Connectivity-Optimized Representation Learning via Persistent Homology

Understand

We study the problem of learning representations with controllable connectivity properties.

• This is beneficial in situations when the imposed structure can be leveraged upstream.
• In particular, we control the connectivity of an autoencoder's latent space via a novel type of loss, operating on information from persistent homology.
• Under mild conditions, this loss is differentiable and we present a theoretical analysis of the properties induced by the loss.