A Novel Convolutional Neural Network Architecture with a Continuous Symmetry

TL;DR

This paper proposes a new CNN architecture inspired by PDEs that incorporates continuous symmetry, enabling flexible weight modifications and offering a novel perspective for analyzing neural networks.

Contribution

It introduces a PDE-inspired CNN with continuous symmetry, marking a significant shift from fixed architectures and promoting symmetry as a desirable property.

Findings

Comparable performance on image classification tasks

Allows weight modifications via continuous symmetry

Highlights PDE perspective in CNN analysis

Abstract

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 the 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.