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On the Parameterization of Second-Order Optimization Effective towards the Infinite Width

Satoki Ishikawa · Ryo Karakida

Halle B #44
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Wed 8 May 1:45 a.m. PDT — 3:45 a.m. PDT


Second-order optimization has been developed to accelerate the training of deep neural networks and it is being applied to increasingly larger-scale models. In this study, towards training on further larger scales, we identify a specific parameterization for second-order optimization that promotes feature learning in a stable manner even if the network width increases significantly. Inspired by a maximal update parametrization, we consider a one-step update of the gradient and reveal the appropriate scales of hyperparameters including random initialization, learning rates, and damping terms. Our approach covers two major second-order optimization algorithms, K-FAC and Shampoo, and we demonstrate that our parametrization achieves higher generalization performance in feature learning.In particular, it enables us to transfer the hyperparameters across models with different widths.

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