The Precision Wall: An Optimizer-Dependent Boundary for Optimization under Power-Law Measurement Spectra

Paper recorded by Signals 4 on 2026-10-29 in cs.LG. Abstract reproduced from arXiv; link to the original below.

Published 2026-10-29 on arXiv · recorded by Signals 4 on 2026-10-30

Category: cs.LG · 机器学习 · first seen 2026-10-30

Abstract

In low-rank matrix sensing of a rank-$D$ factor $U^\ast \in \mathbb{R}^{V \times D}$, replacing isotropic Gaussian designs with power-law measurement covariance $Σ= \mathrm{diag}(j^{-s})_{j=1}^V$ leaves the Burer--Monteiro landscape free of spurious local minima, yet division-normalised first-order optimizers stall above a critical exponent $s^\ast$. We trace this failure to a numerical precision

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