# Latent Representation and Simulation of Markov Processes via Time-Lagged Information Bottleneck

arXiv: https://arxiv.org/abs/2309.07200 · HTML: https://mlsanity.com/paper/2309.07200/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Builds on 37 of its 78 references that are in the map.
- First posted on arXiv 13 Sep 2023.

## Builds on (most cited first, 30 of 37)

- [BERT: Pre-training of Deep Bidirectional Transformers for Language Understanding](https://mlsanity.com/paper/1810.04805/) (2018)
- [A Simple Framework for Contrastive Learning of Visual Representations](https://mlsanity.com/paper/2002.05709/) (2020)
- [Representation Learning with Contrastive Predictive Coding](https://mlsanity.com/paper/1807.03748/) (2018)
- [Group Normalization](https://mlsanity.com/paper/1803.08494/) (2018)
- [Variational Graph Auto-Encoders](https://mlsanity.com/paper/1611.07308/) (2016)
- [Learning deep representations by mutual information estimation and maximization](https://mlsanity.com/paper/1808.06670/) (2018)
- [Deep Graph Infomax](https://mlsanity.com/paper/1809.10341/) (2018)
- [Deep Variational Information Bottleneck](https://mlsanity.com/paper/1612.00410/) (2016)
- [Deep Learning and the Information Bottleneck Principle](https://mlsanity.com/paper/1503.02406/) (2015)
- [On Variational Bounds of Mutual Information](https://mlsanity.com/paper/1905.06922/) (2019)
- [Time Series Forecasting With Deep Learning: A Survey](https://mlsanity.com/paper/2004.13408/) (2020)
- [Flow++: Improving Flow-Based Generative Models with Variational Dequantization and Architecture Design](https://mlsanity.com/paper/1902.00275/) (2019)
- [Learning Robust Representations via Multi-View Information Bottleneck](https://mlsanity.com/paper/2002.07017/) (2020)
- [Formal Limitations on the Measurement of Mutual Information](https://mlsanity.com/paper/1811.04251/) (2018)
- [TorchMD-NET: Equivariant Transformers for Neural Network based Molecular Potentials](https://mlsanity.com/paper/2202.02541/) (2022)
- [Contrastive Learning of General-Purpose Audio Representations](https://mlsanity.com/paper/2010.10915/) (2020)
- [Earthformer: Exploring Space-Time Transformers for Earth System Forecasting](https://mlsanity.com/paper/2207.05833/) (2022)
- [Understanding the Limitations of Variational Mutual Information Estimators](https://mlsanity.com/paper/1910.06222/) (2019)
- [VAMPnets: Deep learning of molecular kinetics](https://mlsanity.com/paper/1710.06012/) (2017)
- [Understanding LSTM -- a tutorial into Long Short-Term Memory Recurrent Neural Networks](https://mlsanity.com/paper/1909.09586/) (2019)
- [The Conditional Entropy Bottleneck](https://mlsanity.com/paper/2002.05379/) (2020)
- [Two for One: Diffusion Models and Force Fields for Coarse-Grained Molecular Dynamics](https://mlsanity.com/paper/2302.00600/) (2023)
- [Machine Learning of coarse-grained Molecular Dynamics Force Fields](https://mlsanity.com/paper/1812.01736/) (2018)
- [Timewarp: Transferable Acceleration of Molecular Dynamics by Learning Time-Coarsened Dynamics](https://mlsanity.com/paper/2302.01170/) (2023)
- [Time-lagged autoencoders: Deep learning of slow collective variables for molecular kinetics](https://mlsanity.com/paper/1710.11239/) (2017)
- [Variational approach for learning Markov processes from time series data](https://mlsanity.com/paper/1707.04659/) (2017)
- [Deeptime: a Python library for machine learning dynamical models from time series data](https://mlsanity.com/paper/2110.15013/) (2021)
- [Understanding Latent Correlation-Based Multiview Learning and Self-Supervision: An Identifiability Perspective](https://mlsanity.com/paper/2106.07115/) (2021)
- [Flow-matching -- efficient coarse-graining of molecular dynamics without forces](https://mlsanity.com/paper/2203.11167/) (2022)
- [Variational Encoding of Complex Dynamics](https://mlsanity.com/paper/1711.08576/) (2017)

## Built on by (most cited first, 6 of 6)

- [Self-Supervised Evolution Operator Learning for High-Dimensional Dynamical Systems](https://mlsanity.com/paper/2505.18671/) (2025)
- [Information Shapes Koopman Representation](https://mlsanity.com/paper/2510.13025/) (2025)
- [Predicting the Energy Landscape of Stochastic Dynamical System via Physics-informed Self-supervised Learning](https://mlsanity.com/paper/2502.16828/) (2025)
- [InfoDPCCA: Information-Theoretic Dynamic Probabilistic Canonical Correlation Analysis](https://mlsanity.com/paper/2506.08884/) (2025)
- [Tracking Temporal Dynamics of Vector Sets with Gaussian Process](https://mlsanity.com/paper/2512.15538/) (2025)
- [Score the Algebra, Not the Span: Dimension Reduction for Transfer Operator Models of Dynamical Systems](https://mlsanity.com/paper/2608.18918/) (2026)

## Abstract (arXiv)

Markov processes are widely used mathematical models for describing dynamic systems in various fields. However, accurately simulating large-scale systems at long time scales is computationally expensive due to the short time steps required for accurate integration. In this paper, we introduce an inference process that maps complex systems into a simplified representational space and models large jumps in time. To achieve this, we propose Time-lagged Information Bottleneck (T-IB), a principled objective rooted in information theory, which aims to capture relevant temporal features while discarding high-frequency information to simplify the simulation task and minimize the inference error. Our experiments demonstrate that T-IB learns information-optimal representations for accurately modeling the statistical properties and dynamics of the original process at a selected time lag, outperforming existing time-lagged dimensionality reduction methods.