Scaling ResNets in the Large-depth Regime
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| Main Authors: | , , , |
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| Format: | Preprint |
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2022
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| _version_ | 1866910851096641536 |
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| author | Marion, Pierre Fermanian, Adeline Biau, Gérard Vert, Jean-Philippe |
| author_facet | Marion, Pierre Fermanian, Adeline Biau, Gérard Vert, Jean-Philippe |
| contents | 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 $α_L$. We show in a probabilistic setting that with standard i.i.d.~initializations, the only non-trivial dynamics is for $α_L = \frac{1}{\sqrt{L}}$; 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 $α_L = \frac{1}{L}$. 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2206_06929 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Scaling ResNets in the Large-depth Regime Marion, Pierre Fermanian, Adeline Biau, Gérard Vert, Jean-Philippe Machine Learning 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 $α_L$. We show in a probabilistic setting that with standard i.i.d.~initializations, the only non-trivial dynamics is for $α_L = \frac{1}{\sqrt{L}}$; 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 $α_L = \frac{1}{L}$. 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. |
| title | Scaling ResNets in the Large-depth Regime |
| topic | Machine Learning |
| url | https://arxiv.org/abs/2206.06929 |