In seeking for sparse and efficient neural network models, many previous works investigated on enforcing L1 or L0 regularizers to encourage weight sparsity during training. The L0 regularizer measures the parameter sparsity directly and is invariant to the scaling of parameter values, but it cannot provide useful gradients, and therefore requires complex optimization techniques. The L1 regularizer is almost everywhere differentiable and can be easily optimized with gradient descent. Yet it is not scale-invariant, causing the same shrinking rate to all parameters, which is inefficient in increasing sparsity. Inspired by the Hoyer measure (the ratio between L1 and L2 norms) used in traditional compressed sensing problems, we present DeepHoyer, a set of sparsity-inducing regularizers that are both differentiable almost everywhere and scale-invariant. Our experiments show that enforcing DeepHoyer regularizers can produce even sparser neural network models than previous works, under the same accuracy level. We also show that DeepHoyer can be applied to both element-wise and structural pruning.

本论文提出了一组可微且尺度不变的模型压缩正则化项DeepHoyer，通过实验表明在相同的精度水平下，使用DeepHoyer压缩神经网络可以得到更加稀疏的模型，可以运用于元素级和结构级剪枝。

使用可微缩不变稀疏度量学习稀疏神经网络的DeepHoyer