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

NeurIPS 2026 · Label-efficient and robust learning › Zero-/few-shot and meta-learning · approach: Robust fine-tuning of zero-shot models · 0 citations (OpenAlex)

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Reduces the DynaMix zero-shot dynamical-systems reconstruction foundation model to a two-parameter nearest-neighbor affine map (DynaBase), showing competitive zero-shot reconstruction and linking it to context parroting.

Problem

Zero-shot dynamical systems reconstruction (DSR) foundation models such as DynaMix achieve strong out-of-domain generalization, but their mechanisms and essential architectural requirements are opaque.

Approach

Iteratively simplify DynaMix into a recursive affine nearest-neighbor map; impose O(N) rotation/reflection equivariance, translation equivariance, and a self-consistency condition to get a 2-parameter (later 1-parameter) map, DynaBase, that blends the current state with the nearest context point and its successor.

Key results

• DynaBase with DSR-optimized alpha achieves better long-term D_stsp than the ahead-prediction-trained variant, with comparable performance to custom-trained DSR baselines (zero-shot alpha=1.006 performs comparably).
• Linear-regression-trained DynaBase gives lower MASE at n=10 (0.13) and n=50 (0.51) than DSR-trained variants, while DSR-trained alpha concentrates near 1.01 with Lyapunov exponent correlation r≈0.90 vs ≈0.18 for least squares.
• Context parroting is recovered exactly at alpha=0 on a delay-embedded context, which cannot produce chaos.

Surprising findings

• A two-parameter nearest-neighbor affine map with a single fixed alpha (~1.006) performs comparably to custom-trained DSR models and to DynaMix in zero-shot mode.
• Least-squares one-step training yields alpha<1 and fails to capture chaos (Lyapunov correlation ~0.18), whereas DSR-objective training recovers chaotic dynamics.

Limitations

• Assumptions of the reduction limit the diversity of dynamical systems and vector field topologies that can be captured.
• Geometric accuracy of the vector field is limited, with visible mismatch in reconstructions.
• Noise effects were only examined qualitatively; the paper is currently more a research tool than a practical forecaster.

Experimental setup

Datasets: 54 test 3d dynamical systems from prior DSR benchmark 30 chaotic DS training set Lorenz-63 Selkov system chaotic laser system

Benchmarks: 54 test DS DSR benchmark (D_stsp, D_H, MASE)

Metrics: D_stsp D_H (Hellinger distance of power spectra) MASE (n=10) Lyapunov exponent correlation

Baselines: DynaMix Chronos-T5-base Chronos-2 context parroting AL-RNN Neural ODE reservoir computer

Builds on: DynaMix AL-RNN context parroting Chronos

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