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Pre-training serves as a broadly adopted starting point for transfer learning on various downstream tasks. Recent investigations of lottery tickets hypothesis (LTH) demonstrate such enormous pre-trained models can be replaced by extremely sparse subnetworks (a.k.a. matching subnetworks) without sacrificing transferability. However, practical security-crucial applications usually pose more challenging requirements beyond standard transfer, which also demand these subnetworks to overcome adversarial vulnerability. In this paper, we formulate a more rigorous concept, Double-Win Lottery Tickets, in which a located subnetwork from a pre-trained model can be independently transferred on diverse downstream tasks, to reach BOTH the same standard and robust generalization, under BOTH standard and adversarial training regimes, as the full pre-trained model can do. We comprehensively examine various pre-training mechanisms and find that robust pre-training tends to craft sparser double-win lottery tickets with superior performance over the standard counterparts. For example, on downstream CIFAR-10/100 datasets, we identify double-win matching subnetworks with the standard, fast adversarial, and adversarial pre-training from ImageNet, at 89.26%/73.79%, 89.26%/79.03%, and 91.41%/83.22% sparsity, respectively. Furthermore, we observe the obtained double-win lottery tickets can be more data-efficient to transfer, under practical data-limited (e.g., 1% and 10%) downstream schemes. Our results show that the benefits from robust pre-training are amplified by the lottery ticket scheme, as well as the data-limited transfer setting. 

Pruning large neural networks to create high-quality, independently trainable sparse masks, which can maintain similar performance to their dense counterparts, is very desirable due to the reduced space and time complexity. As research effort is focused on increasingly sophisticated pruning methods that leads to sparse subnetworks trainable from the scratch, we argue for an orthogonal, under-explored theme: improving training techniques for pruned sub-networks, i.e. sparse training. Apart from the popular belief that only the quality of sparse masks matters for sparse training, in this paper we demonstrate an alternative opportunity: one can carefully customize the sparse training techniques to deviate from the default dense network training protocols, consisting of introducing ``ghost" neurons and skip connections at the early stage of training, and strategically modifying the initialization as well as labels. Our new sparse training recipe is generally applicable to improving training from scratch with various sparse masks. By adopting our newly curated techniques, we demonstrate significant performance gains across various popular datasets (CIFAR-10, CIFAR-100, TinyImageNet), architectures (ResNet-18/32/104, Vgg16, MobileNet), and sparse mask options (lottery ticket, SNIP/GRASP, SynFlow, or even randomly pruning), compared to the default training protocols, especially at high sparsity levels.