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.
Network pruning. A straight forward way to reduce the memory footprint of a neural network is by removing unimportant parameters. This process can be conducted while training @cite_5 @cite_3 @cite_18 @cite_32 , or by analyzing the influence of each parameter once the network has been trained @cite_23 . For instance, in @cite_25 , the authors use tensor low rank constraints to (iteratively) reduce the number of parameters of the fully connected layer.
@cite_18 @cite_32 @cite_3 @cite_23 @cite_5 @cite_25
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Model pruning seeks to induce sparsity in a deep neural network's various connection matrices, thereby reducing the number of nonzero-valued parameters in the model. Recent reports (, 2015; , 2017) prune deep networks at the cost of only a marginal loss in accuracy and achieve a sizable reduction in model size. This hints at the possibility that the baseline models in these experiments are perhaps severely over-parameterized at the outset and a viable alternative for model compression might be to simply reduce the number of hidden units while maintaining the model's dense connection structure, exposing a similar trade-off in model size and accuracy. We investigate these two distinct paths for model compression within the context of energy-efficient inference in resource-constrained environments and propose a new gradual pruning technique that is simple and straightforward to apply across a variety of models datasets with minimal tuning and can be seamlessly incorporated within the training process. We compare the accuracy of large, but pruned models (large-sparse) and their smaller, but dense (small-dense) counterparts with identical memory footprint. Across a broad range of neural network architectures (deep CNNs, stacked LSTM, and seq2seq LSTM models), we find large-sparse models to consistently outperform small-dense models and achieve up to 10x reduction in number of non-zero parameters with minimal loss in accuracy. To reduce the significant redundancy in deep Convolutional Neural Networks (CNNs), most existing methods prune neurons by only considering statistics of an individual layer or two consecutive layers (e.g., prune one layer to minimize the reconstruction error of the next layer), ignoring the effect of error propagation in deep networks. In contrast, we argue that it is essential to prune neurons in the entire neuron network jointly based on a unified goal: minimizing the reconstruction error of important responses in the "final response layer" (FRL), which is the second-to-last layer before classification, for a pruned network to retrain its predictive power. Specifically, we apply feature ranking techniques to measure the importance of each neuron in the FRL, and formulate network pruning as a binary integer optimization problem and derive a closed-form solution to it for pruning neurons in earlier layers. Based on our theoretical analysis, we propose the Neuron Importance Score Propagation (NISP) algorithm to propagate the importance scores of final responses to every neuron in the network. The CNN is pruned by removing neurons with least importance, and then fine-tuned to retain its predictive power. NISP is evaluated on several datasets with multiple CNN models and demonstrated to achieve significant acceleration and compression with negligible accuracy loss. To reduce the significant redundancy in deep Convolutional Neural Networks (CNNs), most existing methods prune neurons by only considering the statistics of an individual layer or two consecutive layers (e.g., prune one layer to minimize the reconstruction error of the next layer), ignoring the effect of error propagation in deep networks. In contrast, we argue that for a pruned network to retain its predictive power, it is essential to prune neurons in the entire neuron network jointly based on a unified goal: minimizing the reconstruction error of important responses in the "final response layer" (FRL), which is the second-to-last layer before classification. Specifically, we apply feature ranking techniques to measure the importance of each neuron in the FRL, formulate network pruning as a binary integer optimization problem, and derive a closed-form solution to it for pruning neurons in earlier layers. Based on our theoretical analysis, we propose the Neuron Importance Score Propagation (NISP) algorithm to propagate the importance scores of final responses to every neuron in the network. The CNN is pruned by removing neurons with least importance, and it is then fine-tuned to recover its predictive power. NISP is evaluated on several datasets with multiple CNN models and demonstrated to achieve significant acceleration and compression with negligible accuracy loss. The learning capability of a neural network improves with increasing depth at higher computational costs. Wider layers with dense kernel connectivity patterns furhter increase this cost and may hinder real-time inference. We propose feature map and kernel level pruning for reducing the computational complexity of a deep convolutional neural network. Pruning feature maps reduces the width of a layer and hence does not need any sparse representation. Further, kernel pruning converts the dense connectivity pattern into a sparse one. Due to coarse nature, these pruning granularities can be exploited by GPUs and VLSI based implementations. We propose a simple and generic strategy to choose the least adversarial pruning masks for both granularities. The pruned networks are retrained which compensates the loss in accuracy. We obtain the best pruning ratios when we prune a network with both granularities. Experiments with the CIFAR-10 dataset show that more than 85 sparsity can be induced in the convolution layers with less than 1 increase in the missclassification rate of the baseline network.