Group Action Equivariance and Generalized Convolution in Multi-layer Neural Networks

Convolutional neural networks have achieved great success in speech, image, and video signal processing tasks in recent years. There have been several attempts to justify the convolutional architecture and to generalize the convolution operation for treatment of other data types such as graphs and manifolds. Based on group representation theory and noncommutative harmonic analysis, it has recently been shown that the so-called group equivariance...