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Don't Pass@k: A Bayesian Framework for Large Language Model Evaluation

Mohsen Hariri, Amirhossein Samandar, Michael Hinczewski, Vipin Chaudhary · Oct 5, 2025 · Citations: 0

Automatic Metrics Coding Rubric Rating Simulation Env
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How to use this page

High trust

Use this as a practical starting point for protocol research, then validate against the original paper.

Best use

Primary benchmark and eval reference

What to verify

Validate the evaluation procedure and quality controls in the full paper before operational use.

Evidence quality

High

Derived from extracted protocol signals and abstract evidence.

Abstract

Pass$@k$ is widely used to report the reasoning performance of LLMs, but it often produces unstable and potentially misleading rankings, especially when the number of trials (samples) is limited and computational resources are constrained. We present a principled Bayesian evaluation framework that replaces Pass$@k$ and average accuracy over $N$ trials (avg$@N$) with posterior estimates of a model's underlying success probability and credible intervals, yielding stable rankings and a transparent decision rule for differences. Evaluation outcomes are modeled as categorical (not just 0/1) with a Dirichlet prior, giving closed-form expressions for the posterior mean and uncertainty of any weighted rubric and enabling the use of prior evidence when appropriate. Theoretically, under a uniform prior, the Bayesian posterior mean is order-equivalent to average accuracy (Pass$@1$), explaining its empirical robustness while adding principled uncertainty. Empirically, in simulations with known ground-truth success rates and on AIME'24/'25, HMMT'25, and BrUMO'25, the posterior-based procedure achieves faster convergence and greater rank stability than Pass$@k$ and recent variants, enabling reliable comparisons at far smaller sample counts. The framework clarifies when observed gaps are statistically meaningful (non-overlapping credible intervals) versus noise, and it naturally extends to graded, rubric-based evaluations. Together, these results recommend replacing Pass$@k$ for LLM evaluation and ranking with a posterior-based, compute-efficient protocol that unifies binary and non-binary evaluation while making uncertainty explicit. Source code is available at https://github.com/mohsenhariri/scorio

Should You Rely On This Paper?

This paper has strong direct human-feedback and evaluation protocol signal and is suitable as a primary eval pipeline reference.

Best use

Primary benchmark and eval reference

Use if you need

A benchmark-and-metrics comparison anchor.

Main weakness

No major weakness surfaced.

Trust level

High

Usefulness score

77/100 • High

Use this as a primary source when designing or comparing eval protocols.

Human Feedback Signal

Detected

Evaluation Signal

Detected

Usefulness for eval research

High-confidence candidate

Extraction confidence 80%

If you are doing eval pipeline work, start here:

Human Eval Hub LLM-as-Judge Hub Pairwise Preference Hub Tool-Use Eval Hub

What We Could Verify

These are the protocol signals we could actually recover from the available paper metadata. Use them to decide whether this paper is worth deeper reading.

Human Feedback Types

strong

Rubric Rating

Directly usable for protocol triage.

"Pass$@k$ is widely used to report the reasoning performance of LLMs, but it often produces unstable and potentially misleading rankings, especially when the number of trials (samples) is limited and computational resources are constrained."

Evaluation Modes

strong

Automatic Metrics, Simulation Env

Includes extracted eval setup.

"Pass$@k$ is widely used to report the reasoning performance of LLMs, but it often produces unstable and potentially misleading rankings, especially when the number of trials (samples) is limited and computational resources are constrained."

Quality Controls

missing

Not reported

No explicit QC controls found.

"Pass$@k$ is widely used to report the reasoning performance of LLMs, but it often produces unstable and potentially misleading rankings, especially when the number of trials (samples) is limited and computational resources are constrained."

Benchmarks / Datasets

strong

AIME

Useful for quick benchmark comparison.

"Empirically, in simulations with known ground-truth success rates and on AIME'24/'25, HMMT'25, and BrUMO'25, the posterior-based procedure achieves faster convergence and greater rank stability than Pass$@k$ and recent variants, enabling reliable comparisons at far smaller sample counts."

