DeepHoyer: Learning Sparser Neural Network with Differentiable Scale-Invariant Sparsity Measures

In seeking for sparse and efficient neural network models, many previous works investigated on enforcing 1 or 0 regularizers to encourage weight sparsity during training. The 0 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 1 regularizer is almost everywhere differentiable and can be easily optimized with gradient descent. Yet it is not scale-invariant and causes the same shrinking rate to all parameters, which is inefficient in increasing sparsity. Inspired by the Hoyer measure (the ratio between 1 and 2 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. The codes are available at https://github.com/yanghr/DeepHoyer .