  Deep convolutional neural networks (CNNs) are deployed in various
applications but demand immense computational requirements. Pruning techniques
and Winograd convolution are two typical methods to reduce the CNN computation.
However, they cannot be directly combined because Winograd transformation fills
in the sparsity resulting from pruning. Li et al. (2017) propose sparse
Winograd convolution in which weights are directly pruned in the Winograd
domain, but this technique is not very practical because Winograd-domain
retraining requires low learning rates and hence significantly longer training
time. Besides, Liu et al. (2018) move the ReLU function into the Winograd
domain, which can help increase the weight sparsity but requires changes in the
network structure. To achieve a high Winograd-domain weight sparsity without
changing network structures, we propose a new pruning method, spatial-Winograd
pruning. As the first step, spatial-domain weights are pruned in a structured
way, which efficiently transfers the spatial-domain sparsity into the Winograd
domain and avoids Winograd-domain retraining. For the next step, we also
perform pruning and retraining directly in the Winograd domain but propose to
use an importance factor matrix to adjust weight importance and weight
gradients. This adjustment makes it possible to effectively retrain the pruned
Winograd-domain network without changing the network structure. For the three
models on the datasets of CIFAR10, CIFAR-100, and ImageNet, our proposed method
can achieve the Winograd domain sparsities of 63%, 50%, and 74%, respectively.
