# Capabilities and Limitations of Time-lagged Autoencoders for Slow Mode Discovery in Dynamical Systems

arXiv: https://arxiv.org/abs/1906.00325 · HTML: https://mlsanity.com/paper/1906.00325/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 2 Jun 2019.

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

- [Latent Representation and Simulation of Markov Processes via Time-Lagged Information Bottleneck](https://mlsanity.com/paper/2309.07200/) (2023)
- [Variational embedding of protein folding simulations using gaussian mixture variational autoencoders](https://mlsanity.com/paper/2108.12493/) (2021)
- [Understanding recent deep-learning techniques for identifying collective variables of molecular dynamics](https://mlsanity.com/paper/2307.00365/) (2023)
- [Machine Learning of Slow Collective Variables and Enhanced Sampling via Spatial Techniques](https://mlsanity.com/paper/2412.20868/) (2024)
- [A Functional approach for Two Way Dimension Reduction in Time Series](https://mlsanity.com/paper/2301.00357/) (2023)

## Abstract (arXiv)

Time-lagged autoencoders (TAEs) have been proposed as a deep learning regression-based approach to the discovery of slow modes in dynamical systems. However, a rigorous analysis of nonlinear TAEs remains lacking. In this work, we discuss the capabilities and limitations of TAEs through both theoretical and numerical analyses. Theoretically, we derive bounds for nonlinear TAE performance in slow mode discovery and show that in general TAEs learn a mixture of slow and maximum variance modes. Numerically, we illustrate cases where TAEs can and cannot correctly identify the leading slowest mode in two example systems: a 2D "Washington beltway" potential and the alanine dipeptide molecule in explicit water. We also compare the TAE results with those obtained using state-free reversible VAMPnets (SRVs) as a variational-based neural network approach for slow modes discovery, and show that SRVs can correctly discover slow modes where TAEs fail.