Representing Closed Transformation Paths in Encoded Network Latent Space
This work addresses the challenge of accurately modeling closed transformation paths in generative networks, which is incremental for applications in complex systems analysis.
The authors tackled the problem of representing closed transformation paths in autoencoder latent spaces by incorporating a generative manifold model to better match the underlying data structure. They demonstrated the model's ability to learn latent dynamics, generate transformation paths, and classify samples on the same path in experiments with natural closed transformation data.
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.