A Topological Framework for Deep Learning

Understand

We utilize classical facts from topology to show that the classification problem in machine learning is always solvable under very mild conditions.

• Furthermore, we show that a softmax classification network acts on an input topological space by a finite sequence of topological moves to achieve the classification task.
• Moreover, given a training dataset, we show how topological formalism can be used to suggest the appropriate architectural choices for neural networks designed to be trained as classifiers on the data.
• Finally, we show how the architecture of a neural network cannot be chosen independently from the shape of the underlying data.