippet: Pass@k is a widely used performance metric for verifiable large language model tasks, including mathematical reasoning, code generation, and short-answer reasoning.

Benchmarks / Datasets

missing

Not extracted

Confidence: Low Source: Persisted extraction missing

No benchmark anchors detected.

Evidence snippet: Pass@k is a widely used performance metric for verifiable large language model tasks, including mathematical reasoning, code generation, and short-answer reasoning.

Reported Metrics

partial

Pass@k, Pass@1, Latency, Cost

Confidence: Low Source: Persisted extraction evidenced

Useful for evaluation criteria comparison.

Evidence snippet: Pass@k is a widely used performance metric for verifiable large language model tasks, including mathematical reasoning, code generation, and short-answer reasoning.

Rater Population

missing

Unknown

Confidence: Low Source: Persisted extraction missing

Rater source not explicitly reported.

Evidence snippet: Pass@k is a widely used performance metric for verifiable large language model tasks, including mathematical reasoning, code generation, and short-answer reasoning.

Human Data Lens

  • Uses human feedback: No
  • Feedback types: None
  • Rater population: Unknown
  • Unit of annotation: Unknown
  • Expertise required: Math, Coding
  • Extraction source: Persisted extraction

Evaluation Lens

  • Evaluation modes: Automatic Metrics
  • Agentic eval: None
  • Quality controls: Not reported
  • Confidence: 0.35
  • Flags: low_signal, possible_false_positive

Protocol And Measurement Signals

Benchmarks / Datasets

No benchmark or dataset names were extracted from the available abstract.

Reported Metrics

pass@kpass@1latencycost

Research Brief

Deterministic synthesis

Pass@k is a widely used performance metric for verifiable large language model tasks, including mathematical reasoning, code generation, and short-answer reasoning. HFEPX signals include Automatic Metrics with confidence 0.35. Updated from current HFEPX corpus.

Generated Apr 13, 2026, 6:43 AM · Grounded in abstract + metadata only

Key Takeaways

  • Pass@k is a widely used performance metric for verifiable large language model tasks, including mathematical reasoning, code generation, and short-answer reasoning.
  • This multi-sample inference metric has motivated inference-aware fine-tuning methods that directly optimize pass@k.
  • Abstract shows limited direct human-feedback or evaluation-protocol detail; use as adjacent methodological context.

Researcher Actions

  • Treat this as method context, then pivot to protocol-specific HFEPX hubs.
  • Identify benchmark choices from full text before operationalizing conclusions.
  • Validate metric comparability (pass@k, pass@1, latency).

Caveats

  • Generated from title, abstract, and extracted metadata only; full-paper implementation details are not parsed.
  • Low-signal flag detected: protocol relevance may be indirect.

Research Summary

Contribution Summary

  • Pass@k is a widely used performance metric for verifiable large language model tasks, including mathematical reasoning, code generation, and short-answer reasoning.
  • This multi-sample inference metric has motivated inference-aware fine-tuning methods that directly optimize pass@k.
  • 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…

Why It Matters For Eval

  • Abstract shows limited direct human-feedback or evaluation-protocol detail; use as adjacent methodological context.

Researcher Checklist

  • Gap: Human feedback protocol is explicit

    No explicit human feedback protocol detected.

  • Pass: Evaluation mode is explicit

    Detected: Automatic Metrics

  • Gap: Quality control reporting appears

    No calibration/adjudication/IAA control explicitly detected.

  • Gap: Benchmark or dataset anchors are present

    No benchmark/dataset anchor extracted from abstract.

  • Pass: Metric reporting is present

    Detected: pass@k, pass@1, latency, cost

Category-Adjacent Papers (Broader Context)

These papers are nearby in arXiv category and useful for broader context, but not necessarily protocol-matched to this paper.

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