ICLR 2025

Published as a conference paper at ICLR 2025
IDENTIFYING LATENT STATE TRANSITIONS IN
NON-LINEAR DYNAMICAL SYSTEMS
C¸ a˘glar Hızlı
Aalto University
caglar.hizli@aalto.fi
C¸ a˘gatay Yıldız
University of T¨ubingen
T¨ubingen AI Center
Matthias Bethge
University of T¨ubingen
T¨ubingen AI Center
ST John
Aalto University
Pekka Marttinen
Aalto University
ABSTRACT
This work aims to recover the underlying states and their time evolution in a
latent dynamical system from high-dimensional sensory measurements. Previous
works on identifiable representation learning in dynamical systems focused on
identifying the latent states, often with linear transition approximations. As such,
they cannot identify nonlinear transition dynamics, and hence fail to reliably
predict complex future behavior. Inspired by the advances in nonlinear ICA, we
propose a state-space modeling framework in which we can identify not just
the latent states but also the unknown transition function that maps the past
states to the present. Our identifiability theory relies on two key assumptions: (i)
sufficient variability in the latent noise, and (ii) the bijectivity of the augmented
transition function. Drawing from this theory, we introduce a practical algorithm
based on variational auto-encoders. We empirically demonstrate that it improves
generalization and interpretability of target dynamical systems by (i) recovering
latent state dynamics with high accuracy, (ii) correspondingly achieving high future
prediction accuracy, and (iii) adapting fast to new environments. Additionally, for
complex real-world dynamics, (iv) it produces state-of-the-art future prediction
results for long horizons, highlighting its usefulness for practical scenarios.
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INTRODUCTION
We focus on the problem of understanding the underlying states of a dynamical system from its
high-dimensional sensory measurements. This task is prevalent across various fields, including
reinforcement learning (Hafner et al., 2019a) and robotics (Levi...