On the Transformation of Latent Space in Autoencoders

Noting the importance of the latent variables in inference and learning, we propose a novel framework for autoencoders based on the homeomorphic transformation of latent variables --- which could reduce the distance between vectors in the transformed space, while preserving the topological properties of the original space --- and investigate the effect of the transformation in both learning generative models and denoising corrupted data. The results of our experiments show that the proposed model can work as both a generative model and a denoising model with improved performance due to the transformation compared to conventional variational and denoising autoencoders.