On the Lipschitz Constant of Deep Networks and Double Descent
Matteo Gamba (KTH),* Hossein Azizpour (KTH (Royal Institute of Technology)), Marten Bjorkman (KTH)
The 34th British Machine Vision Conference
Abstract
Existing bounds on the generalization error of deep networks assume some form of smooth or bounded dependence on the input variable, falling short of investigating the mechanisms controlling such factors in practice. In this work, we present an extensive experimental study of the empirical Lipschitz constant of deep networks undergoing double descent, and highlight non-monotonic trends strongly correlating with the test error. Building a connection between parameter-space and input-space gradients for SGD around a critical point, we isolate two important factors - namely loss landscape curvature and distance of parameters from initialization - respectively controlling optimization dynamics around a critical point and bounding model function complexity, even beyond the training data. Our study presents novel insights on implicit regularization via overparameterization, and effective model complexity for networks trained in practice.Video
Citation
@inproceedings{Gamba_2023_BMVC,
author = {Matteo Gamba and Hossein Azizpour and Marten Bjorkman},
title = {On the Lipschitz Constant of Deep Networks and Double Descent},
booktitle = {34th British Machine Vision Conference 2023, {BMVC} 2023, Aberdeen, UK, November 20-24, 2023},
publisher = {BMVA},
year = {2023},
url = {https://papers.bmvc2023.org/0871.pdf}
}
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