Universality and sharp thresholds for ellipsoid fitting

arXiv:2608.27372 · math.PR, cond-mat.dis-nn, cs.DS, cs.LG, math.ST, stat.TH · Submitted 2026-08-27 · Read on arXiv

math.PR, cond-mat.dis-nn, cs.DS, cs.LG, math.ST, stat.TH

Submitted: 2026-08-27

Updated: 2026-08-27

Comments: 79 pages, 4 figures

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

Terminology

• Regularization — 17× in this paper · explained in 3 episodes
• Trace — 11× in this paper · explained in 2 episodes
• Homogeneity — 4× in this paper · explained in 2 episodes
• Core — 2× in this paper · explained in 2 episodes
• Anisotropy — 1× in this paper · explained in 3 episodes
• Anticoncentration — 1× in this paper · explained in 1 episode
• Exchangeability — 1× in this paper · explained in 2 episodes
• Generalization — 1× in this paper · explained in 13 episodes
• Generative Model — 1× in this paper · explained in 2 episodes
• Generative Models — 1× in this paper · explained in 2 episodes
• Gibbs State — 1× in this paper · explained in 2 episodes
• Hilbert Space — 1× in this paper · explained in 2 episodes
• Inverse Problem — 1× in this paper · explained in 2 episodes
• Phase Transitions — 1× in this paper · explained in 2 episodes
• Robustness — 1× in this paper · explained in 5 episodes
• Spectral Gap — 1× in this paper · explained in 5 episodes
• Symmetry Breaking — 1× in this paper · explained in 3 episodes

Sources

• Sharp Phase Transition for Ellipsoid Fitting
• Universality of max-margin classifiers
• Universality of empirical risk minimization
• The sharp SAT/UNSAT phase transition in random ellipsoid fitting

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