Efficient Bound of Lipschitz Constant for Convolutional Layers by Gram
Iteration
- URL: http://arxiv.org/abs/2305.16173v3
- Date: Mon, 19 Jun 2023 19:10:21 GMT
- Title: Efficient Bound of Lipschitz Constant for Convolutional Layers by Gram
Iteration
- Authors: Blaise Delattre, Quentin Barth\'elemy, Alexandre Araujo, Alexandre
Allauzen
- Abstract summary: We introduce a precise, fast, and differentiable upper bound for the spectral norm of convolutional layers using circulant matrix theory.
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.
It proves highly effective for the Lipschitz regularization of convolutional neural networks, with competitive results against concurrent approaches.
- Score: 122.51142131506639
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- 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. Code is available at
https://github.com/blaisedelattre/lip4conv.
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