  With the rise in interest of sparse neural networks, we study how neural
network pruning with synthetic data leads to sparse networks with unique
training properties. We find that distilled data, a synthetic summarization of
the real data, paired with Iterative Magnitude Pruning (IMP) unveils a new
class of sparse networks that are more stable to SGD noise on the real data,
than either the dense model, or subnetworks found with real data in IMP. That
is, synthetically chosen subnetworks often train to the same minima, or exhibit
linear mode connectivity. We study this through linear interpolation, loss
landscape visualizations, and measuring the diagonal of the hessian. While
dataset distillation as a field is still young, we find that these properties
lead to synthetic subnetworks matching the performance of traditional IMP with
up to 150x less training points in settings where distilled data applies.
