Author

Jin-Ze Zhao

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Preprint Sep 2026

A Two-Dimensional Extremizer for Relatively Inexact Gradient Descent

We give an explicit extremal function for one step of gradient descent when the gradient error is bounded relative to the true gradient. The function is the sum of a quadratic in one coordinate and a Huber function in the other. It attains, for every admissible relative error level and every stepsize in the intermediat...

Jin-Ze Zhao · 0 citations

Preprint Sep 2026

Small-Ball Marginals Do Not Control Restricted Eigenvalues by Euclidean Gaussian Width

Banerjee, Chen, and Sivakumar asked at COLT 2015 whether a uniform small-ball condition on the rows of a random design matrix forces a restricted-eigenvalue lower bound whose sample complexity is governed by the ordinary Euclidean Gaussian width of an arbitrary spherical subset. We give a negative answer to the natural...

Jin-Ze Zhao · 0 citations

Preprint Aug 2026

Predicting Diagonalizability of a Mean Matrix

Wu and Santhanam asked whether one can determine, from an increasing i.i.d. sample of binary random matrices, whether the unknown mean matrix is diagonalizable while making only finitely many errors almost surely. We answer this question affirmatively, for diagonalizability over either $\mathbb{R}$ or $\mathbb{C}$. The...

Jin-Ze Zhao · 0 citations