The scattering transform is a multilayered, wavelet-based transform initially introduced as a mathematical model of convolutional neural networks (CNNs) that has played a foundational role in our understanding of these networks' stability and invariance properties. In subsequent years, there has been widespread interest in extending the success of CNNs to data sets with non-Euclidean structure, such as graphs and manifolds, leading to the emerging field of geometric deep learning. In order to improve our understanding of the architectures used in this new field, several papers have proposed generalizations of the scattering transform for non-Euclidean data structures such as undirected graphs and compact Riemannian manifolds without boundary. Analogous to the original scattering transform, these works prove that these variants of the scattering transform have desirable stability and invariance properties and aim to improve our understanding of the neural networks used in geometric deep learning.

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测量空间上的几何散射

散射变换是一种基于小波的多层变换，最初是作为卷积神经网络 (CNN) 的数学模型引入的，它在我们理解这些网络的稳定性和不变性特性方面发挥了基础作用。在随后的几年中，人们广泛关注将 CNN 的成功扩展到具有非欧几里得结构的数据集（例如图和流形），从而催生了几何深度学习这一新兴领域。为了提高我们对这个新领域中使用的体系结构的理解，几篇论文提出了非欧几里得数据结构（例如无向图和无边界紧致黎曼流形）的散射变换的推广。与原始的散射变换类似，这些工作证明了散射变换的这些变体具有理想的稳定性和不变性，旨在提高我们对几何深度学习中使用的神经网络的理解。