  Since sparse neural networks usually contain many zero weights, these
unnecessary network connections can potentially be eliminated without degrading
network performance. Therefore, well-designed sparse neural networks have the
potential to significantly reduce FLOPs and computational resources. In this
work, we propose a new automatic pruning method - Sparse Connectivity Learning
(SCL). Specifically, a weight is re-parameterized as an element-wise
multiplication of a trainable weight variable and a binary mask. Thus, network
connectivity is fully described by the binary mask, which is modulated by a
unit step function. We theoretically prove the fundamental principle of using a
straight-through estimator (STE) for network pruning. This principle is that
the proxy gradients of STE should be positive, ensuring that mask variables
converge at their minima. After finding Leaky ReLU, Softplus, and Identity STEs
can satisfy this principle, we propose to adopt Identity STE in SCL for
discrete mask relaxation. We find that mask gradients of different features are
very unbalanced, hence, we propose to normalize mask gradients of each feature
to optimize mask variable training. In order to automatically train sparse
masks, we include the total number of network connections as a regularization
term in our objective function. As SCL does not require pruning criteria or
hyper-parameters defined by designers for network layers, the network is
explored in a larger hypothesis space to achieve optimized sparse connectivity
for the best performance. SCL overcomes the limitations of existing automatic
pruning methods. Experimental results demonstrate that SCL can automatically
learn and select important network connections for various baseline network
structures. Deep learning models trained by SCL outperform the SOTA
human-designed and automatic pruning methods in sparsity, accuracy, and FLOPs
reduction.
