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Small-SNR no-outlier regime and monotonicity in SNR

Sourced from the work of Gerard Ben Arous, Reza Gheissari, Jiaoyang Huang, Aukosh Jagannath

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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”), immediately after Corollary 1.8 (comment on possible non-monotonicity and missing small-$\lambda$ no-outlier result), p. 12 (arXiv v3; numbered Corollary 1.9 in earlier versions).

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