# Information bottleneck for learning the phase space of dynamics from high-dimensional experimental data

arXiv: https://arxiv.org/abs/2604.24662 · HTML: https://mlsanity.com/paper/2604.24662/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 27 of its 81 references that are in the map.
- First posted on arXiv 27 Apr 2026.

## Builds on (most cited first, 27 of 27)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Language Models are Few-Shot Learners](https://mlsanity.com/paper/2005.14165/) (2020)
- [Representation Learning with Contrastive Predictive Coding](https://mlsanity.com/paper/1807.03748/) (2018)
- [Neural Ordinary Differential Equations](https://mlsanity.com/paper/1806.07366/) (2018)
- [Self-Supervised Learning from Images with a Joint-Embedding Predictive Architecture](https://mlsanity.com/paper/2301.08243/) (2023)
- [Deep Variational Information Bottleneck](https://mlsanity.com/paper/1612.00410/) (2016)
- [On Variational Bounds of Mutual Information](https://mlsanity.com/paper/1905.06922/) (2019)
- [Deep learning for universal linear embeddings of nonlinear dynamics](https://mlsanity.com/paper/1712.09707/) (2017)
- [LeWorldModel: Stable End-to-End Joint-Embedding Predictive Architecture from Pixels](https://mlsanity.com/paper/2603.19312/) (2026)
- [LeJEPA: Provable and Scalable Self-Supervised Learning Without the Heuristics](https://mlsanity.com/paper/2511.08544/) (2025)
- [Estimating the intrinsic dimension of datasets by a minimal neighborhood information](https://mlsanity.com/paper/1803.06992/) (2018)
- [Multiscale Simulations of Complex Systems by Learning their Effective Dynamics](https://mlsanity.com/paper/2006.13431/) (2020)
- [Deep learning to discover and predict dynamics on an inertial manifold](https://mlsanity.com/paper/2001.04263/) (2019)
- [Joint Embedding vs Reconstruction: Provable Benefits of Latent Space Prediction for Self Supervised Learning](https://mlsanity.com/paper/2505.12477/) (2025)
- [Multivariate Information Bottleneck](https://mlsanity.com/paper/1301.2270/) (2013)
- [Neural Canonical Transformation with Symplectic Flows](https://mlsanity.com/paper/1910.00024/) (2019)
- [Panda: A pretrained forecast model for chaotic dynamics](https://mlsanity.com/paper/2505.13755/) (2025)
- [Deep Variational Multivariate Information Bottleneck -- A Framework for Variational Losses](https://mlsanity.com/paper/2310.03311/) (2023)
- [Simultaneous Dimensionality Reduction: A Data Efficient Approach for Multimodal Representations Learning](https://mlsanity.com/paper/2310.04458/) (2023)
- [Stacked SVD or SVD stacked? A Random Matrix Theory perspective on data integration](https://mlsanity.com/paper/2507.22170/) (2025)
- [Data efficiency, dimensionality reduction, and the generalized symmetric information bottleneck](https://mlsanity.com/paper/2309.05649/) (2023)
- [Spectral Thresholds in Correlated Spiked Models and Fundamental Limits of Partial Least Squares](https://mlsanity.com/paper/2510.17561/) (2025)
- [Automated, predictive, and interpretable inference of C. elegans escape dynamics](https://mlsanity.com/paper/1809.09321/) (2018)
- [Information theory for dimensionality reduction in dynamical systems](https://mlsanity.com/paper/2312.06608/) (2023)
- [Physics-tailored machine learning reveals unexpected physics in dusty plasmas](https://mlsanity.com/paper/2310.05273/) (2023)
- [Accurate Estimation of Mutual Information in High Dimensional Data](https://mlsanity.com/paper/2506.00330/) (2025)
- [Mutual information and task-relevant latent dimensionality](https://mlsanity.com/paper/2602.08105/) (2026)

## Built on by (most cited first, 1 of 1)

- [Contrast encodes inductive bias: separating slow noise from dynamics in predictive representation learning](https://mlsanity.com/paper/2606.07770/) (2026)

## Abstract (arXiv)

Identifying the dynamical state variables of a system from high-dimensional observations is a central problem across physical sciences. The challenge is that the state variables are not directly observable and must be inferred from raw high-dimensional data without supervision. Here we introduce DySIB (Dynamical Symmetric Information Bottleneck) as a method to learn low-dimensional representations of time-series data by maximizing predictive mutual information between past and future observation windows while penalizing representation complexity. This objective operates entirely in latent space and avoids reconstruction of the observations. We apply DySIB to an experimental video dataset of a physical pendulum, where the underlying state space is known. The method, with hyperparameters of the learning architecture set self-consistently by the data, recovers a two-dimensional representation that matches the dimensionality, topology, and geometry of the pendulum phase space, with the learned coordinates aligning smoothly with the canonical angle and angular velocity. These results demonstrate, on a well-characterized experimental system, that predictive information in latent space can be used to recover interpretable dynamical coordinates directly from high-dimensional data.