LLM Evaluation as Tensor Completion: Low Rank Structure and Semiparametric Efficiency

arXiv:2604.05460v2 Announce Type: replace-cross Abstract: Large language model (LLM) evaluation platforms increasingly rely on pairwise human judgments.

These data are noisy, sparse, and non-uniform, yet leaderboards are reported with limited uncertainty quantification.

We study this as semiparametric inference for a low-rank latent score tensor observed through pairwise comparisons under Bradley-Terry-Luce-type models. This places LLM evaluation in a new tensor completion setting with structured observations, non-uniform sampling, and pairwise contrasts.

Our target is a smooth functional $\psi(T^\star)$, including linear estimands such as ability gaps and nonlinear ones such as win probabilities. We derive the information operator on the low-rank tangent space, the efficient influence function, and the semiparametric efficiency bound, then construct a one-step debiased estimator with asymptotic normality.

A central challenge is that the information operator is anisotropic and does not commute with the tangent-space projection, creating a bottleneck absent from isotropic models. We introduce a score-whitening method that equalizes local Fisher information and restores stable inference at the optimal sample-complexity scale.

Our results provide a principled framework for uncertainty quantification in LLM evaluation and more broadly for inference on low-rank structures from pairwise data.