Topological Autoencoders

Code

• github.com/BorgwardtLab/topological-autoencoders
  OfficialIn paperpytorch★ 0
• github.com/BorgwardtLab/topo-ae-distances
  pytorch★ 8

Abstract

We propose a novel approach for preserving topological structures of the input space in latent representations of autoencoders. Using persistent homology, a technique from topological data analysis, we calculate topological signatures of both the input and latent space to derive a topological loss term. Under weak theoretical assumptions, we construct this loss in a differentiable manner, such that the encoding learns to retain multi-scale connectivity information. We show that our approach is theoretically well-founded and that it exhibits favourable latent representations on a synthetic manifold as well as on real-world image data sets, while preserving low reconstruction errors.

Tasks

Benchmark Results

Reproductions