  Randomly initialized dense networks contain subnetworks that achieve high
accuracy without weight learning -- strong lottery tickets (SLTs). Recently,
Gadhikar et al. (2023) demonstrated 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 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. In addition to reducing search
space, the proposed random freezing can also provide the benefit of reducing
the model size for inference. Furthermore, experimental results show that the
proposed method finds SLTs with better accuracy-to-model size trade-off than
the SLTs obtained from dense or randomly pruned source networks. In particular,
the SLTs found in Frozen ResNets on image classification using ImageNet
significantly improve the accuracy-to-search space and accuracy-to-model size
trade-offs over SLTs within dense (non-freezing) or sparse (non-locking) random
networks.
