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Split LBI for Deep Learning: Structural Sparsity via Differential Inclusion Paths

Over-parameterization is ubiquitous nowadays in training neural networks to benefit both optimization in seeking global optima and generalization in reducing prediction error. However, compressive networks are desired in many real world applications and direct training of small networks may be trapped in local optima. In this paper, instead of pruning or distilling over-parameterized models to compressive ones, we propose a new approach based on \emph{differential inclusions of inverse scale spaces}, that generates a family of models from simple to complex ones by coupling gradient descent and mirror descent to explore model structural sparsity. It has a simple discretization, called the Split Linearized Bregman Iteration (SplitLBI), whose global convergence analysis in deep learning is established that from any initializations, algorithmic iterations converge to a critical point of empirical risks. Experimental evidence shows that\ SplitLBI may achieve state-of-the-art performance in large scale training on ImageNet-2012 dataset etc., while with \emph{early stopping} it unveils effective subnet architecture with comparable test accuracies to dense models after retraining instead of pruning well-trained ones.

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