The Lottery Ticket Hypothesis (LTH) states that for a reasonably sized neural network, a sub-network within the same network yields no less performance than the dense counterpart when trained from the same initialization. This work investigates the relation between model size and the ease of finding these sparse sub-networks. We show through experiments that, surprisingly, under a finite budget, smaller models benefit more from Ticket Search (TS).
The search for efficient, sparse deep neural network models is most prominently performed by pruning: training a dense, overparameterized network and removing parameters, usually via following a manually-crafted heuristic. Additionally, the recent Lottery Ticket Hypothesis conjectures that, for a typically-sized neural network, it is possible to find small sub-networks which, when trained from scratch on a comparable budget, match the performance of the original dense counterpart. We revisit fundamental aspects of pruning algorithms, pointing out missing ingredients in previous approaches, and develop a method, Continuous Sparsification, which searches for sparse networks based on a novel approximation of an intractable $\ell_0$ regularization. We compare against dominant heuristic-based methods on pruning as well as ticket search -- finding sparse subnetworks that can be successfully re-trained from an early iterate. Empirical results show that we surpass the state-of-the-art for both objectives, across models and datasets, including VGG trained on CIFAR-10 and ResNet-50 trained on ImageNet. In addition to setting a new standard for pruning, Continuous Sparsification also offers fast parallel ticket search, opening doors to new applications of the Lottery Ticket Hypothesis.