Convex Smoothed Autoencoder-Optimal Transport model

TL;DR

This paper introduces a novel generative model that leverages convex smoothing techniques to overcome mode collapse and mode mixture issues in autoencoder-based optimal transport models, supported by theoretical error bounds.

Contribution

It proposes a convex smoothed autoencoder-optimal transport model that improves sample generation and provides theoretical analysis of approximation errors.

Findings

Model effectively generates diverse, realistic samples.

Theoretical bounds on approximation errors are established.

Addresses shortcomings of previous AE-OT models.

Abstract

Generative modelling is a key tool in unsupervised machine learning which has achieved stellar success in recent years. Despite this huge success, even the best generative models such as Generative Adversarial Networks (GANs) and Variational Autoencoders (VAEs) come with their own shortcomings, mode collapse and mode mixture being the two most prominent problems. In this paper we develop a new generative model capable of generating samples which resemble the observed data, and is free from mode collapse and mode mixture. Our model is inspired by the recently proposed Autoencoder-Optimal Transport (AE-OT) model and tries to improve on it by addressing the problems faced by the AE-OT model itself, specifically with respect to the sample generation algorithm. Theoretical results concerning the bound on the error in approximating the non-smooth Brenier potential by its smoothed estimate, and approximating the discontinuous optimal transport map by a smoothed optimal transport map estimate have also been established in this paper.