Decoupled Orthogonal Dynamics: Regularization for Deep Network Optimizers
This addresses optimization stability and generalization issues for deep learning practitioners, though it is incremental as it builds on existing AdamW methods.
The paper tackled the problem of suboptimal weight decay in AdamW by identifying the Radial Tug-of-War conflict, which causes radial oscillations and degrades feature learning, and proposed AdamO to decouple magnitude and direction updates, resulting in improved generalization and stability over AdamW on vision and language tasks.
Is the standard weight decay in AdamW truly optimal? Although AdamW decouples weight decay from adaptive gradient scaling, a fundamental conflict remains: the Radial Tug-of-War. In deep learning, gradients tend to increase parameter norms to expand effective capacity while steering directions to learn features, whereas weight decay indiscriminately suppresses norm growth. This push--pull interaction induces radial oscillations, injecting noise into Adam's second-moment estimates and potentially degrading delicate tangential feature learning. We argue that magnitude and direction play distinct roles and should be decoupled in optimizer dynamics. We propose Orthogonal Dynamics Decoupling and instantiate it as AdamO: an SGD-style update handles the one-dimensional norm control, while Adam's adaptive preconditioning is confined to the tangential subspace. AdamO further incorporates curvature-adaptive radial step sizing and architecture-aware rules and projections for scale-invariant layers and low-dimensional parameters. Experiments on vision and language tasks show that AdamO improves generalization and stability over AdamW without introducing additional complex constraints.