LEARNING TO SHARE: SIMULTANEOUS PARAMETER TYING AND SPARSIFICATION IN DEEP LEARNING

Deep neural networks (DNNs) usually contain millions, maybe billions, of parameters/weights, making both storage and computation very expensive. This has motivated a large body of work to reduce the complexity of the neural network by using sparsity-inducing regularizers. Another well-known approach for controlling the complexity of DNNs is parameter sharing/tying, where certain sets of weights are forced to share a common value. Some forms of weight sharing are hard-wired to express certain in- variances, with a notable example being the shift-invariance of convolutional layers. However, there may be other groups of weights that may be tied together during the learning process, thus further re- ducing the complexity of the network. In this paper, we adopt a recently proposed sparsity-inducing regularizer, named GrOWL (group ordered weighted l1), which encourages sparsity and, simulta- neously, learns which groups of parameters should share a common value. GrOWL has been proven effective in linear regression, being able to identify and cope with strongly correlated covariates. Unlike standard sparsity-inducing regularizers (e.g., l1 a.k.a. Lasso), GrOWL not only eliminates unimportant neurons by setting all the corresponding weights to zero, but also explicitly identifies strongly correlated neurons by tying the corresponding weights to a common value. This ability of GrOWL motivates the following two-stage procedure: (i) use GrOWL regularization in the training process to simultaneously identify significant neurons and groups of parameter that should be tied together; (ii) retrain the network, enforcing the structure that was unveiled in the previous phase, i.e., keeping only the significant neurons and enforcing the learned tying structure. We evaluate the proposed approach on several benchmark datasets, showing that it can dramatically compress the network with slight or even no loss on generalization performance.