Spectral Tensor Layers for Communication-Free Distributed Deep Learning

In this article, we propose a novel spectral tensor layer for communication-free distributed deep learning. The overall framework is as follows: first, we represent the data in tensor form (instead of vector form) and replace the matrix product in conventional neural networks with the tensor product, which in effect imposes certain transformed-induced structure on the original weight matrices, e.g., a block-circulant structure; then, we apply a linear transform along a certain dimension to split the original dataset into multiple spectral subdatasets; as a result, the proposed spectral tensor network consists of parallel branches where each branch is a conventional neural network trained on a spectral subdataset with ZERO communication cost. The parallel branches are directly ensembled (i.e., the weighted sum of their outputs) to generate an overall network with substantially stronger generalization capability than that of each branch. Moreover, the proposed method enjoys a byproduct of decentralization gain in terms of memory and computation, compared with traditional networks. It is a natural yet elegant solution for heterogeneous data in federated learning (FL), where data at different nodes have different resolutions. Finally, we evaluate the proposed spectral tensor networks on the MNIST, CIFAR-10, ImageNet-1K, and ImageNet-21K datasets, respectively, to verify that they simultaneously achieve communication-free distributed learning, distributed storage reduction, parallel computation speedup, and learning with multiresolution data.