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We propose unitary group convolutions (UGConvs), a building block for CNNswhich compose a group convolution with unitary transforms in feature space tolearn a richer set of representations than group convolution alone. UGConvsgeneralize two disparate ideas in CNN architecture, channel shuffling (i.e.ShuffleNet) and block-circulant networks (i.e. CirCNN), and provide unifyinginsights that lead to a deeper understanding of each technique. Weexperimentally demonstrate that dense unitary transforms can outperform channelshuffling in DNN accuracy. On the other hand, different dense transformsexhibit comparable accuracy performance. Based on these observations we proposeHadaNet, a UGConv network using Hadamard transforms. HadaNets achieve similaraccuracy to circulant networks with lower computation complexity, and betteraccuracy than ShuffleNets with the same number of parameters and floating-pointmultiplies.

Building Efficient Deep Neural Networks with Unitary Group Convolutions