Reported Metrics

strong

Accuracy, Pass@k

Useful for evaluation criteria comparison.

"We present a principled Bayesian evaluation framework that replaces Pass$@k$ and average accuracy over $N$ trials (avg$@N$) with posterior estimates of a model's underlying success probability and credible intervals, yielding stable rankings and a transparent decision rule for differences."

Human Feedback Details

  • Uses human feedback: Yes
  • Feedback types: Rubric Rating
  • Rater population: Not reported
  • Unit of annotation: Multi Dim Rubric
  • Expertise required: Coding

Evaluation Details

  • Evaluation modes: Automatic Metrics, Simulation Env
  • Agentic eval: None
  • Quality controls: Not reported
  • Evidence quality: High
  • Use this page as: Primary benchmark and eval reference

Protocol And Measurement Signals

Benchmarks / Datasets

AIME

Reported Metrics

accuracypass@k

Research Brief

Metadata summary

Pass$@k$ is widely used to report the reasoning performance of LLMs, but it often produces unstable and potentially misleading rankings, especially when the number of trials (samples) is limited and computational resources are constrained.

Based on abstract + metadata only. Check the source paper before making high-confidence protocol decisions.

Key Takeaways

  • Pass$@k$ is widely used to report the reasoning performance of LLMs, but it often produces unstable and potentially misleading rankings, especially when the number of trials (samples) is limited and computational resources are constrained.
  • We present a principled Bayesian evaluation framework that replaces Pass$@k$ and average accuracy over $N$ trials (avg$@N$) with posterior estimates of a model's underlying success probability and credible intervals, yielding stable rankings and a transparent decision rule for differences.
  • Evaluation outcomes are modeled as categorical (not just 0/1) with a Dirichlet prior, giving closed-form expressions for the posterior mean and uncertainty of any weighted rubric and enabling the use of prior evidence when appropriate.

Researcher Actions

  • Compare this paper against nearby papers in the same arXiv category before using it for protocol decisions.
  • Validate inferred eval signals (Automatic metrics) against the full paper.
  • Use related-paper links to find stronger protocol-specific references.

Caveats

  • Generated from abstract + metadata only; no PDF parsing.
  • Signals below are heuristic and may miss details reported outside the abstract.

Research Summary

Contribution Summary

  • We present a principled Bayesian evaluation framework that replaces Pass@k and average accuracy over N trials (avg@N) with posterior estimates of a model's underlying success probability and credible intervals, yielding stable rankings and…
  • Evaluation outcomes are modeled as categorical (not just 0/1) with a Dirichlet prior, giving closed-form expressions for the posterior mean and uncertainty of any weighted rubric and enabling the use of prior evidence when appropriate.
  • Together, these results recommend replacing Pass@k for LLM evaluation and ranking with a posterior-based, compute-efficient protocol that unifies binary and non-binary evaluation while making uncertainty explicit.

Why It Matters For Eval

  • We present a principled Bayesian evaluation framework that replaces Pass@k and average accuracy over N trials (avg@N) with posterior estimates of a model's underlying success probability and credible intervals, yielding stable rankings and…
  • Together, these results recommend replacing Pass@k for LLM evaluation and ranking with a posterior-based, compute-efficient protocol that unifies binary and non-binary evaluation while making uncertainty explicit.

Researcher Checklist

  • Pass: Human feedback protocol is explicit

    Detected: Rubric Rating

  • Pass: Evaluation mode is explicit

    Detected: Automatic Metrics, Simulation Env

  • Gap: Quality control reporting appears

    No calibration/adjudication/IAA control explicitly detected.

  • Pass: Benchmark or dataset anchors are present

    Detected: AIME

  • Pass: Metric reporting is present

    Detected: accuracy, pass@k

Related Papers

Papers are ranked by protocol overlap, extraction signal alignment, and semantic proximity.

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