  A novel method to identify salient computational paths within randomly wired
neural networks before training is proposed. The computational graph is pruned
based on a node mass probability function defined by local graph measures and
weighted by hyperparameters produced by a reinforcement learning-based
controller neural network. We use the definition of Ricci curvature to remove
edges of low importance before mapping the computational graph to a neural
network. We show a reduction of almost $35\%$ in the number of floating-point
operations (FLOPs) per pass, with no degradation in performance. Further, our
method can successfully regularize randomly wired neural networks based on
purely structural properties, and also find that the favourable characteristics
identified in one network generalise to other networks. The method produces
networks with better performance under similar compression to those pruned by
lowest-magnitude weights. To our best knowledge, this is the first work on
pruning randomly wired neural networks, as well as the first to utilize the
topological measure of Ricci curvature in the pruning mechanism.
