A Topology Layer for Machine Learning

Code

• github.com/bruel-gabrielsson/TopologyLayer
  OfficialIn paperpytorch★ 0
• github.com/tlacombe/topt
  tf★ 6
• github.com/yuanl12/tda_updating_persistence
  pytorch★ 0

Abstract

Topology applied to real world data using persistent homology has started to find applications within machine learning, including deep learning. We present a differentiable topology layer that computes persistent homology based on level set filtrations and edge-based filtrations. We present three novel applications: the topological layer can (i) regularize data reconstruction or the weights of machine learning models, (ii) construct a loss on the output of a deep generative network to incorporate topological priors, and (iii) perform topological adversarial attacks on deep networks trained with persistence features. The code (www.github.com/bruel-gabrielsson/TopologyLayer) is publicly available and we hope its availability will facilitate the use of persistent homology in deep learning and other gradient based applications.

Tasks

Reproductions