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Over-parameterization is ubiquitous nowadays in training neural networks tobenefit both optimization in seeking global optima and generalization inreducing prediction error. However, compressive networks are desired in manyreal world applications and direct training of small networks may be trapped inlocal optima. In this paper, instead of pruning or distillingover-parameterized models to compressive ones, we propose a new approach basedon differential inclusions of inverse scale spaces. Specifically, it generatesa family of models from simple to complex ones that couples a pair ofparameters to simultaneously train over-parameterized deep models andstructural sparsity on weights of fully connected and convolutional layers.Such a differential inclusion scheme has a simple discretization, proposed asDeep structurally splitting Linearized Bregman Iteration (DessiLBI), whoseglobal convergence analysis in deep learning is established that from anyinitializations, algorithmic iterations converge to a critical point ofempirical risks. Experimental evidence shows that DessiLBI achieve comparableand even better performance than the competitive optimizers in exploring thestructural sparsity of several widely used backbones on the benchmark datasets.Remarkably, with early stopping, DessiLBI unveils "winning tickets" in earlyepochs: the effective sparse structure with comparable test accuracy to fullytrained over-parameterized models.

DessiLBI: Exploring Structural Sparsity of Deep Networks via Differential Inclusion Paths