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.
@article{arxiv.1902.03364,
title = {Latent Representations of Dynamical Systems: When Two is Better Than One},
author = {Max Tegmark},
journal= {arXiv preprint arXiv:1902.03364},
year = {2019}
}
Comments
Improved references and explanation of why two representations generally outperform one for time-irreversible processes. 6 pages, 4 figs