arXiv:2505.06503math.DScs.AI2025-05

用注意力机制分析捕食者-猎物系统,发现注意力权重与系统稳定性直接相关。

Attention Mechanisms in Dynamical Systems: A Case Study with Predator-Prey Models

  • 用线性注意力模型从噪声时间序列重建动态轨迹。
  • 注意力高时对应系统稳定区,低时对应敏感扰动区。
  • 无需方程就能通过注意力捕捉相空间关键特性,适合生物建模。

注意力机制在人工智能中广泛用于提升性能与可解释性。本文研究其在经典动力系统建模中的应用,聚焦含噪声的捕食者-猎物(Lotka-Volterra)系统。我们用简单线性注意力模型在受扰时间序列上训练,以重构系统轨迹。惊人的是,学习到的注意力权重与李雅普诺夫函数的几何结构一致:高注意力对应平坦区域(扰动影响小),低注意力对应陡峭区域(扰动影响大)。进一步表明,基于注意力的加权可作为敏感性分析的代理,无需系统方程知识即可捕捉关键相空间性质。结果揭示了人工智能生成注意力在非线性系统可解释性数据驱动分析与控制中的新用途。例如,该框架可支持未来在昼夜节律等生物建模中的应用,以及动态环境下的可解释机器学习。

原文摘要 · Abstract (English)

Attention mechanisms are widely used in artificial intelligence to enhance performance and interpretability. In this paper, we investigate their utility in modeling classical dynamical systems -- specifically, a noisy predator-prey (Lotka-Volterra) system. We train a simple linear attention model on perturbed time-series data to reconstruct system trajectories. Remarkably, the learned attention weights align with the geometric structure of the Lyapunov function: high attention corresponds to flat regions (where perturbations have small effect), and low attention aligns with steep regions (where perturbations have large effect). We further demonstrate that attention-based weighting can serve as a proxy for sensitivity analysis, capturing key phase-space properties without explicit knowledge of the system equations. These results suggest a novel use of AI-derived attention for interpretable, data-driven analysis and control of nonlinear systems. For example our framework could support future work in biological modeling of circadian rhythms, and interpretable machine learning for dynamical environments.

注意力机制动力系统可解释性生物建模

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