# Latent Representations of Dynamical Systems: When Two is Better Than One

arXiv: https://arxiv.org/abs/1902.03364 · HTML: https://mlsanity.com/paper/1902.03364/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 9 Feb 2019.

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

- [AI-Newton: A Concept-Driven Physical Law Discovery System without Prior Physical Knowledge](https://mlsanity.com/paper/2504.01538/) (2025)

## Abstract (arXiv)

A popular approach for predicting the future of dynamical systems involves mapping them into a lower-dimensional "latent space" where prediction is easier. We show that the information-theoretically optimal approach uses different mappings for present and future, in contrast to state-of-the-art machine-learning approaches where both mappings are the same. We illustrate this dichotomy by predicting the time-evolution of coupled harmonic oscillators with dissipation and thermal noise, showing how the optimal 2-mapping method significantly outperforms principal component analysis and all other approaches that use a single latent representation, and discuss the intuitive reason why two representations are better than one. We conjecture that a single latent representation is optimal only for time-reversible processes, not for e.g. text, speech, music or out-of-equilibrium physical systems.