  The redundancy is widely recognized in Convolutional Neural Networks (CNNs),
which enables to remove unimportant filters from convolutional layers so as to
slim the network with acceptable performance drop. Inspired by the linear and
combinational properties of convolution, we seek to make some filters
increasingly close and eventually identical for network slimming. To this end,
we propose Centripetal SGD (C-SGD), a novel optimization method, which can
train several filters to collapse into a single point in the parameter
hyperspace. When the training is completed, the removal of the identical
filters can trim the network with NO performance loss, thus no finetuning is
needed. By doing so, we have partly solved an open problem of constrained
filter pruning on CNNs with complicated structure, where some layers must be
pruned following others. Our experimental results on CIFAR-10 and ImageNet have
justified the effectiveness of C-SGD-based filter pruning. Moreover, we have
provided empirical evidences for the assumption that the redundancy in deep
neural networks helps the convergence of training by showing that a redundant
CNN trained using C-SGD outperforms a normally trained counterpart with the
equivalent width.
