BenchScope: How Many Independent Signals Does Your Benchmark Provide?

TL;DR

This paper introduces Effective Dimensionality (ED), a diagnostic tool to assess the independence and measurement breadth of AI benchmarks, revealing redundancy and guiding benchmark design.

Contribution

It proposes ED as a fast, population-conditional upper-bound diagnostic for benchmark scores, with a practical workflow and reference atlas for maintainers.

Findings

ED reveals substantial redundancy in benchmarks

The Open LLM Leaderboard behaves like roughly two measurement axes

Measurement breadth varies more than 20x across benchmarks

Abstract

AI evaluation suites often report many scores without checking whether those scores carry independent information. We introduce Effective Dimensionality (ED), the participation ratio of a centered benchmark-score spectrum, as a fast, population-conditional upper-bound diagnostic of measurement breadth. Applied at per-instance granularity to 22 benchmarks across 8 domains and more than 8,400 model evaluations, ED reveals substantial redundancy: the six-score Open LLM Leaderboard behaves like roughly two effective measurement axes (ED = 1.7), BBH and MMLU-Pro are near-interchangeable (rho = 0.96, stable across seven subpopulations), and measurement breadth varies more than 20x across current benchmarks. We show that relative ED rankings are stable under matched-dimension controls and that ED can flag redundant suite components, monitor performance-conditional compression, and guide benchmark maintenance. Because binary spectra overestimate absolute latent dimensionality, we interpret ED as a screening statistic rather than a literal factor count and complement it with null, reliability, and saturation analyses. We provide a 22-benchmark reference atlas and a four-step diagnostic workflow that benchmark maintainers can run with a score matrix and a few lines of code.