Learning the Number of Neurons in Deep Networks

Nowadays, the number of layers and of neurons in each layer of a deep network are typically set manually. While very deep and wide networks have proven effective in general, they come at a high memory and computation cost, thus making them impractical for constrained platforms. These networks, however, are known to have many redundant parameters, and could thus, in principle, be replaced by more compact architectures. In this paper, we introduce an approach to automatically determining the number of neurons in each layer of a deep network during learning. To this end, we propose to make use of structured sparsity during learning. More precisely, we use a group sparsity regularizer on the parameters of the network, where each group is defined to act on a single neuron. Starting from an overcomplete network, we show that our approach can reduce the number of parameters by up to 80\% while retaining or even improving the network accuracy.

Domain-adaptive deep network compression

Deep Neural Networks trained on large datasets can be easily transferred to new domains with far fewer labeled examples by a process called fine-tuning. This has the advantage that representations learned in the large source domain can be exploited on smaller target domains. However, networks designed to be optimal for the source task are often prohibitively large for the target task. In this work we address the compression of networks after domain transfer. We focus on compression algorithms based on low-rank matrix decomposition. Existing methods base compression solely on learned network weights and ignore the statistics of network activations. We show that domain transfer leads to large shifts in network activations and that it is desirable to take this into account when compressing. We demonstrate that considering activation statistics when compressing weights leads to a rank-constrained regression problem with a closed-form solution. Because our method takes into account the target domain, it can more optimally remove the redundancy in the weights. Experiments show that our Domain Adaptive Low Rank (DALR) method significantly outperforms existing low-rank compression techniques. With our approach, the fc6 layer of VGG19 can be compressed more than 4x more than using truncated SVD alone -- with only a minor or no loss in accuracy. When applied to domain-transferred networks it allows for compression down to only 5-20% of the original number of parameters with only a minor drop in performance.