NeurIPS 2026 Paper Introduces DynaBase, a Minimal 1-Parameter Architecture for Zero-Shot Dynamical System Reconstruction

A new NeurIPS 2026 paper introduces DynaBase, a minimal interpretable architecture designed for the zero-shot reconstruction of dynamical systems (DS). The model reduces a DS foundation model to two core ingredients: a piecewise affine map controlled by a single parameter α, and a context selector that chooses the data point closest to the current state. This design ensures generated dynamics remain close to the context in both temporal and geometrical properties.

Core Mechanism and Regimes

DynaBase reproduces all major dynamical regimes based on the value of α:

• Fixed points: α < 1
• Limit cycles: α = 1
• Chaotic attractors: α > 1

Unlike simpler mechanisms such as context parroting, DynaBase preserves the correct dynamical regime. The authors report 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 short-term predictions, even when run in zero-shot mode.

Training and Implications

Inference and training are extremely cheap. Training can be performed analytically in one step via linear regression on forward-predictions, or through a 1-parameter grid search directly on DS reconstruction objectives. The paper notes that different training mechanisms induce interesting performance differences. The authors argue that DynaBase’s formal simplicity provides a tractable mathematical handle for analyzing, improving, and understanding the performance and training of time series and DS foundation models.