Efficient Bound of Lipschitz Constant for Convolutional Layers by Gram Iteration

Blaise Delattre; Quentin Barthélemy; Alexandre Araujo; Alexandre Allauzen

ICML 2023poster16 citations

Efficient Bound of Lipschitz Constant for Convolutional Layers by Gram Iteration

Blaise Delattre, Quentin Barthélemy, Alexandre Araujo, Alexandre Allauzen

Abstract

Since the control of the Lipschitz constant has a great impact on the training stability, generalization, and robustness of neural networks, the estimation of this value is nowadays a real scientific challenge. In this paper we introduce a precise, fast, and differentiable upper bound for the spectral norm of convolutional layers using circulant matrix theory and a new alternative to the Power iteration. Called the Gram iteration, our approach exhibits a superlinear convergence. First, we show through a comprehensive set of experiments that our approach outperforms other state-of-the-art methods in terms of precision, computational cost, and scalability. Then, it proves highly effective for the Lipschitz regularization of convolutional neural networks, with competitive results against concurrent approaches.

BibTeX

@inproceedings{icml2023_efficientboundof,
  title = {Efficient Bound of Lipschitz Constant for Convolutional Layers by Gram Iteration},
  author = {Blaise Delattre and Quentin Barthélemy and Alexandre Araujo and Alexandre Allauzen},
  booktitle = {ICML 2023},
  year = {2023}
}