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 7 h agohigh
Arxiv announce type: replace
Source:arXiv (Atom API + RSS)T1observed 7 h agohigh
arXiv id: 2607.24041
Source:arXiv (Atom API + RSS)T1observed 7 h agohigh
Categories: math.ST, cs.LG, stat.ML, stat.TH
Source:arXiv (Atom API + RSS)T1observed 7 h agohigh
PDF: arxiv.org/pdf/2607.24041
Source:arXiv (Atom API + RSS)T1observed 7 h agohigh
Primary category: math.ST
Source:arXiv (Atom API + RSS)T1observed 7 h agohigh
Published: 11 Sept 2026
Source:arXiv (Atom API + RSS)T1observed 7 h agohigh

Each value shows its source, tier and observation time. Conflicting claims are kept side by side and flagged — never averaged. How AI Atlas records facts →

Provenance

Attributed facts

9

Source tiers

T19

Freshest observation

7 h ago

Conflicts

None

No models linked to this paper yet.

Authors: Kevin Han Huang, Haoyu Ye, Somak Laha

As of

Rewind the record: see this entity's attributes exactly as AI Atlas knew them on a given day.

Claim history

9 claims · 9 properties

Official pageofficial_url1

Claim history for Official page
Value	Valid from → to	Status	Source	Confidence	Extractor
https://arxiv.org/abs/2607.24041	11 Sept 2026 21:02 UTC → current	current	arXiv (Atom API + RSS)T1	high	deterministic

Abstractabstract1

Claim history for Abstract
Value	Valid from → to	Status	Source	Confidence	Extractor
-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.	11 Sept 2026 21:02 UTC → current	current	arXiv (Atom API + RSS)T1	high	deterministic

Arxiv announce typearxiv_announce_type1

Claim history for Arxiv announce type
Value	Valid from → to	Status	Source	Confidence	Extractor
replace	11 Sept 2026 21:02 UTC → current	current	arXiv (Atom API + RSS)T1	high	deterministic

arXiv idarxiv_id1

Claim history for arXiv id
Value	Valid from → to	Status	Source	Confidence	Extractor
2607.24041	11 Sept 2026 21:02 UTC → current	current	arXiv (Atom API + RSS)T1	high	deterministic

Authorsauthors1

Claim history for Authors
Value	Valid from → to	Status	Source	Confidence	Extractor
Kevin Han Huang, Haoyu Ye, Somak Laha, Morgane Austern	11 Sept 2026 21:02 UTC → current	current	arXiv (Atom API + RSS)T1	high	deterministic

Categoriescategories1

Claim history for Categories
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

PDFpdf_url1

Claim history for PDF
Value	Valid from → to	Status	Source	Confidence	Extractor
https://arxiv.org/pdf/2607.24041	11 Sept 2026 21:02 UTC → current	current	arXiv (Atom API + RSS)T1	high	deterministic

Primary categoryprimary_category1

Claim history for Primary category
Value	Valid from → to	Status	Source	Confidence	Extractor
math.ST	11 Sept 2026 21:02 UTC → current	current	arXiv (Atom API + RSS)T1	high	deterministic

Publishedpublished_at1

Claim history for Published
Value	Valid from → to	Status	Source	Confidence	Extractor
11 Sept 2026	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
arxiv
rss.arxiv.org

Full timeline →

Source documents
Source	Document	Type	Tier	Last observed	Snapshots
arXiv (Atom API + RSS)	rss.arxiv.org/rss/cs.LG	feed	T1· Official	5 h ago	1

Tier 1 = official/primary, 2 = quality secondary, 3 = community, 4 = unverified. Every snapshot is archived; see all sources and the methodology.