Low-Cost Parameterizations of Deep Convolution Neural Networks
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The main computational cost in the training of and prediction with Convolution Neural Networks (CNNs) typically stems from the convolution. In this paper, we present three novel ways to parameterize the convolution more efficiently, significantly decreasing the computational complexity. Commonly used CNNs filter the input data using a series of spatial convolutions with compact stencils that couple features from all channels and point-wise nonlinearities. In this paper, we propose three architectures that are cheaper to couple the channel dimension and thereby reduce both the number of trainable weights and the computational cost of the CNN. The first architecture is inspired by tensor-products and imposes a circulant coupling of the channels. The second and third architectures arise as discretizations of a new type of residual neural network (ResNet) that is inspired by Partial Differential Equations (PDEs) or reaction-diffusion type. The coupling patterns of the first two architectures are applicable to a large class of CNNs. We outline in our numerical experiments that the proposed architectures, although considerably reducing the number of trainable weights, yield comparable accuracy to existing CNNs that are fully coupled in the channel dimension.
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