A Minimal Interpretable Architecture for Zero-Shot Reconstruction of Dynamical Systems [R]

In our #NeurIPS2026 paper “A Minimal Interpretable Architecture for Zero-Shot Reconstruction of Dynamical Systems (DS)” (preprint: arxiv.org/abs/2607.14937 ) we reduce a DS foundation model to the ingredients minimally necessary to faithfully reproduce long-term statistical and geometrical properties of DS : 1) A piecewise affine map with only a single (!!) parameter α that controls local con-/divergence rates, and … 2) … a context selector that chooses from the provided context signal the data point closest to the current state of the map, thus ensuring the generated dynamics stays close to the context in its temporal and geometrical properties. With just these two mechanisms, this minimal form – which we coined DynaBase – can reproduce all major dynamical regimes , including fixed points (α<1), limit cycles (α=1), and chaotic attractors (α>1). Thus, unlike other simple mechanisms like context parroting, DynaBase even preserves the correct dynamical regime ! Surprisingly, it turns out that this simple context-driven 1-parameter map outperforms most major time series and DS foundation models , as well as custom-trained models, in both long-term statistics and even short-term predictions, even when run in zero-shot mode . Both inference and training are extremely cheap – training can be done either analytically in one step by linear regression on forward-predictions, or by 1-parameter grid search directly on DS reconstruction objectives → this reveals interesting performance differences induced by different training mechanisms. Most importantly in our minds, DynaBase owing to its formal simplicity may thus provide a tractable mathematical handle on analyzing, improving & understanding the performance and training of some time series and DS foundation models. preview.redd.it/jmlcnocq5gth1.png