In Gaussian multi-index models, the paper rigorously characterizes the bulk spectrum and BBP-type phase transition of matrix-valued spectral estimators, and proves the AMP-derived preprocessing map attains the minimal spectral threshold, resolving Conjecture 3.10 of Defilippis et al. (2025).
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Spectral phase transitions in Gaussian multi-index models
In Gaussian multi-index models, the paper rigorously characterizes the bulk spectrum and BBP-type phase transition of matrix-valued spectral estimators, and proves the AMP-derived preprocessing map attains the minimal spectral threshold, resolving Conjecture 3.10 of Defilippis et al. (2025).