Depthwise Hyperparameter Transfer in Residual Networks: Dynamics and Scaling Limit

• URL: http://arxiv.org/abs/2309.16620v2
• Date: Fri, 8 Dec 2023 18:19:44 GMT
• Title: Depthwise Hyperparameter Transfer in Residual Networks: Dynamics and Scaling Limit
• Authors: Blake Bordelon, Lorenzo Noci, Mufan Bill Li, Boris Hanin, Cengiz Pehlevan
• Abstract summary: We provide experiments demonstrating that residual architectures including convolutional ResNets and Vision Transformers exhibit transfer of optimal hyper parameters across width and depth. Using recent developments in the dynamical mean field theory (DMFT) description of neural network learning dynamics, we show that this parameterization of ResNets admits a well-defined feature learning joint infinite-width and infinite-depth limit.
• Score: 48.291961660957384
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: The cost of hyperparameter tuning in deep learning has been rising with model sizes, prompting practitioners to find new tuning methods using a proxy of smaller networks. One such proposal uses $\mu$P parameterized networks, where the optimal hyperparameters for small width networks transfer to networks with arbitrarily large width. However, in this scheme, hyperparameters do not transfer across depths. As a remedy, we study residual networks with a residual branch scale of $1/\sqrt{\text{depth}}$ in combination with the $\mu$P parameterization. We provide experiments demonstrating that residual architectures including convolutional ResNets and Vision Transformers trained with this parameterization exhibit transfer of optimal hyperparameters across width and depth on CIFAR-10 and ImageNet. Furthermore, our empirical findings are supported and motivated by theory. Using recent developments in the dynamical mean field theory (DMFT) description of neural network learning dynamics, we show that this parameterization of ResNets admits a well-defined feature learning joint infinite-width and infinite-depth limit and show convergence of finite-size network dynamics towards this limit.

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