Finding Stable Subnetworks at Initialization with Dataset Distillation

Abstract: Recent works have shown that Dataset Distillation, the process for summarizing the training data, can be leveraged to accelerate the training of deep learning models. However, its impact on training dynamics, particularly in neural network pruning, remains largely unexplored. In our work, we use distilled data in the inner loop of iterative magnitude pruning to produce sparse, trainable subnetworks at initialization -- more commonly known as lottery tickets. While using 150x less training points, our algorithm matches the performance of traditional lottery ticket rewinding on ResNet-18 & CIFAR-10. Previous work highlights that lottery tickets can be found when the dense initialization is stable to SGD noise (i.e. training across different ordering of the data converges to the same minima). We extend this discovery, demonstrating that stable subnetworks can exist even within an unstable dense initialization. In our linear mode connectivity studies, we find that pruning with distilled data discards parameters that contribute to the sharpness of the loss landscape. Lastly, we show that by first generating a stable sparsity mask at initialization, we can find lottery tickets at significantly higher sparsities than traditional iterative magnitude pruning.