Partial Search in a Frozen Network is Enough to Find a Strong Lottery Ticket

Randomly initialized dense networks contain subnetworks that achieve high accuracy without weight learning -- strong lottery tickets (SLTs). Recently, Gadhikar et al. (2023) demonstrated theoretically and experimentally that SLTs can also be found within a randomly pruned source network, thus reducing the SLT search space. However, this limits the search to SLTs that are even sparser than the source, leading to worse accuracy due to unintentionally high sparsity. This paper proposes a method that reduces the SLT search space by an arbitrary ratio that is independent of the desired SLT sparsity. A random subset of the initial weights is excluded from the search space by freezing it -- i.e., by either permanently pruning them or locking them as a fixed part of the SLT. Indeed, the SLT existence in such a reduced search space is theoretically guaranteed by our subset-sum approximation with randomly frozen variables. In addition to reducing search space, the random freezing pattern can also be exploited to reduce model size in inference. Furthermore, experimental results show that the proposed method finds SLTs with better accuracy and model size trade-off than the SLTs obtained from dense or randomly pruned source networks. In particular, the SLT found in a frozen graph neural network achieves higher accuracy than its weight trained counterpart while reducing model size by $40.3\times$.