Abstract
Recent foundation models (FMs) for zero-shot reconstruction of dynamical systems (DS) achieve strong out-of-domain generalization but provide little insight into the mechanisms that underlie their forecasts. Such understanding could help strip down overladen FM architectures to their bare essence and expose the minimal requirements for in-context learning in the DS domain.
Toward this goal, we iteratively reduce a recent powerful SOTA model for DS reconstruction, DynaMix, to a minimal interpretable two-parameter form, which we call DynaBase.
DynaBase produces forecasts through a linear blend of the current latent state and the nearest in-context neighbor and its temporal successor. Surprisingly, despite its extreme simplicity, DynaBase produces highly competitive zero-shot DS reconstructions across chaotic and cyclic systems, with a negligible parameter load, many orders of magnitude below that of other FMs.
Furthermore, this extreme simplicity permits direct model optimization on DS reconstruction measures, as well as closed-form one-step analytical solutions on prediction MSE.
Theoretical and empirical analysis of DynaBase further leads to a 1-parameter family of maps, with the context-parroting algorithm of (Zhang & Gilpin, 2026) recovered at one end, and chaotic (divergent but bounded) behavior at the other. We also show how different training strategies lead to models either optimal for short-term prediction or for DS reconstruction.
Thus, DynaBase not only exposes the minimal mechanisms required for producing zero-shot DS reconstruction but also reconciles divergent observations in the literature within an accessible mathematical frame.
Blogger's Review: The introduction of DynaBase simplifies the reconstruction of dynamic systems and provides new insights into understanding complex models. In practical applications, such a minimalist architecture may yield higher efficiency and interpretability, warranting further exploration and implementation.