Exploiting Local Structures with the Kronecker Layer in Convolutional Networks

In this paper, we propose and study a technique to reduce the number of parameters and computation time in convolutional neural networks. We use Kronecker product to exploit the local structures within convolution and fully-connected layers, by replacing the large weight matrices by combinations of multiple Kronecker products of smaller matrices. Just as the Kronecker product is a generalization of the outer product from vectors to matrices, our method is a generalization of the low rank approximation method for convolution neural networks. We also introduce combinations of different shapes of Kronecker product to increase modeling capacity. Experiments on SVHN, scene text recognition and ImageNet dataset demonstrate that we can achieve $3.3 \times$ speedup or $3.6 \times$ parameter reduction with less than 1\% drop in accuracy, showing the effectiveness and efficiency of our method. Moreover, the computation efficiency of Kronecker layer makes using larger feature map possible, which in turn enables us to outperform the previous state-of-the-art on both SVHN(digit recognition) and CASIA-HWDB (handwritten Chinese character recognition) datasets.