Topological Constraints on Homeomorphic Auto-Encoding

27 Dec 2018Pim de HaanLuca Falorsi

When doing representation learning on data that lives on a known non-trivial manifold embedded in high dimensional space, it is natural to desire the encoder to be homeomorphic when restricted to the manifold, so that it is bijective and continuous with a continuous inverse. Using topological arguments, we show that when the manifold is non-trivial, the encoder must be globally discontinuous and propose a universal, albeit impractical, construction... (read more)

PDF Abstract

Code


No code implementations yet. Submit your code now

Results from the Paper


  Submit results from this paper to get state-of-the-art GitHub badges and help the community compare results to other papers.

Methods used in the Paper


METHOD TYPE
🤖 No Methods Found Help the community by adding them if they're not listed; e.g. Deep Residual Learning for Image Recognition uses ResNet