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Your Benchmark Is an Empirical Measure Over Difficulty

Yifan Sun, Naicheng Yu, Jiawen Gong, Jingyan Shen, Huan Zhang · 2026 · arXiv

DOI: 10.48550/arXiv.2610.29927 · open-access PDF

Abstract

A benchmark is not merely a collection of test questions; it naturally induces an empirical measure over difficulty. In this work, we develop this measure-based view of benchmark evaluation. This perspective allows us to identify and formalize two central failure modes: measure mismatch, where the benchmark difficulty distribution differs from the intended difficulty distribution, and coverage gaps, where uncovered regions along the difficulty axis prevent benchmarks from detecting meaningful localized training progress. We propose two diagnostic metrics that capture these two failure modes an

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