A new paper explores the differing behaviors of optimization algorithms, specifically gradient descent and Adam, when applied to factored matrix models. The research indicates that gradient descent inherently favors low-rank solutions due to a gauge symmetry in the loss function, a property that Adam and other coordinate-wise optimizers lack. This difference leads to divergent solutions in applications like transformers and sensing tasks. The study proposes that gauge equivariance is crucial for optimizers to recover low-rank solutions and suggests that a spectrum of preconditioning methods can restore this bias. AI
IMPACT Understanding optimizer behavior is crucial for developing more efficient and effective training methods for large AI models.
RANK_REASON The item is a research paper detailing theoretical findings about optimization algorithms. [lever_c_demoted from research: ic=1 ai=1.0]
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