Representing Closed Transformation Paths in Encoded Network Latent Space

TL;DR

This paper introduces a generative manifold model within autoencoders to better represent closed transformation paths in data, enabling more accurate latent space modeling of complex systems and their dynamics.

Contribution

It proposes a novel approach that incorporates a generative manifold into the latent space to capture closed transformation paths, improving latent dynamics learning and classification.

Findings

Successfully models closed transformation paths in latent space

Enables generation of transformation paths for complex systems

Improves classification of samples on the same transformation path

Abstract

Deep generative networks have been widely used for learning mappings from a low-dimensional latent space to a high-dimensional data space. In many cases, data transformations are defined by linear paths in this latent space. However, the Euclidean structure of the latent space may be a poor match for the underlying latent structure in the data. In this work, we incorporate a generative manifold model into the latent space of an autoencoder in order to learn the low-dimensional manifold structure from the data and adapt the latent space to accommodate this structure. In particular, we focus on applications in which the data has closed transformation paths which extend from a starting point and return to nearly the same point. Through experiments on data with natural closed transformation paths, we show that this model introduces the ability to learn the latent dynamics of complex systems, generate transformation paths, and classify samples that belong on the same transformation path.