This paper leverages the use of \emph{Gram iteration} an efficient, deterministic, and differentiable method for computing spectral norm with an upper bound guarantee. Designed for circular convolutional layers, we generalize the use of the Gram iteration to zero padding convolutional layers and prove its quadratic convergence. We also provide theorems for bridging the gap between circular and zero padding convolution's spectral norm. We design a \emph{spectral rescaling} that can be used as a competitive $1$-Lipschitz layer that enhances network robustness. Demonstrated through experiments, our method outperforms state-of-the-art techniques in precision, computational cost, and scalability. The code of experiments is available at https://github.com/blaisedelattre/lip4conv.

翻译：本文利用Gram迭代这一高效、确定且可微的方法，在保证上界的前提下计算谱范数。针对循环卷积层设计的方法，我们将其推广至零填充卷积层，并证明其二次收敛性。同时，我们提出连接循环卷积与零填充卷积谱范数差距的定理，并设计了一种谱重缩放方法，可作为具有竞争力的1-Lipschitz层以增强网络鲁棒性。实验表明，本方法在精度、计算成本和可扩展性上均优于现有技术。实验代码详见https://github.com/blaisedelattre/lip4conv。