Bootstrap Confidence Intervals for LLM Evaluation🔒 SSL Verified

Table of Contents

• ↓ Introduction
• ↓ Bootstrap methods
• ↓ Simulation
• ↓ Results
• ↓ Choosing N and k
• ↓ Use a normal approximation instead?
• ↓ Top Alternatives to indeedblog.com

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"As Large Language Models (LLMs) move from research prototypes to production systems, the developers of these systems need rigorous performance evaluation. In particular, we need confidence intervals around estimates of system accuracy. However, LLMs introduce a challenge that is unusual for ML systems: they are (operationally) non-deterministic. Even with the temperature set to zero, variations in hardware, batching, and API behavior can lead to different outputs for the exact same input, and variance of model outputs can exceed variance from data sampling (Wang, 2026)."

"On the other hand, LLMs introduce an advantage over many other non-deterministic systems, where it can be difficult, if not impossible, to expand your data after initial collection. You cannot, for example, ask a patient to develop a disease a second time to see if the outcome changes. With LLMs, we can generate additional outputs at any time, and do so comparatively cheaply, either on the same inputs or with additional inputs."

"When we create multiple LLM outputs per input, this creates a hierarchical or “clustered” data structure: we have N independent inputs, each with k correlated model runs. How should we create confidence intervals when the LLM outputs are non-deterministic? How should we make effective use of multiple LLM outputs?"

"The answer we propose here is the bootstrap. We simulate categorical LLM predictions and evaluate five candidate bootstrapping strategies to find out how well they correctly account for both the sampling of inputs and the non-determinism of the model itself. We’ll judge the methods based on whether their coverage matches our intended coverage, and whether they can do so with narrow confidence intervals. We then derive practical N-vs-k guidance for reducing confidence interval width, and apply the bootstrap to a well-known benchmark."

Key Topics & Focus Areas for indeedblog.com:

Introduction

Bootstrap methods

Simulation

Results

Choosing N and k

Use a normal approximation instead?