Efficient Bound of Lipschitz Constant for Convolutional Layers by Gram Iteration
This work addresses a key challenge in improving the stability and robustness of convolutional neural networks, though it appears incremental as it builds on existing methods for Lipschitz constant estimation.
The paper tackles the problem of estimating the Lipschitz constant for convolutional neural networks, which is crucial for training stability, generalization, and robustness, by introducing a precise, fast, and differentiable upper bound using circulant matrix theory and a new Gram iteration method with superlinear convergence. The result shows that this approach outperforms state-of-the-art methods in precision, computational cost, and scalability, and proves effective for Lipschitz regularization with competitive results.
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.