Spartan: Differentiable Sparsity via Regularized Transportation
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We present Spartan, a method for training sparse neural network models with a predetermined level of sparsity. Spartan is based on a combination of two techniques: (1) soft top-k masking of low-magnitude parameters via a regularized optimal transportation problem and (2) dual averaging-based parameter updates with hard sparsification in the forward pass. This scheme realizes an exploration-exploitation tradeoff: early in training, the learner is able to explore various sparsity patterns, and as the soft top-k approximation is gradually sharpened over the course of training, the balance shifts towards parameter optimization with respect to a fixed sparsity mask. Spartan is sufficiently flexible to accommodate a variety of sparsity allocation policies, including both unstructured and block structured sparsity, as well as general cost-sensitive sparsity allocation mediated by linear models of per-parameter costs. On ImageNet-1K classification, Spartan yields 95 sparse ResNet-50 models and 90 absolute top-1 accuracy losses of less than 1 training.
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