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Critical SNR for outlier emergence at fixed summary statistics
Sourced from the work of Gerard Ben Arous, Reza Gheissari, Jiaoyang Huang, Aukosh Jagannath
§ Problem Statement
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§ Significance & Implications
§ Known Partial Results
§ References
[1]
Local geometry of high-dimensional mixture models: Effective spectral theory and dynamical transitions
Gerard Ben Arous, Reza Gheissari, Jiaoyang Huang, Aukosh Jagannath (2025)
Annals of Statistics (to appear)
📍 Section 1.3.2 (“The effective spectrum at initialization and along the training trajectory”), paragraph immediately preceding Corollary 1.8 (arXiv v3; Corollary 1.9 in earlier numbering) where the small-$\beta$ no-outlier/critical-threshold question is explicitly stated, p. unknown
Source paper where this problem appears.