  The sparsity of Deep Neural Networks is well investigated to maximize the
performance and reduce the size of overparameterized networks as possible.
Existing methods focus on pruning parameters in the training process by using
thresholds and metrics. Meanwhile, feature similarity between different layers
has not been discussed sufficiently before, which could be rigorously proved to
be highly correlated to the network sparsity in this paper. Inspired by
interlayer feature similarity in overparameterized models, we investigate the
intrinsic link between network sparsity and interlayer feature similarity.
Specifically, we prove that reducing interlayer feature similarity based on
Centered Kernel Alignment (CKA) improves the sparsity of the network by using
information bottleneck theory. Applying such theory, we propose a plug-and-play
CKA-based Sparsity Regularization for sparse network training, dubbed CKA-SR,
which utilizes CKA to reduce feature similarity between layers and increase
network sparsity. In other words, layers of our sparse network tend to have
their own identity compared to each other. Experimentally, we plug the proposed
CKA-SR into the training process of sparse network training methods and find
that CKA-SR consistently improves the performance of several State-Of-The-Art
sparse training methods, especially at extremely high sparsity. Code is
included in the supplementary materials.
