BenchScope: How Many Independent Signals Does Your Benchmark Provide?
Summary: arXiv:2603.29357v1 Announce Type: new
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.
Introduction
In the rapidly evolving field of artificial intelligence, the effectiveness of evaluation benchmarks is paramount. These benchmarks often produce a multitude of scores, which may not always reflect distinct, independent information. This article introduces a novel metric termed Effective Dimensionality (ED), which seeks to quantify the independence of these scores and diagnose the breadth of benchmark measurements.
Understanding Effective Dimensionality (ED)
Effective Dimensionality is defined as the participation ratio of a centered benchmark-score spectrum. This metric serves as a rapid, population-conditional upper-bound diagnostic that allows researchers and practitioners to assess the measurement breadth of various benchmarks.
Key Findings
In a comprehensive analysis conducted on 22 benchmarks across 8 domains—encompassing over 8,400 model evaluations—ED has unveiled significant redundancies in the scores reported by these benchmarks. Here are some of the key findings:
- The six-score Open LLM Leaderboard functions similarly to only two effective measurement axes, with an ED value of 1.7.
- Benchmarks such as BBH and MMLU-Pro have been found to be nearly interchangeable, showing a correlation coefficient (rho) of 0.96, stable across seven different subpopulations.
- Measurement breadth varies significantly, with a disparity of over 20 times across current benchmarks.
Stability and Reliability of ED Rankings
The relative rankings of Effective Dimensionality have shown stability even under matched-dimension controls. This consistency suggests that ED is a reliable tool for identifying redundant components within benchmark suites. Additionally, it can be employed to monitor performance-conditional compression and assist in the ongoing maintenance of benchmarks.
Interpreting ED
It is essential to note that while binary spectra tend to overestimate absolute latent dimensionality, ED should be viewed as a screening statistic rather than a literal count of factors. To complement the insights provided by ED, we recommend conducting null, reliability, and saturation analyses.
Practical Applications
To facilitate the implementation of this diagnostic, we provide a reference atlas detailing the 22 benchmarks analyzed, along with a straightforward four-step diagnostic workflow. This process allows benchmark maintainers to easily assess their score matrices with just a few lines of code.
Conclusion
The introduction of Effective Dimensionality offers a valuable perspective on the independence and redundancy of scores reported by AI benchmarks. By adopting this metric, researchers can ensure that their evaluation suites provide meaningful and distinct insights, ultimately enhancing the robustness of AI development and evaluation.