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

arXiv: https://arxiv.org/abs/2604.05460 · HTML: https://mlsanity.com/paper/2604.05460/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 10 of its 29 references that are in the map.
- First posted on arXiv 7 Apr 2026.

## Builds on (most cited first, 10 of 10)

- [Chatbot Arena: An Open Platform for Evaluating LLMs by Human Preference](https://mlsanity.com/paper/2403.04132/) (2024)
- [The Leaderboard Illusion](https://mlsanity.com/paper/2504.20879/) (2025)
- [LoRe: Personalizing LLMs via Low-Rank Reward Modeling](https://mlsanity.com/paper/2504.14439/) (2025)
- [Doubly Robust Alignment for Large Language Models](https://mlsanity.com/paper/2506.01183/) (2025)
- [Uncertainty Quantification for Ranking with Heterogeneous Preferences](https://mlsanity.com/paper/2509.01847/) (2025)
- [Evaluating LLMs When They Do Not Know the Answer: Statistical Evaluation of Mathematical Reasoning via Comparative Signals](https://mlsanity.com/paper/2602.03061/) (2026)
- [Unpacking Human Preference for LLMs: Demographically Aware Evaluation with the HUMAINE Framework](https://mlsanity.com/paper/2603.04409/) (2026)
- [Generalized Tensor Completion with Non-Random Missingness](https://mlsanity.com/paper/2509.06225/) (2025)
- [Statistical Inference in Tensor Completion: Optimal Uncertainty Quantification and Statistical-to-Computational Gaps](https://mlsanity.com/paper/2410.11225/) (2024)
- [Statistical Inference for Matching Decisions via Matrix Completion under Dependent Missingness](https://mlsanity.com/paper/2510.26478/) (2025)

## Built on by (most cited first, 3 of 3)

- [Low Rank for Rank: Uncertainty-Aware Task-Specific LLM Ranking under Sparse Pairwise Comparisons](https://mlsanity.com/paper/2605.29395/) (2026)
- [Anytime-Valid LLM Leaderboards via Benchmark-weighted and Block-Factorized e-Processes](https://mlsanity.com/paper/2609.32248/) (2026)
- [Conditional Evaluation of Language Models with Cheap Auxiliary Signals](https://mlsanity.com/paper/2608.16210/) (2026)

## Abstract (arXiv)

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.