Compressibility Loss for Neural Network Weights

In this paper we apply a compressibility loss that enables learning highly compressible neural network weights. The loss was previously proposed as a measure of negated sparsity of a signal, yet in this paper we show that minimizing this loss also enforces the non-zero parts of the signal to have very low entropy, thus making the entire signal more compressible. For an optimization problem where the goal is to minimize the compressibility loss (the objective), we prove that at any critical point of the objective, the weight vector is a ternary signal and the corresponding value of the objective is the squared root of the number of non-zero elements in the signal, thus directly related to sparsity. In the experiments, we train neural networks with the compressibility loss and we show that the proposed method achieves weight sparsity and compression ratios comparable with the state-of-the-art.