When Mean CE Fails: Median CE Can Better Track Language Model Quality

Fidelity metrics, such as per-token KL divergence (KLD) against a high-precision reference, are often used in practice as low-cost proxies for benchmark quality. We test this practice on a 28-quant cohort of Qwen3.6-35B-A3B and a 41-quant cohort of Devstral-Small-2-24B, evaluated across a suite of downstream benchmarks. We find that KLD is strongly correlated with benchmark score over the full cohort ($ρ=-0.72$ on Qwen and $ρ=-0.86$ on Devstral, both with $p<0.001$). However, this relationship collapses to non-significance in the near-baseline silent zone ($ρ=+0.00$ on Qwen and $ρ=-0.24$, $p=0.36$, on Devstral). This collapse persists across 14 measurement variants, including different KLD aggregations, perplexity formulations, top-1 agreement, calibration corpora, and context lengths. At the per-prompt level, KLD has only weak failure-prediction power on code, with failed-vs-passed geometric-mean ratios in $[1.08,1.22]$ across five models on LiveCodeBench, and fails as a cross-model router, achieving only $42.3\%-49.4\%$ accuracy on disagreement prompts. We trace the collapse to a structural decomposition: KLD primarily measures the volume of disagreement with the reference, with silent-zone composite $ρ=+0.94$ ($p<0.001$) on Qwen and $+0.55$ ($p=0.03$) on Devstral, while its relationship to the direction of those disagreements is weak and task-conditional.

Progress in language model development is often driven by comparative decisions: which architecture to adopt, which pretraining corpus to use, or which training recipe to apply. Making these decisions well requires reliable performance forecasts, yet the two commonly used signals are fundamentally limited. Cross-entropy loss is poorly aligned with downstream capabilities, and direct downstream evaluation is expensive, sparse, and often uninformative at early training stages. Instead, we propose to construct proxy metrics by aggregating token-level statistics, such as entropy, top-k accuracy, and expert token rank, from a candidate model's next token distribution over expert-written solutions. Across three settings, our proxies consistently outperform loss- and compute-based baselines: 1) For cross-family model selection, they rank a heterogeneous population of reasoning models with mean Spearman Rho = 0.81 (vs. Rho = 0.36 for cross-entropy loss); 2) For pretraining data selection, they reliably rank 25 candidate corpora for a target model at roughly $10{,}000\times$ less compute than direct evaluation, pushing the Pareto frontier beyond existing methods; and 3) for training-time forecasting, they extrapolate downstream accuracy across an $18\times$ compute horizon with roughly half the error of existing alternatives. Together, these results suggest that expert trajectories are a broadly useful source of signal for assessing model capabilities, enabling reliable performance forecasting throughout the model development life cycle.

The dominant practice in language model evaluation is to report a single accuracy number per model and declare the higher one better, without testing whether the gap could plausibly be sampling noise. On benchmarks of a few thousand items, and under temperature sampling where a model can differ from itself run to run by more than the reported gap between models, this practice routinely overstates confidence in headline claims. The statistical machinery to fix this -- confidence intervals, paired significance tests, power analysis, clustered standard errors, multiple-comparison correction -- is well established, but no standard, pip-installable tool packages it in the shape an evaluation actually takes: a per-item results table. We present evalci, a pure-Python library (numpy/scipy/pandas only) that turns a per-item results table into a publication-ready claim -- e.g., "Model A beats Model B, $Δ=3.1$ pts, 95% CI [1.2, 5.0], paired permutation $p=0.002$, $n=1{,}319$" -- in one function call, with adapters for lm-evaluation-harness and HELM output. Every routine is validated against an independent reference (statsmodels, or brute-force exact enumeration) rather than only against itself. As a case study, we re-analyze a public comparison of nine language models' MMLU accuracy and find that 3 of the 8 adjacent leaderboard-rank gaps are not statistically significant after correcting for the 36 pairwise comparisons the ranking implies. evalci is available at https://pypi.org/project/evalci/ (source: https://github.com/Shreyaskc/evalci, DOI: https://doi.org/10.5281/zenodo.21201815)