用神经微分方程构建带吸引子的流场，实现分类任务
Approximating velocity fields with planted attractors via Neural-ODEs for classification purposes
- 在神经微分方程中预设吸引子作为类别标识
- 通过可逼近任意流场的架构塑造动力学景观
- 适合对动态系统建模感兴趣的研究者
本文利用带有精心设计平衡点的神经微分方程完成分类任务。预设的吸引子作为目标类别的指示器，而基于网络架构通用逼近能力的流场则塑造了动力学格局。该过程定义了训练模型的吸引盆，有效引导每个输入（作为初始条件）向其对应的目标位置移动。
原文摘要 · Abstract (English)
In this work, Neural ODEs equipped with a curated collection of equilibrium points have been successfully employed for classification tasks. The planted attractors serve as indicators for the target classes, while the velocity field leveraging the universal approximation capabilities of the architecture shapes the dynamical landscape. This process defines the basins of attraction of the trained model, effectively directing each input (provided as an initial condition) toward its corresponding destination target.
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