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Your Benchmark Is an Empirical Measure Over Difficulty

Yifan Sun, Naicheng Yu, Jiawen Gong, Jingyan Shen, Huan Zhang · 2026 · arXiv (Cornell University)

DOI: 10.48550/arxiv.2610.29927 · cited by 0 works (OpenAlex) · open-access PDF

German

Ein Benchmark ist nicht nur eine Sammlung von Testfragen; es induziert natürlich eine empirische Messung über Schwierigkeit. In dieser Arbeit entwickeln wir diese maßgebliche Sicht der Benchmark-Bewertung. Diese Perspektive ermöglicht es uns, zwei zentrale Misserfolge-Modi zu identifizieren und zu formalisieren: Messung Mismatch, wo die Benchmark-Schwierigkeitsverteilung von der beabsichtigten Schwierigkeitsverteilung abweicht, und Abdeckung Lücken, wo entdeckte Regionen entlang der Schwierigkeitsachse verhindern, dass Benchmarks signifikante lokalisierte Ausbildung Fortschritte erkennen. Wir schlagen zwei Diagnosemetriken vor, die diese beiden Misserfolge-Modi erfassen und strenge theoretische Garantien bieten. Empirisch

Machine translation (Meta M2M100); the English original follows.

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 and provide rigorous theoretical guarantees. Empirically, we analyze 25 popular benchmarks spanning 7 domains using carefully estimated item difficulties. Our results show that many benchmarks implicitly overweight certain difficulty regions, so their leaderboard conclusions should be interpreted with caution; others leave substantial portions of the difficulty axis uncovered, limiting their ability to monitor the model improvement process. Finally, we turn diagnosis into action by introducing BenchFill, a simple difficulty-targeted item rewriting algorithm that effectively reduces local coverage gaps.

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Topics: Benchmark (surveying), Measure (data warehouse), Computer science, Perspective (graphical), Limiting, Machine learning

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