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.

本文提出了一种名为Sparse Connectivity Learning的新型自动裁剪方法，通过使用二进制掩码描述网络连接，同时使用Identity STE进行离散掩码松弛。在目标函数中加入网络总连接数的正则化项，无需定义裁剪标准或超参数即可探索网络以实现最佳性能。实验结果表明，使用SCL训练的深度学习模型在稀疏度、准确性和FLOPs减少方面优于其他自动剪枝方法。

神经网络的自动稀疏连通性学习