New Adam Theorem Unveiled for Spectral Heavy-Tail Onset in ML Models

Researchers have developed a comprehensive theoretical framework, termed a "full Adam theorem," to analyze the spectral heavy-tail onset in Gaussian Stein-Hermite teacher-student models. This theorem meticulously details each step of the Adam optimization algorithm, from momentum and denominator calculations to the derivation of a projected update response and approximate-target KL contraction. The findings establish a hitting time law dependent on the spectral gap and demonstrate the impossibility of a stronger arbitrary-gradient Adam theorem for this model. AI

IMPACT Provides a deeper theoretical understanding of optimization dynamics in machine learning models.

RANK_REASON The item is a research paper published on arXiv detailing a new theoretical theorem. [lever_c_demoted from research: ic=1 ai=1.0]

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• Adam
• arXiv
• Charles Hermite
• Gaussian Stein-Hermite
• Stein-Hermite

• paper
• other

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