用于动态系统零样本重建的最小可解释架构
A Minimal Interpretable Architecture for Zero-Shot Reconstruction of Dynamical Systems
- Central Institute of Mental Health, Mannheim, Germany（德国曼海姆中央精神卫生研究所）
- Interdisciplinary Center for Scientific Computing (IWR), Heidelberg, Germany（德国海德堡跨学科科学计算中心 (IWR)）
- Faculty of Physics and Astronomy, Heidelberg University, Heidelberg, Germany（德国海德堡大学物理与天文学系）
机构由 AI 辅助整理，请以论文原文为准。
中文总结 AI 辅助
研究针对动态系统零样本重建基础模型缺乏预测机制洞察的问题，将DynaMix简化为DynaBase，其通过简单线性混合预测，参数负载低，表现出色，还得出映射族及不同训练策略效果，揭示最小机制并协调文献观察。
中文摘要 AI 辅助
近期用于动态系统零样本重建的基础模型虽有强大的域外泛化能力，但对预测机制缺乏洞察。为此，本文将强大的SOTA模型DynaMix迭代简化为最小可解释的双参数形式DynaBase。它通过当前潜在状态与最近上下文邻居及其时间后继的线性混合进行预测。尽管简单，却在零样本动态系统重建中表现出色，参数负载极低。理论和实证分析还得出了一个单参数映射族，展示了不同训练策略如何导致适用于短期预测或动态系统重建的模型。DynaBase不仅揭示了零样本动态系统重建所需的最小机制，还在可及的数学框架内协调了文献中的不同观察结果。
英文摘要
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 an understanding could help to 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, here we iteratively reduce a recent powerful SOTA model for DS reconstruction, DynaMix (Hemmer & Durstewitz, 2025), 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. Even more, 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 further 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 within an accessible mathematical frame divergent observations in the literature.
