arXiv:2607.14937cs.LGcs.AI2026-07

极简模型实现零样本动力系统重建,揭示核心机制。

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

论文配图:A Minimal Interpretable Architecture for Zero-Shot Reconstruction of Dynamical Systems
图 1 · 摘自论文原文
  • 用两个参数线性融合当前状态与最近上下文邻近项进行预测。
  • 在混沌与周期系统上表现接近顶尖模型,参数量少多个数量级。
  • 可直接优化且有解析解,适合研究短期预测与系统重建的差异。

近期用于零样本动力系统(DS)重建的基础模型虽具强跨域泛化能力,但缺乏对预测机制的解释性。为揭示其本质,本文逐步简化当前领先模型DynaMix(Hemmer & Durstewitz, 2025),提炼出一个极简可解释的双参数模型DynaBase。该模型通过线性组合当前隐状态与最近上下文邻居及其时间后继项进行预测。令人惊讶的是,尽管结构极简,DynaBase在混沌与周期系统上仍实现高度竞争性的零样本重建效果,参数量远低于其他基础模型,近乎可忽略。更进一步,其极简性支持基于重建指标的直接模型优化,并能导出预测均方误差的闭式一步解析解。理论与实证分析表明,DynaBase可扩展为一参数映射族,一端恢复了(Zhang & Gilpin, 2026)的上下文复读算法,另一端呈现混沌(发散但有界)行为。我们还揭示不同训练策略可导向短期预测最优或系统重建最优的模型。因此,DynaBase不仅揭示了零样本动力系统重建的最小机制要求,还在统一数学框架下调和了文献中看似矛盾的观测结果。

原文摘要 · Abstract (English)

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.

动力系统零样本可解释性极简模型

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