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We consider a general framework for reducing the number of trainable modelparameters in deep learning networks by decomposing linear operators as aproduct of sums of simpler linear operators. Recently proposed deep learningarchitectures such as CNN, KFC, Dilated CNN, etc. are all subsumed in thisframework and we illustrate other types of neural network architectures withinthis framework. We show that good accuracy on MNIST and Fashion MNIST can beobtained using a relatively small number of trainable parameters. In addition,since implementation of the convolutional layer is resource-heavy, we consideran approach in the transform domain that obviates the need for convolutionallayers. One of the advantages of this general framework over prior approachesis that the number of trainable parameters is not fixed and can be variedarbitrarily. In particular, we illustrate the tradeoff of varying the number oftrainable variables and the corresponding error rate. As an example, by usingthis decomposition on a reference CNN architecture for MNIST with over 3x10^6trainable parameters, we are able to obtain an accuracy of 98.44% using only3554 trainable parameters.

ProdSumNet: reducing model parameters in deep neural networks via product-of-sums matrix decompositions