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This paper introduces Effective Dimensionality (ED), a metric based on the participation ratio of a centered benchmark-score spectrum, to quantify the amount of independent information provided by AI evaluation suites. Applying ED to 22 benchmarks, the authors find significant redundancy, with some benchmarks like the Open LLM Leaderboard effectively measuring only two dimensions despite reporting six scores. The study demonstrates ED's utility in identifying redundant components, monitoring performance-conditional compression, and guiding benchmark maintenance.
AI benchmarks may be giving you a false sense of comprehensive evaluation: the six scores on the Open LLM Leaderboard effectively boil down to just two independent measurements.
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.
