  The geometry of weight spaces and functional manifolds of neural networks
play an important role towards 'understanding' the intricacies of ML. In this
paper, we attempt to solve certain open questions in ML, by viewing them
through the lens of geometry, ultimately relating it to the discovery of points
or paths of equivalent function in these spaces. We propose a mathematical
framework to evaluate geodesics in the functional space, to find
high-performance paths from a dense network to its sparser counterpart. Our
results are obtained on VGG-11 trained on CIFAR-10 and MLP's trained on MNIST.
Broadly, we demonstrate that the framework is general, and can be applied to a
wide variety of problems, ranging from sparsification to alleviating
catastrophic forgetting.
