# Hyperspherical Variational Auto-Encoders

arXiv: https://arxiv.org/abs/1804.00891 · HTML: https://mlsanity.com/paper/1804.00891/

## Key facts

- Cited by 189 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 3 Apr 2018.

## Built on by (most cited first, 30 of 189)

- [Neural Bellman-Ford Networks: A General Graph Neural Network Framework for Link Prediction](https://mlsanity.com/paper/2106.06935/) (2021)
- [Diffusion Models for Medical Image Analysis: A Comprehensive Survey](https://mlsanity.com/paper/2211.07804/) (2022)
- [Hyperbolic Deep Neural Networks: A Survey](https://mlsanity.com/paper/2101.04562/) (2021)
- [Priors in Bayesian Deep Learning: A Review](https://mlsanity.com/paper/2105.06868/) (2021)
- [Waffling around for Performance: Visual Classification with Random Words and Broad Concepts](https://mlsanity.com/paper/2306.07282/) (2023)
- [Learning from Counterfactual Links for Link Prediction](https://mlsanity.com/paper/2106.02172/) (2021)
- [SQ-VAE: Variational Bayes on Discrete Representation with Self-annealed Stochastic Quantization](https://mlsanity.com/paper/2205.07547/) (2022)
- [Unifying Diffusion Models' Latent Space, with Applications to CycleDiffusion and Guidance](https://mlsanity.com/paper/2210.05559/) (2022)
- [von Mises-Fisher Loss: An Exploration of Embedding Geometries for Supervised Learning](https://mlsanity.com/paper/2103.15718/) (2021)
- [Linkless Link Prediction via Relational Distillation](https://mlsanity.com/paper/2210.05801/) (2022)
- [Energy-Based Sliced Wasserstein Distance](https://mlsanity.com/paper/2304.13586/) (2023)
- [Learning with Hyperspherical Uniformity](https://mlsanity.com/paper/2103.01649/) (2021)
- [Spherical Sliced-Wasserstein](https://mlsanity.com/paper/2206.08780/) (2022)
- [Pseudo-Riemannian Graph Convolutional Networks](https://mlsanity.com/paper/2106.03134/) (2021)
- [Probabilistic Contrastive Learning Recovers the Correct Aleatoric Uncertainty of Ambiguous Inputs](https://mlsanity.com/paper/2302.02865/) (2023)
- [Data Augmentation in High Dimensional Low Sample Size Setting Using a Geometry-Based Variational Autoencoder](https://mlsanity.com/paper/2105.00026/) (2021)
- [Autoencoding Under Normalization Constraints](https://mlsanity.com/paper/2105.05735/) (2021)
- [Pythae: Unifying Generative Autoencoders in Python -- A Benchmarking Use Case](https://mlsanity.com/paper/2206.08309/) (2022)
- [A Geometric Perspective on Variational Autoencoders](https://mlsanity.com/paper/2209.07370/) (2022)
- [Pulling back information geometry](https://mlsanity.com/paper/2106.05367/) (2021)
- [SphereFace Revived: Unifying Hyperspherical Face Recognition](https://mlsanity.com/paper/2109.05565/) (2021)
- [MaGNET: Uniform Sampling from Deep Generative Network Manifolds Without Retraining](https://mlsanity.com/paper/2110.08009/) (2021)
- [A survey on Variational Autoencoders from a GreenAI perspective](https://mlsanity.com/paper/2103.01071/) (2021)
- [Representation Uncertainty in Self-Supervised Learning as Variational Inference](https://mlsanity.com/paper/2203.11437/) (2022)
- [Language Modeling with Hyperspherical Flows](https://mlsanity.com/paper/2605.11125/) (2026)
- [Manifold Integrated Gradients: Riemannian Geometry for Feature Attribution](https://mlsanity.com/paper/2405.09800/) (2024)
- [Beyond Euclid: An Illustrated Guide to Modern Machine Learning with Geometric, Topological, and Algebraic Structures](https://mlsanity.com/paper/2407.09468/) (2024)
- [A Non-isotropic Probabilistic Take on Proxy-based Deep Metric Learning](https://mlsanity.com/paper/2207.03784/) (2022)
- [Geodesic Graph Neural Network for Efficient Graph Representation Learning](https://mlsanity.com/paper/2210.02636/) (2022)
- [Energy-Based Models for Anomaly Detection: A Manifold Diffusion Recovery Approach](https://mlsanity.com/paper/2310.18677/) (2023)

## Abstract (arXiv)

The Variational Auto-Encoder (VAE) is one of the most used unsupervised machine learning models. But although the default choice of a Gaussian distribution for both the prior and posterior represents a mathematically convenient distribution often leading to competitive results, we show that this parameterization fails to model data with a latent hyperspherical structure. To address this issue we propose using a von Mises-Fisher (vMF) distribution instead, leading to a hyperspherical latent space. Through a series of experiments we show how such a hyperspherical VAE, or S-VAE, is more suitable for capturing data with a hyperspherical latent structure, while outperforming a normal, N-VAE, in low dimensions on other data types. Code at http://github.com/nicola-decao/s-vae-tf and https://github.com/nicola-decao/s-vae-pytorch