Bounded Difference Concentration for Infinitely Exchangeable Sequences with Applications to AI Benchmark Uncertainty

Modern artificial intelligence is supported by machine learning models (e.g., foundation models) that are pretrained on a massive data corpus and then adapted to solve a variety of downstream tasks. To summarize performance across multiple tasks, evaluation metrics are often aggregated into a summary metric, e.g., average accuracy across 10 question-answering tasks. When aggregating evaluation metrics, it is useful to incorporate uncertainty in the aggregate metric in order to gain a more realistic understanding of model performance. Our objective in this work is to demonstrate how statistical methodology can be used for quantifying uncertainty in metrics that have been aggregated across multiple tasks. The methods we emphasize are bootstrapping, Bayesian hierarchical (i.e., multilevel) modeling, and the visualization of task weightings that consider standard errors. These techniques reveal insights such as the dominance of a specific model for certain types of tasks despite an overall poor performance. We use a popular ML benchmark, the Visual Task Adaptation Benchmark (VTAB), to demonstrate the usefulness of our approaches.

We adapt split conformal prediction and adaptive conformal inference (ACI) to continuous AI agent evaluation, providing distribution-free coverage guarantees for forecasted quality scores. Conformal intervals achieve calibration error below 0.02 across all nominal levels at the 24h horizon, while ACI correctly widens intervals by 35% following agent releases then reconverges. We further develop compositional uncertainty bounds for multi-agent pipelines (validated via simulation across inter-stage correlations rho in [-0.5, 0.9]), a conformal abstention rule for pairwise rankings with controlled false-ranking rate, and FDR-corrected abstention for leaderboard-scale multiple testing. Evaluating 50 agents via 18 real-time signals collected hourly, we show that per-agent conditional coverage is well-concentrated around the nominal level (mean 80.4%, 90% of agents within [72%, 90%]), and that cross-source sentiment divergence predicts ranking instability (r=0.64, p<0.01). A circularity-controlled validation confirms the framework captures signal beyond benchmarks (rho_s=0.52, p<0.01, n=35). Code and data are released under CC BY 4.0.

While aggregate leaderboard scores drive AI development, they contain substantial measurement noise whose sources and magnitudes remain unquantified, making it unclear when rankings reflect genuine capability differences versus evaluation artifacts. We introduce a framework for measuring the latent landscape in AI benchmark ecosystems. Applying Confirmatory Factor Analysis (CFA) and Generalizability Theory to 4,000+ models from the Open LLM Leaderboard, we decompose sources of ranking variance and establish: (1) structures assumed in current reporting practice underestimate the strength of relationships between benchmarks; (2) evidence of local dependence among leaderboard items, undermining uses of benchmarks as measurement instruments under current scoring systems; (3) contributor metadata explains more rank-relevant variance ($\approx9\%$) than architecture or deployment categories in this context; (4) a manifest-score "scaling law" slope has low reliability ($R_β=0.53$); by contrast, the latent general-factor size slope is highly stable across ecosystem controls ($R_g=0.97$). We are able to provide unique insights into benchmark dynamics, such as which benchmarks are a function of LLM size and which can be oppositely impacted by post-training practices. We provide actionable diagnostics to determine how benchmark rankings can be trusted and how benchmark design can be improved.