Evaluating Multiple LLM Generations with Validated Task Coverage

Benchmark scores increasingly influence the development, marketing, and selection of large language models (LLMs). Yet an overall score is interpretable only in relation to the system tested, the questions included, and the conditions of evaluation. This perspective examines five connected limitations of general LLM rankings: differences between evaluated and publicly available systems; commercial incentives and dependencies in external evaluation; benchmark saturation, defective tests, and data contamination; models exploiting scoring procedures; and the limited relevance of general scores to users' tasks. Documented cases illustrate why these problems require different responses. I argue for evaluation procedures that disclose the tested configuration, validate questions and successful task completion, report performance alongside cost and execution time, and make the scope of generalization explicit. I then discuss Isotanta, a crowdsourced benchmarking platform, as a practical example of contributed questions and repeated evaluation. A larger question pool may improve task coverage, while repeated sampling can improve the stability of estimates on that pool; neither guarantees validity or personalization. The paper distinguishes the platform's current shared ranking from proposed task-specific and user-provided evaluations. Its central argument is that model selection requires evidence about performance on the intended work, not simply a high position on a general leaderboard.

We give a stereological theory of LLM benchmark coverage. For any suite with effective dimensionality d_eff, the visible Hausdorff distance between two convex capability profiles consistent with the same scores is bounded by epsilon + C R m^(-1/(d_eff-1)), with matching Lipschitz lower bound. Empirically, three independent leaderboards (Open LLM v2, an extended 12-benchmark suite, LiveBench) all have d_eff in [2.86, 4.80] on their competitive frontier; the structural blind spot exceeds the observed runner-up score gap by two orders of magnitude and dominates statistical noise by 52-127x. Under a chi-squared projection model, the isotropic prior is the optimistic case; across six hidden-capability priors and four ambient dimensions the simulated half-split swap rate of the top two models stays in [0.38, 0.49], and a 500-trial random visible/held-out split shows that 92% of trials swap the top-1 ranking with on average 2.83 of 5 top-5 models changing. A submodular greedy algorithm with the Nemhauser (1 - 1/e) guarantee finds a stable core of 4 benchmarks; 7 of 12 suffice for 90% coverage, and the trained subset transfers across temporal quarters with 93-97% retention. A counterfactual validation across 12 internal benchmarks and 27 Chatbot Arena categories confirms that the eigenstructure predicts which evaluations are irreplaceable (rho = -0.69, p = 0.013 for removal disruption) and which external evaluations bring new information (rho = +0.38). As a second, independent theoretical contribution, we resolve Gardner's Problem 1.5 (1995) for C^2 support functions, establishing the minimax rate Theta(R/(kappa m^(2/(D-1)))) in general dimension via optimal recovery theory on S^(D-1).

Automated generation of LLM harnesses promises to improve inference through task specialization. Yet additional answer coverage can arise from repeated execution of the same program, making specialization difficult to identify. We introduce a controlled evaluation that separates answer coverage, repeatable task advantages, and gains from pre-execution selection. On 386 MATH-500 tasks, we compare eight generated harnesses plus a baseline with nine byte-identical baseline copies, using three executions per member. Identical programs yield 2.16 percentage points of repeat-averaged oracle headroom. Generated programs exhibit substantially more repeatable score patterns, but these chiefly reveal persistent weaknesses: losses relative to the baseline persist across all three repeats on 100 tasks, while persistent wins occur on only one task and are sensitive to answer extraction. The frozen selector gains 0.00 percentage points, and both populations reach 98.70% oracle coverage at 27 harness executions. Stable complementarity remains unresolved at three repeats. Supporting BIRD traces locate failures in mechanism implementation, activation, and output validity. Together, these findings establish why coverage and repeatability alone cannot justify claims of useful specialization. They motivate an evaluation standard for harness diversity: task advantages should persist across executions, guide usable decisions, and improve on additional fixed-program executions under matched inference budgets.