# From latent dynamics to meaningful representations

arXiv: https://arxiv.org/abs/2209.00905 · HTML: https://mlsanity.com/paper/2209.00905/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 29 of its 67 references that are in the map.
- First posted on arXiv 2 Sep 2022.

## Builds on (most cited first, 29 of 29)

- [An Introduction to Variational Autoencoders](https://mlsanity.com/paper/1906.02691/) (2019)
- [Challenging Common Assumptions in the Unsupervised Learning of Disentangled Representations](https://mlsanity.com/paper/1811.12359/) (2018)
- [Deep Variational Information Bottleneck](https://mlsanity.com/paper/1612.00410/) (2016)
- [Hamiltonian Neural Networks](https://mlsanity.com/paper/1906.01563/) (2019)
- [Variational Autoencoders and Nonlinear ICA: A Unifying Framework](https://mlsanity.com/paper/1907.04809/) (2019)
- [Lagrangian Neural Networks](https://mlsanity.com/paper/2003.04630/) (2020)
- [Wasserstein Auto-Encoders](https://mlsanity.com/paper/1711.01558/) (2017)
- [A Recurrent Latent Variable Model for Sequential Data](https://mlsanity.com/paper/1506.02216/) (2015)
- [Unsupervised Feature Extraction by Time-Contrastive Learning and Nonlinear ICA](https://mlsanity.com/paper/1605.06336/) (2016)
- [Physics-Constrained Deep Learning for High-dimensional Surrogate Modeling and Uncertainty Quantification without Labeled Data](https://mlsanity.com/paper/1901.06314/) (2019)
- [VAE with a VampPrior](https://mlsanity.com/paper/1705.07120/) (2017)
- [Deep Unsupervised Clustering with Gaussian Mixture Variational Autoencoders](https://mlsanity.com/paper/1611.02648/) (2016)
- [Deep Lagrangian Networks: Using Physics as Model Prior for Deep Learning](https://mlsanity.com/paper/1907.04490/) (2019)
- [ChemRL-GEM: Geometry Enhanced Molecular Representation Learning for Property Prediction](https://mlsanity.com/paper/2106.06130/) (2021)
- [Variational Lossy Autoencoder](https://mlsanity.com/paper/1611.02731/) (2016)
- [Hamiltonian Generative Networks](https://mlsanity.com/paper/1909.13789/) (2019)
- [Recent Advances in Autoencoder-Based Representation Learning](https://mlsanity.com/paper/1812.05069/) (2018)
- [Dynamical Variational Autoencoders: A Comprehensive Review](https://mlsanity.com/paper/2008.12595/) (2020)
- [Disentangled Sequential Autoencoder](https://mlsanity.com/paper/1803.02991/) (2018)
- [Unsupervised Learning of Disentangled and Interpretable Representations from Sequential Data](https://mlsanity.com/paper/1709.07902/) (2017)
- [Hidden Markov Nonlinear ICA: Unsupervised Learning from Nonstationary Time Series](https://mlsanity.com/paper/2006.12107/) (2020)
- [Variational Integrator Networks for Physically Structured Embeddings](https://mlsanity.com/paper/1910.09349/) (2019)
- [Distribution Matching in Variational Inference](https://mlsanity.com/paper/1802.06847/) (2018)
- [Identifying Latent Stochastic Differential Equations](https://mlsanity.com/paper/2007.06075/) (2020)
- [Independent Innovation Analysis for Nonlinear Vector Autoregressive Process](https://mlsanity.com/paper/2006.10944/) (2020)
- [A Commentary on the Unsupervised Learning of Disentangled Representations](https://mlsanity.com/paper/2007.14184/) (2020)
- [Physics-aware, probabilistic model order reduction with guaranteed stability](https://mlsanity.com/paper/2101.05834/) (2021)
- [Hamiltonian latent operators for content and motion disentanglement in image sequences](https://mlsanity.com/paper/2112.01641/) (2021)
- [Finding simplicity: unsupervised discovery of features, patterns, and order parameters via shift-invariant variational autoencoders](https://mlsanity.com/paper/2106.12472/) (2021)

## Built on by (most cited first, 5 of 5)

- [Automated Scientific Discovery: From Equation Discovery to Autonomous Discovery Systems](https://mlsanity.com/paper/2305.02251/) (2023)
- [Transferable Generative Models Bridge Femtosecond to Nanosecond Time-Step Molecular Dynamics](https://mlsanity.com/paper/2510.07589/) (2025)
- [Flow Matching for Optimal Reaction Coordinates of Biomolecular System](https://mlsanity.com/paper/2408.17139/) (2024)
- [Neumann eigenmaps for landmark embedding](https://mlsanity.com/paper/2502.06689/) (2025)
- [AtomWorld-Mem: Memory-Restored World States for Long-Horizon Atomistic Evolution](https://mlsanity.com/paper/2609.31133/) (2026)

## Abstract (arXiv)

While representation learning has been central to the rise of machine learning and artificial intelligence, a key problem remains in making the learned representations meaningful. For this, the typical approach is to regularize the learned representation through prior probability distributions. However, such priors are usually unavailable or are ad hoc. To deal with this, recent efforts have shifted towards leveraging the insights from physical principles to guide the learning process. In this spirit, we propose a purely dynamics-constrained representation learning framework. Instead of relying on predefined probabilities, we restrict the latent representation to follow overdamped Langevin dynamics with a learnable transition density - a prior driven by statistical mechanics. We show this is a more natural constraint for representation learning in stochastic dynamical systems, with the crucial ability to uniquely identify the ground truth representation. We validate our framework for different systems including a real-world fluorescent DNA movie dataset. We show that our algorithm can uniquely identify orthogonal, isometric and meaningful latent representations.