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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

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[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

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