Unmasking the Lottery Ticket Hypothesis: What's Encoded in a Winning Ticket's Mask?
This provides theoretical insights into neural network pruning for researchers, though it is incremental as it builds on existing IMP methods.
The paper tackled the problem of understanding why iterative magnitude pruning (IMP) finds sparse subnetworks (winning tickets) in deep learning, revealing that masks encode axial subspaces intersecting linearly connected modes, and showing that SGD's robustness and landscape flatness determine pruning limits.
Modern deep learning involves training costly, highly overparameterized networks, thus motivating the search for sparser networks that can still be trained to the same accuracy as the full network (i.e. matching). Iterative magnitude pruning (IMP) is a state of the art algorithm that can find such highly sparse matching subnetworks, known as winning tickets. IMP operates by iterative cycles of training, masking smallest magnitude weights, rewinding back to an early training point, and repeating. Despite its simplicity, the underlying principles for when and how IMP finds winning tickets remain elusive. In particular, what useful information does an IMP mask found at the end of training convey to a rewound network near the beginning of training? How does SGD allow the network to extract this information? And why is iterative pruning needed? We develop answers in terms of the geometry of the error landscape. First, we find that$\unicode{x2014}$at higher sparsities$\unicode{x2014}$pairs of pruned networks at successive pruning iterations are connected by a linear path with zero error barrier if and only if they are matching. This indicates that masks found at the end of training convey the identity of an axial subspace that intersects a desired linearly connected mode of a matching sublevel set. Second, we show SGD can exploit this information due to a strong form of robustness: it can return to this mode despite strong perturbations early in training. Third, we show how the flatness of the error landscape at the end of training determines a limit on the fraction of weights that can be pruned at each iteration of IMP. Finally, we show that the role of retraining in IMP is to find a network with new small weights to prune. Overall, these results make progress toward demystifying the existence of winning tickets by revealing the fundamental role of error landscape geometry.