How many different problems can a neural network solve? Well, what makes two problems different? In this talk, we’ll show how Topological Data Analysis (TDA) can be used to partition classification problems into equivalence classes, and how the complexity of decision boundaries can be quantified using persistent homology. Then we will look at a network's learning process from a manifold disentanglement perspective. We’ll demonstrate why analyzing decision boundaries from a topological standpoint provides clearer insights than previous approaches. We use the topology of the decision boundaries realized by a neural network as a measure of a neural network’s expressive power. We show how such a measure of expressive power depends on the properties of the neural networks' architectures, like depth, width and other related quantities.

The talk is based on joint work with Giovanni Petri, available at: https://openreview.net/pdf?id=I44kJPuvqPD