Autoregressive transformers predict complex chaos from limited data
Learning Chaos Without Seeing Chaos: Extrapolation of Global Dynamics in Autoregressive Transformers
Machine Learning
Summary
Understanding how complex systems behave over time can be really hard, especially when we only have small pieces of information. The authors trained a type of neural network called an autoregressive transformer on short sequences from simple chaotic systems, like the logistic map and the Lorenz system. Surprisingly, even when tested on situations very different from the training examples, these models could recreate complicated patterns of chaos and order that happen in those systems. This suggests that these models can learn deep global behaviors from very limited local observations.
What this means in practice
- •For control system engineers: Predict system-wide behavior using small sets of observations for systems with unknown global dynamics.
- •For weather modelers: Use autoregressive transformers to extrapolate chaotic weather patterns beyond traditional simulation parameters.
Tested on simulated data.
Authors
Yilun Liu, Yi Zhang, Ganyu Wu, Sikuan Yan, Mengyue Wang, Alois Knoll, Volker Tresp, Yunpu Ma
Abstract
Autoregressive models are trained to predict a system's behavior one step at a time, and recursive generation allows the learned dynamics to unfold over long horizons. To what extent can such dynamics learned from local observations recover broader organization of an underlying system that was only partially observed during training? Here we study small autoregressive transformers trained from scratch on trajectories sampled from restricted parameter regimes of several non-linear dynamical systems, including logistic and sine maps, the Lorenz system, and the generalized Hopf system, with control parameters and state trajectories represented as sequences of continuous tokens. Under closed-loop evaluation at parameters far outside the training distribution, the models can recover self-similar period-doubling cascades, chaotic dynamics, and attractor structures with remarkable visual and numerical fidelity. For the logistic map, a transformer reproduces successive period doublings up to period 128, yielding a finite-order scaling ratio of 4.6687, matching the Feigenbaum constant to within $5\times10^{-4}$. We further investigate how these structures emerge over the course of training, and reveal with causal interventions how control-parameter information is processed through attention into state prediction and shapes the resulting closed-loop dynamics. These results suggest that a surprisingly narrow window into a system's local behavior may suffice for autoregressive transformers to generalize to its unseen global dynamical organization.