Measuring Five-Nines Reliability: Sample-Efficient LLM Evaluation in Saturated Benchmarks

TL;DR

This paper introduces a sample-efficient method for evaluating extremely high reliability (five-nines) in large language models by focusing on failure-prone inputs, significantly reducing inference requirements.

Contribution

The authors propose a failure-focused sampling approach using the cross-entropy method to efficiently estimate rare failure probabilities in LLMs.

Findings

Achieved up to 156.22x reduction in inferences needed for failure estimation.

Models with similar benchmark accuracy can have vastly different failure rates.

The framework enables reliable evaluation of LLMs for safety-critical applications.

Abstract

While existing benchmarks demonstrate the near-perfect performance of large language models (LLMs) on various tasks, this apparent saturation often obscures the need for rigorous evaluation of their reliability. In real-world deployment, however, achieving extremely high reliability (e.g., "five-nines" (99.999%) vs. "three-nines" (99.9%)) is fundamentally critical, as this gap results in an order-of-magnitude increase in failures, which is catastrophic in reliability-critical applications. Still, estimating such a rare failure probability with tight confidence bounds requires prohibitively large LLM inference sizes, making standard Monte Carlo evaluation infeasible under limited compute budgets. In this paper, we observe that LLM failures exhibit strong systematic patterns: across broad parameterized input spaces, a small subset of inputs disproportionately accounts for the majority of failures. Leveraging this observation, we propose to learn a sampling distribution concentrated on failure-prone inputs via the cross-entropy method (CEM). We evaluate our framework on three LLMs, Qwen2.5-Math-7B-Instruct, gpt-oss-20b-low, and Gemini 2.5 Flash Lite, across parameterized GSM8K templates and achieve up to 156.22x reduction in required inferences compared to naive uniform sampling. Our estimates reveal that models with indistinguishable accuracy on standard benchmarks can differ substantially in estimated failure rates, underscoring that reliability is a distinct and measurable axis of model quality. Our simple yet practical framework enables the evaluation of extreme reliability in LLMs, a distinct and underexplored dimension of evaluation beyond existing benchmarks, for their growing use in reliability-sensitive applications.