# Symmetric Variational Autoencoder and Connections to Adversarial Learning

arXiv: https://arxiv.org/abs/1709.01846 · HTML: https://mlsanity.com/paper/1709.01846/

## Key facts

- Cited by 14 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 6 Sep 2017.

## Built on by (most cited first, 14 of 14)

- [MiniLLM: On-Policy Distillation of Large Language Models](https://mlsanity.com/paper/2306.08543/) (2023)
- [Variational Discriminator Bottleneck: Improving Imitation Learning, Inverse RL, and GANs by Constraining Information Flow](https://mlsanity.com/paper/1810.00821/) (2018)
- [Survey on Knowledge Distillation for Large Language Models: Methods, Evaluation, and Application](https://mlsanity.com/paper/2407.01885/) (2024)
- [GATSBI: Generative Adversarial Training for Simulation-Based Inference](https://mlsanity.com/paper/2203.06481/) (2022)
- [Continual Variational Autoencoder Learning via Online Cooperative Memorization](https://mlsanity.com/paper/2207.10131/) (2022)
- [Lifelong Mixture of Variational Autoencoders](https://mlsanity.com/paper/2107.04694/) (2021)
- [Improving Adversarial Energy-Based Model via Diffusion Process](https://mlsanity.com/paper/2403.01666/) (2024)
- [Bi-level Doubly Variational Learning for Energy-based Latent Variable Models](https://mlsanity.com/paper/2203.14702/) (2022)
- [Lifelong Generative Modelling Using Dynamic Expansion Graph Model](https://mlsanity.com/paper/2112.08370/) (2021)
- [An Interpretable Neural Network for Parameter Inference](https://mlsanity.com/paper/2106.05536/) (2021)
- [Symmetric Wasserstein Autoencoders](https://mlsanity.com/paper/2106.13024/) (2021)
- [Variational Autoencoder Kernel Interpretation and Selection for Classification](https://mlsanity.com/paper/2209.04715/) (2022)
- [Joint-stochastic-approximation Autoencoders with Application to Semi-supervised Learning](https://mlsanity.com/paper/2505.18558/) (2025)
- [KDFP: A first-principles approach to knowledge distillation in large language models](https://mlsanity.com/paper/2610.10854/) (2026)

## Abstract (arXiv)

A new form of the variational autoencoder (VAE) is proposed, based on the symmetric Kullback-Leibler divergence. It is demonstrated that learning of the resulting symmetric VAE (sVAE) has close connections to previously developed adversarial-learning methods. This relationship helps unify the previously distinct techniques of VAE and adversarially learning, and provides insights that allow us to ameliorate shortcomings with some previously developed adversarial methods. In addition to an analysis that motivates and explains the sVAE, an extensive set of experiments validate the utility of the approach.