The Zero Pattern of a Design Matrix Drives Multiple Descent in Over-parameterized Regression — Paper

Abstract

-cross Abstract: Over-parameterized linear regression has been widely studied over the last decade. However, most existing works assume that the covariates are independent and that their covariance matrices are non-degenerate. In this paper, we relax both assumptions and derive deterministic equivalents for the prediction risk in a vanishing-ridge regime. We show that degeneracy of the covariance matrices and dependence can lead to multiple descent, and characterize where the corresponding peaks can occur. Our proofs use a novel graph representation of the variance profile. We show that maximum matchings and the Dulmage--Mendelsohn decomposition of the associated bipartite graph identify the configurations at which the variance becomes singular.

Authors 4

Kevin Han Huang, Haoyu Ye, Somak Laha, Morgane Austern

Specification

Official page: arxiv.org/abs/2607.24041
Source:arXiv (Atom API + RSS)T1observed 6 h agohigh
Arxiv announce type: replace
Source:arXiv (Atom API + RSS)T1observed 6 h agohigh
arXiv id: 2607.24041
Source:arXiv (Atom API + RSS)T1observed 6 h agohigh
Categories: math.ST, cs.LG, stat.ML, stat.TH
Source:arXiv (Atom API + RSS)T1observed 6 h agohigh
PDF: arxiv.org/pdf/2607.24041
Source:arXiv (Atom API + RSS)T1observed 6 h agohigh
Primary category: math.ST
Source:arXiv (Atom API + RSS)T1observed 6 h agohigh
Published: 11 Sept 2026
Source:arXiv (Atom API + RSS)T1observed 6 h agohigh

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9

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T19

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6 h ago

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Authors: Kevin Han Huang, Haoyu Ye, Somak Laha

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Value	Valid from → to	Status	Source	Confidence	Extractor
math.ST, cs.LG, stat.ML, stat.TH	11 Sept 2026 21:02 UTC → current	current	arXiv (Atom API + RSS)T1	high	deterministic

Claims are temporal and append-only: a new observation closes the previous claim (valid_to) instead of overwriting it. Conflicting claims from different sources are kept side by side and flagged — never averaged. Methodology →

11 Sept 2026
New paperPaperThe Zero Pattern of a Design Matrix Drives Multiple Descent in Over-parameterized Regression
New paper: The Zero Pattern of a Design Matrix Drives Multiple Descent in Over-parameterized Regression
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Source documents
Source	Document	Type	Tier	Last observed	Snapshots
arXiv (Atom API + RSS)	rss.arxiv.org/rss/cs.LG	feed	T1· Official	4 h ago	1

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