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

• URL: http://arxiv.org/abs/2505.06503v1
• Date: Sat, 10 May 2025 04:14:28 GMT
• Title: Attention Mechanisms in Dynamical Systems: A Case Study with Predator-Prey Models
• Authors: David Balaban,
• Abstract summary: We train a simple linear attention model on time-series data to reconstruct system trajectories.<n>Remarkably, the learned attention weights align with the geometric structure of the Lyapunov function.<n>Results suggest a novel use of AI-derived attention for interpretable, data-driven analysis and control of nonlinear systems.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: 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.

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