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Stability Enhanced Gaussian Process Variational Autoencoders

arXiv 2604.09331 ↗First posted 10 Apr 2026cs.LG cs.SY eess.SYcited by 0

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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.

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References · 15

  1. 2021Geometric Deep Learning: Grids, Groups, Graphs, Geodesics, and Gaugescited by 1,131
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  3. 2016Tutorial on Variational Autoencoderscited by 404
  4. 2015DRAW: A Recurrent Neural Network For Image Generationcited by 190
  5. 2017A Disentangled Recognition and Nonlinear Dynamics Model for Unsupervised Learningcited by 107
  6. 2018Gaussian Process Prior Variational Autoencoderscited by 72
  7. 2018Variational Message Passing with Structured Inference Networkscited by 17
  8. 2024Neural Contractive Dynamical Systemscited by 14
  9. 2020Dissipative Deep Neural Dynamical Systemscited by 12
  10. 2024Learning Neural Contracting Dynamics: Extended Linearization and Global Guaranteescited by 11
  11. 2025Safe Physics-Informed Machine Learning for Dynamics and Controlcited by 9
  12. 2020tvGP-VAE: Tensor-variate Gaussian Process Prior Variational Autoencodercited by 4
3 more
  1. 2022Visual anomaly detection in video by variational autoencodercited by 3
  2. 2024Perspectives on Contractivity in Control, Optimization, and Learningcited by 3
  3. 2023Physics-enhanced Gaussian Process Variational Autoencodercited by 2

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