Restricted Eigenvalues Beyond Gaussian Width: Threshold Occupancy under Heavy Tails

arXiv:2609.03504 · cs.LG · Submitted 2026-09-03 · Read on arXiv

cs.LG

Submitted: 2026-09-03

Updated: 2026-09-03

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

Terminology

• VC Dimension — 27× in this paper · explained in 2 episodes
• Ambient Dimension — 4× in this paper · explained in 1 episode
• Robustness — 4× in this paper · explained in 5 episodes
• Sample Complexity — 4× in this paper · explained in 15 episodes
• Benchmark — 3× in this paper · explained in 2 episodes
• Inverse Problem — 3× in this paper · explained in 2 episodes
• Regularization — 3× in this paper · explained in 3 episodes
• Phase Transitions — 2× in this paper · explained in 2 episodes
• Approximation Bound — 1× in this paper · explained in 1 episode
• Generative AI — 1× in this paper · explained in 2 episodes
• Homogeneity — 1× in this paper · explained in 2 episodes
• Sparsity — 1× in this paper · explained in 4 episodes
• Trace — 1× in this paper · explained in 2 episodes

Sources

• Necessary moment conditions for exact reconstruction via basis pursuit
• Sparse recovery under weak moment assumptions
• Structured Recovery with Heavy-tailed Measurements: A Thresholding Procedure and Optimal Rates

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