Knowledge Index of Noah's Ark

Standard evaluation of large language models assumes stable model rankings across inference conditions. We challenge this assumption by varying the token generation budget, i.e., the maximum tokens a model may produce, across seven levels (64--4,096), evaluating four models on three reasoning benchmarks (56,476 inferences). We report four findings: (i) 3--19% of items exhibit non-monotone behavior (accuracy decreasing with more budget), even after controlling for truncation, and this phenomenon is model-specific (cross-model overlap: 6--14%). (ii) Model rankings reverse across budgets on all benchmarks ($p {<} 0.01$, McNemar). (iii) Oracle analysis reveals model complementarity up to $+27.8$pp, most pronounced at constrained budgets. (iv) A budget-aware router captures 14.1% of the oracle gap cross-domain; budget features help within-domain ($+1.6$ to $+5.7$pp) but are domain-specific and hurt transfer ($-1.2$pp). These results argue for budget-conditioned evaluation protocols.

Existing benchmarks typically report accuracy for a single model on a single run. This systematically understates real-world LLM capabilities, particularly under heterogeneous data distributions: (i) different models get different questions correct according to their specializations, and (ii) given a budget, multiple generations can be sampled and selectively retained. To quantify this gap, we introduce the Capability Frontier: a Pareto frontier over a set of models that characterizes the best achievable performance at each cost level under optimal selection across models and generations (i.e., via an oracle). Our construction corrects for two opposing biases: underestimation from single-model evaluation and overestimation from taking maxima over noisy samples. We study 21 LLMs across 16 widely used benchmarks spanning coding, reasoning, medicine, factuality, instruction following, and agentic tasks, comparing Capability Frontier performance at matched cost to each benchmark's top-performing model. Correcting for single-model evaluation yields a 54% error rate reduction; additionally correcting for single runs yields an 82% improvement, with SOTA accuracy matched at 85% cost reduction. Complementing these empirical results, we use controlled probabilistic simulations to show that higher query topic entropy produces a near-monotonic increase in the performance gap between oracle routing and the best single model. Our findings suggest collective LLM capabilities are substantially underestimated, with implications for evaluation and deployment in data-heterogeneous, multi-domain settings.

Parametric knowledge in large language models (LLMs) is a cornerstone of their success, yet remains poorly understood. Existing knowledge benchmarks typically rely on predefined questions (e.g., "What is the birth date of M.L. King?"), evaluating only knowledge that benchmark designers explicitly choose to query, a problematic availability bias. In this paper, we introduce open knowledge evaluation, a new paradigm for LLM knowledge benchmarking. Instead of asking narrow questions, it evaluates models on the knowledge they choose to surface in response to open-ended elicitation prompts (e.g., "Tell me everything you know about M.L. King"). This shifts the focus from predefined answer retrieval toward characterizing the knowledge models naturally express. We instantiate this paradigm with BeQu (Beyond Questions), a benchmark of 10,000 entities paired with reference corpora for statement verification. Using BeQu, we evaluate a broad range of language models and analyze the effects of reasoning effort, model scale, prompt format, and knowledge domain. Data and leaderboard are available on this work's GitHub repository and at the benchmark's website.