This paper introduces a new Convolutional Neural Network (ConvNet) architecture inspired by a class of partial differential equations (PDEs) called quasi-linear hyperbolic systems. With comparable performance on image classification task, it allows for the modification of the weights via a continuous group of symmetry. This is a significant shift from traditional models where the architecture and weights are essentially fixed. We wish to promote the (internal) symmetry as a new desirable property for a neural network, and to draw attention to the PDE perspective in analyzing and interpreting ConvNets in the broader Deep Learning community.

翻译：本文提出了一种受拟线性双曲型偏微分方程组启发的卷积神经网络新架构。在图像分类任务中，该架构在保持同等性能的同时，允许通过连续对称群对权重进行动态调整。这与传统模型架构与权重本质上固定的特征形成重大突破。我们倡导将（内部）对称性确立为神经网络的新理想特性，并希望引起深度学习领域对偏微分方程视角分析和解读卷积神经网络的广泛关注。