  Network pruning is a promising avenue for compressing deep neural networks. A
typical approach to pruning starts by training a model and then removing
redundant parameters while minimizing the impact on what is learned.
Alternatively, a recent approach shows that pruning can be done at
initialization prior to training, based on a saliency criterion called
connection sensitivity. However, it remains unclear exactly why pruning an
untrained, randomly initialized neural network is effective. In this work, by
noting connection sensitivity as a form of gradient, we formally characterize
initialization conditions to ensure reliable connection sensitivity
measurements, which in turn yields effective pruning results. Moreover, we
analyze the signal propagation properties of the resulting pruned networks and
introduce a simple, data-free method to improve their trainability. Our
modifications to the existing pruning at initialization method lead to improved
results on all tested network models for image classification tasks.
Furthermore, we empirically study the effect of supervision for pruning and
demonstrate that our signal propagation perspective, combined with unsupervised
pruning, can be useful in various scenarios where pruning is applied to
non-standard arbitrarily-designed architectures.
