  Modern-day neural networks are famously large, yet also highly redundant and
compressible; there exist numerous pruning strategies in the deep learning
literature that yield over 90% sparser sub-networks of fully-trained, dense
architectures while still maintaining their original accuracies. Amongst these
many methods though -- thanks to its conceptual simplicity, ease of
implementation, and efficacy -- Iterative Magnitude Pruning (IMP) dominates in
practice and is the de facto baseline to beat in the pruning community.
However, theoretical explanations as to why a simplistic method such as IMP
works at all are few and limited. In this work, we leverage the notion of
persistent homology to gain insights into the workings of IMP and show that it
inherently encourages retention of those weights which preserve topological
information in a trained network. Subsequently, we also provide bounds on how
much different networks can be pruned while perfectly preserving their zeroth
order topological features, and present a modified version of IMP to do the
same.
