标题： 卷积层的谱范数与循环填充和零填充 显示英文标题

标题： Spectral Norm of Convolutional Layers with Circular and Zero Paddings

摘要： 本文利用了\emph{Gram迭代}一种高效、确定性和可微的方法，用于计算具有上界保证的谱范数。 专为循环卷积层设计，我们推广了Gram迭代在零填充卷积层中的使用，并证明了其二次收敛性。 我们还提供了定理，以弥合循环和零填充卷积的谱范数之间的差距。 我们设计了一个\emph{谱重标度}，可以作为具有竞争力的$1$-Lipschitz 层，以增强网络的鲁棒性。 通过实验表明，我们的方法在精度、计算成本和可扩展性方面优于最先进技术。 实验代码可在 https://github.com/blaisedelattre/lip4conv 获取。 显示英文摘要

摘要： 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.