Scaling ResNets in the Large-depth Regime

• URL: http://arxiv.org/abs/2206.06929v2
• Date: Mon, 10 Jun 2024 14:28:26 GMT
• Title: Scaling ResNets in the Large-depth Regime
• Authors: Pierre Marion, Adeline Fermanian, Gérard Biau, Jean-Philippe Vert,
• Abstract summary: Deep ResNets are recognized for achieving state-of-the-art results in machine learning tasks. Deep ResNets rely on a training procedure that needs to be carefully crafted to avoid vanishing or exploding gradients. No consensus has been reached on how to mitigate this issue, although a widely discussed strategy consists in scaling the output of each layer by a factor $alpha_L$.
• Score: 11.374578778690623
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Deep ResNets are recognized for achieving state-of-the-art results in complex machine learning tasks. However, the remarkable performance of these architectures relies on a training procedure that needs to be carefully crafted to avoid vanishing or exploding gradients, particularly as the depth $L$ increases. No consensus has been reached on how to mitigate this issue, although a widely discussed strategy consists in scaling the output of each layer by a factor $\alpha_L$. We show in a probabilistic setting that with standard i.i.d.~initializations, the only non-trivial dynamics is for $\alpha_L = \frac{1}{\sqrt{L}}$; other choices lead either to explosion or to identity mapping. This scaling factor corresponds in the continuous-time limit to a neural stochastic differential equation, contrarily to a widespread interpretation that deep ResNets are discretizations of neural ordinary differential equations. By contrast, in the latter regime, stability is obtained with specific correlated initializations and $\alpha_L = \frac{1}{L}$. Our analysis suggests a strong interplay between scaling and regularity of the weights as a function of the layer index. Finally, in a series of experiments, we exhibit a continuous range of regimes driven by these two parameters, which jointly impact performance before and after training.

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