# Radon Sobolev Variational Auto-Encoders

arXiv: https://arxiv.org/abs/1911.13135 · HTML: https://mlsanity.com/paper/1911.13135/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 29 Nov 2019.

## Built on by (most cited first, 2 of 2)

- [Towards Theoretical Understandings of Self-Consuming Generative Models](https://mlsanity.com/paper/2402.11778/) (2024)
- [The convergence of the Stochastic Gradient Descent (SGD) : a self-contained proof](https://mlsanity.com/paper/2103.14350/) (2021)

## Abstract (arXiv)

The quality of generative models (such as Generative adversarial networks and Variational Auto-Encoders) depends heavily on the choice of a good probability distance. However some popular metrics like the Wasserstein or the Sliced Wasserstein distances, the Jensen-Shannon divergence, the Kullback-Leibler divergence, lack convenient properties such as (geodesic) convexity, fast evaluation and so on. To address these shortcomings, we introduce a class of distances that have built-in convexity. We investigate the relationship with some known paradigms (sliced distances - a synonym for Radon distances -, reproducing kernel Hilbert spaces, energy distances). The distances are shown to possess fast implementations and are included in an adapted Variational Auto-Encoder termed Radon Sobolev Variational Auto-Encoder (RS-VAE) which produces high quality results on standard generative datasets. Keywords: Variational Auto-Encoder; Generative model; Sobolev spaces; Radon Sobolev Variational Auto-Encoder;