When Stability Fails: Hidden Failure Modes Of LLMS in Data-Constrained Scientific Decision-Making

A benchmark score is a measurement whose uncertainty has two sources: an aleatoric component from stochastic decoding and an epistemic component from the finite problem set. Using 16 models on 99 recent LeetCode-style problems with two prompts and five runs each (15,840 judged runs in a fully crossed design), we estimate both components and ask a design question: how much can repeated running buy? First, the pooled-binomial interval that repeated-run protocols invite answers neither question of interest---it is about $2\times$ too narrow for generalisation to new problems and $2\times$ too wide for the fixed problem set---and under correctly clustered intervals, 12 of 15 adjacent leaderboard pairs are statistically unresolved. Second, the variance ceiling $1+μ_w/σ_b^2$, the largest factor by which repetition can reduce score variance, has median 1.34 across models (range 1.05--1.71), so repetition can narrow confidence intervals by at most 23% on this benchmark, and by 14% for the median model. Third, once the cost of adding verified problems is priced in, the precision-optimal repeat count is $R^{*}=\sqrt{μ_w c_p/(σ_b^2 c_g)}$, and the variance curve is flat around it: on this benchmark the decisive reason to repeat is not precision but identification---two to three runs suffice to estimate the components that the ceiling and the fixed-benchmark interval require. All three are measurements of one benchmark at one decoding temperature, and we state explicitly what they do and do not license.

Evaluations of LLM systems routinely average over small prompt sets and report models as a ranked table. We ask how much confidence such a table deserves, using LLM-based prompt-structure inference as the case study: eight open model variants across five families and 8B to 675B parameters, caching disabled, 293 raw intermediate representations persisted. The measured phenomenon is unstable to begin with. Identical calls do not reliably recover identical structure, with mean node-set Jaccard from 0.39 to 0.96 and 72% of prompt-model cells never node-set-perfect. Auditing the evaluation weakens its conclusions further, and this is our main contribution. Under a joint cluster bootstrap over prompts, only the bottom of the ranking is firm: the two least reproducible models hold rank in 99% and 86% of replicates, the middle four in 27% to 48%, and the top two in 68% each, so the table identifies the worst model reliably but does not reliably identify the best. Two equally defensible rules for merging repeated campaigns change four of eight rows and move the study-wide headline by 7 percentage points. Checking the inferred structure against ground-truth annotations shows reproducibility cannot be read as accuracy. And four of the eight endpoints were withdrawn within ten weeks of measurement, so the study as specified can no longer be run. Small-sample LLM evaluations can therefore look far more definitive than their evidence supports. We recommend reporting rank stability, per-cell provenance, executed sensitivity comparisons, raw per-run outputs, and a measurement date alongside any ranking.

Existing benchmarks for scientific data analysis evaluate LLMs primarily on code execution or workflow completion, overlooking that scientific analysis serves to support distinct types of scientific claims: hypothesis exploration, statistical inference, mechanistic explanation, each with different assumptions and validity criteria. We introduce SDABench, a benchmark that reorganizes evaluation around six capabilities (descriptive, exploratory, inferential, predictive, causal, and mechanistic) across five domains (Biology, Chemistry, Environment, Geography, Physics). SDABench comprises 527 real-data instances (SDA-Real) and 6000 synthetic instances (SDA-Synth), each in both multiple-choice and open-ended formats, constructed through an automated pipeline. Evaluating 15 representative LLMs, we find that models handle descriptive analysis well but degrade sharply on tasks requiring assumption selection, latent-process modeling, or mechanistic reasoning. SDABench further provides a five-stage error analysis framework that locates where LLMs fail: more advanced models more reliably identify the relevant scope and variables, but still struggle to select appropriate analytical procedures, model variable relationships, and draw valid conclusions.