# Probabilistic Autoencoder using Fisher Information

arXiv: https://arxiv.org/abs/2110.14947 · HTML: https://mlsanity.com/paper/2110.14947/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 22 of its 43 references that are in the map.
- First posted on arXiv 28 Oct 2021.

## Builds on (most cited first, 22 of 22)

- [Rethinking the Inception Architecture for Computer Vision](https://mlsanity.com/paper/1512.00567/) (2015)
- [Fashion-MNIST: a Novel Image Dataset for Benchmarking Machine Learning Algorithms](https://mlsanity.com/paper/1708.07747/) (2017)
- [Variational Inference with Normalizing Flows](https://mlsanity.com/paper/1505.05770/) (2015)
- [Density estimation using Real NVP](https://mlsanity.com/paper/1605.08803/) (2016)
- [An Introduction to Variational Autoencoders](https://mlsanity.com/paper/1906.02691/) (2019)
- [Pixel Recurrent Neural Networks](https://mlsanity.com/paper/1601.06759/) (2016)
- [Improving Variational Inference with Inverse Autoregressive Flow](https://mlsanity.com/paper/1606.04934/) (2016)
- [Wasserstein Auto-Encoders](https://mlsanity.com/paper/1711.01558/) (2017)
- [MADE: Masked Autoencoder for Distribution Estimation](https://mlsanity.com/paper/1502.03509/) (2015)
- [Adversarially Learned Inference](https://mlsanity.com/paper/1606.00704/) (2016)
- [GANs Trained by a Two Time-Scale Update Rule Converge to a Local Nash Equilibrium](https://mlsanity.com/paper/1706.08500/) (2017)
- [DRAW: A Recurrent Neural Network For Image Generation](https://mlsanity.com/paper/1502.04623/) (2015)
- [Recent Advances in Autoencoder-Based Representation Learning](https://mlsanity.com/paper/1812.05069/) (2018)
- [Hierarchical Variational Models](https://mlsanity.com/paper/1511.02386/) (2015)
- [Auxiliary Deep Generative Models](https://mlsanity.com/paper/1602.05473/) (2016)
- [Distribution Matching in Variational Inference](https://mlsanity.com/paper/1802.06847/) (2018)
- [Do GANs actually learn the distribution? An empirical study](https://mlsanity.com/paper/1706.08224/) (2017)
- [Metric Gaussian Variational Inference](https://mlsanity.com/paper/1901.11033/) (2019)
- [Geometric variational inference](https://mlsanity.com/paper/2105.10470/) (2021)
- [Fisher Auto-Encoders](https://mlsanity.com/paper/2007.06120/) (2020)
- [Encoding prior knowledge in the structure of the likelihood](https://mlsanity.com/paper/1812.04403/) (2018)
- [A Brief Introduction to Generative Models](https://mlsanity.com/paper/2103.00265/) (2021)

## Built on by (most cited first, 3 of 3)

- [Attention to Entropic Communication](https://mlsanity.com/paper/2307.11423/) (2023)
- [Complex variational autoencoders admit K"ahler structure](https://mlsanity.com/paper/2511.15172/) (2025)
- [Commutator-Induced Uncertainty in VAEs](https://mlsanity.com/paper/2605.23449/) (2026)

## Abstract (arXiv)

Neural Networks play a growing role in many science disciplines, including physics. Variational Autoencoders (VAEs) are neural networks that are able to represent the essential information of a high dimensional data set in a low dimensional latent space, which have a probabilistic interpretation. In particular the so-called encoder network, the first part of the VAE, which maps its input onto a position in latent space, additionally provides uncertainty information in terms of a variance around this position. In this work, an extension to the Autoencoder architecture is introduced, the FisherNet. In this architecture, the latent space uncertainty is not generated using an additional information channel in the encoder, but derived from the decoder, by means of the Fisher information metric. This architecture has advantages from a theoretical point of view as it provides a direct uncertainty quantification derived from the model, and also accounts for uncertainty cross-correlations. We can show experimentally that the FisherNet produces more accurate data reconstructions than a comparable VAE and its learning performance also apparently scales better with the number of latent space dimensions.