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

• URL: http://arxiv.org/abs/2604.05460v1
• Date: Tue, 07 Apr 2026 05:44:08 GMT
• Title: LLM Evaluation as Tensor Completion: Low Rank Structure and Semiparametric Efficiency
• Abstract summary: Large language model (LLM) evaluation platforms increasingly rely on pairwise human judgments.<n>We study this as semiparametric inference for a low-rank latent score observed through pairwise comparisons.
• Score: 16.73008463123115
• License: http://creativecommons.org/licenses/by/4.0/
• 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 $ψ(T^\star)$, 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.

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