Lasso Universality Under Linearly Dependent Covariates in the Sparse Regime

arXiv:2608.08390 · math.ST, cs.IT, math.IT, stat.ML, stat.TH · Submitted 2026-08-09 · Read on arXiv

Soroush Mesforush, Rahul Parhi

math.ST, cs.IT, math.IT, stat.ML, stat.TH

Submitted: 2026-08-09

Updated: 2026-08-11

Comments: 31 pages

License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/

Terminology

• Objective Function — 5× in this paper · explained in 2 episodes
• Phase Transitions — 3× in this paper · explained in 2 episodes
• Transfer Learning — 3× in this paper · explained in 10 episodes
• Generalization — 2× in this paper · explained in 13 episodes
• Regularization — 2× in this paper · explained in 3 episodes
• Sparsity — 2× in this paper · explained in 4 episodes
• Verification — 2× in this paper · explained in 2 episodes
• Consistency — 1× in this paper · explained in 3 episodes
• Inverse Problem — 1× in this paper · explained in 2 episodes
• Robustness — 1× in this paper · explained in 5 episodes

Sources

• Long-time dynamics and universality of nonconvex gradient descent
• High-Dimensional Statistics: Reflections on Progress and Open Problems
• When does Gaussian equivalence fail and how to fix it: Non-universal behavior of random features with quadratic scaling

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