Compression of Fully-Connected Layer in Neural Network by Kronecker Product

In this paper we propose and study a technique to reduce the number of parameters and computation time in fully-connected layers of neural networks using Kronecker product, at a mild cost of the prediction quality. The technique proceeds by replacing Fully-Connected layers with so-called Kronecker Fully-Connected layers, where the weight matrices of the FC layers are approximated by linear combinations of multiple Kronecker products of smaller matrices. In particular, given a model trained on SVHN dataset, we are able to construct a new KFC model with 73% reduction in total number of parameters, while the error only rises mildly. In contrast, using low-rank method can only achieve 35% reduction in total number of parameters given similar quality degradation allowance. If we only compare the KFC layer with its counterpart fully-connected layer, the reduction in the number of parameters exceeds 99%. The amount of computation is also reduced as we replace matrix product of the large matrices in FC layers with matrix products of a few smaller matrices in KFC layers. Further experiments on MNIST, SVHN and some Chinese Character recognition models also demonstrate effectiveness of our technique.