# Stability Enhanced Gaussian Process Variational Autoencoders

arXiv: https://arxiv.org/abs/2604.09331 · HTML: https://mlsanity.com/paper/2604.09331/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 15 of its 37 references that are in the map.
- First posted on arXiv 10 Apr 2026.

## Builds on (most cited first, 15 of 15)

- [Geometric Deep Learning: Grids, Groups, Graphs, Geodesics, and Gauges](https://mlsanity.com/paper/2104.13478/) (2021)
- [End-to-End Training of Deep Visuomotor Policies](https://mlsanity.com/paper/1504.00702/) (2015)
- [Tutorial on Variational Autoencoders](https://mlsanity.com/paper/1606.05908/) (2016)
- [DRAW: A Recurrent Neural Network For Image Generation](https://mlsanity.com/paper/1502.04623/) (2015)
- [A Disentangled Recognition and Nonlinear Dynamics Model for Unsupervised Learning](https://mlsanity.com/paper/1710.05741/) (2017)
- [Gaussian Process Prior Variational Autoencoders](https://mlsanity.com/paper/1810.11738/) (2018)
- [Variational Message Passing with Structured Inference Networks](https://mlsanity.com/paper/1803.05589/) (2018)
- [Neural Contractive Dynamical Systems](https://mlsanity.com/paper/2401.09352/) (2024)
- [Dissipative Deep Neural Dynamical Systems](https://mlsanity.com/paper/2011.13492/) (2020)
- [Learning Neural Contracting Dynamics: Extended Linearization and Global Guarantees](https://mlsanity.com/paper/2402.08090/) (2024)
- [Safe Physics-Informed Machine Learning for Dynamics and Control](https://mlsanity.com/paper/2504.12952/) (2025)
- [tvGP-VAE: Tensor-variate Gaussian Process Prior Variational Autoencoder](https://mlsanity.com/paper/2006.04788/) (2020)
- [Visual anomaly detection in video by variational autoencoder](https://mlsanity.com/paper/2203.03872/) (2022)
- [Perspectives on Contractivity in Control, Optimization, and Learning](https://mlsanity.com/paper/2404.11707/) (2024)
- [Physics-enhanced Gaussian Process Variational Autoencoder](https://mlsanity.com/paper/2305.09006/) (2023)

## Abstract (arXiv)

A novel stability-enhanced Gaussian process variational autoencoder (SEGP-VAE) is proposed for indirectly training a low-dimensional linear time invariant (LTI) system, using high-dimensional video data. The mean and covariance function of the novel SEGP prior are derived from the definition of an LTI system, enabling the SEGP to capture the indirectly observed latent process using a combined probabilistic and interpretable physical model. The search space of LTI parameters is restricted to the set of semi-contracting systems via a complete and unconstrained parametrisation. As a result, the SEGP-VAE can be trained using unconstrained optimisation algorithms. Furthermore, this parametrisation prevents numerical issues caused by the presence of a non-Hurwitz state matrix. A case study applies SEGP-VAE to a dataset containing videos of spiralling particles. This highlights the benefits of the approach and the application-specific design choices that enabled accurate latent state predictions.