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Zesheng Cai

Publications and source records attributed to Zesheng Cai.

2 recordsLinked to original sources

DIAL: Position-Debiased LLM Judges with Adaptive Human Preference Calibration

Large language models (LLMs) as a judge enable scalable evaluation, but their judgments can be sensitive to response order and, even after removing such position effects, can still diverge systematically from human preferences.We introduce DIAL, a unified framework that combines abundant LLM comparisons with limited human comparisons to separate judge-specific position effects, learn shared structure in position-debiased LLM preferences, and adaptively calibrate that structure toward the human preference target. Theoretically, we study three aspects of DIAL: (i) identification of latent LLM preferences, position effects, and human calibration; (ii) adaptive estimation that balances LLM anchoring against limited human evidence; and (iii) fixed-weight uncertainty quantification for the calibrated human preference. Empirically, we evaluate position debiasing and human alignment separately in controlled simulations and on three human-preference benchmarks, showing that DIAL remains robust to unbalanced response order, achieves strong human-aligned rankings with limited labels, and adapts toward human evidence when LLM information is imperfect. Our real-data study collects over 410K judgments from 21 LLM judges in both display orders, providing a resource for future studies of LLM-judge bias, heterogeneity, and human alignment.

cs.AI↗

Global convergence of the subgradient method for robust signal recovery

We study the subgradient method for factorized robust signal recovery problems, including robust PCA, robust phase retrieval, and robust matrix sensing. The resulting objectives are nonsmooth and nonconvex, and can have unbounded sublevel sets, so standard analyses based on descent and coercivity do not apply. For locally Lipschitz semialgebraic objectives, we develop a convergence framework that replaces these requirements with a boundedness condition on continuous-time subgradient trajectories. Under this condition and sufficiently small step sizes of order $1/k$, we show that iterates of the subgradient method remain bounded and the full sequence converges to a critical point. We then verify the required boundedness property for the three robust objectives by adapting existing trajectory analyses, assuming a mild nondegeneracy condition in the matrix sensing case. Finally, for rank-one symmetric robust PCA, we prove that for almost every initialization, the method cannot converge to spurious critical points; consequently, under the same step-size regime, it converges to a global minimum.

math.OC↗