  Deep neural networks have achieved great success in many data processing
applications. However, the high computational complexity and storage cost makes
deep learning hard to be used on resource-constrained devices, and it is not
environmental-friendly with much power cost. In this paper, we focus on
low-rank optimization for efficient deep learning techniques. In the space
domain, deep neural networks are compressed by low rank approximation of the
network parameters, which directly reduces the storage requirement with a
smaller number of network parameters. In the time domain, the network
parameters can be trained in a few subspaces, which enables efficient training
for fast convergence. The model compression in the spatial domain is summarized
into three categories as pre-train, pre-set, and compression-aware methods,
respectively. With a series of integrable techniques discussed, such as sparse
pruning, quantization, and entropy coding, we can ensemble them in an
integration framework with lower computational complexity and storage. Besides
of summary of recent technical advances, we have two findings for motivating
future works: one is that the effective rank outperforms other sparse measures
for network compression. The other is a spatial and temporal balance for
tensorized neural networks.
