Approximating velocity fields with planted attractors via Neural-ODEs for classification purposes

2026-06-22

AI Summary

This work proposes an interpretable classification method grounded in the attractor structure of dynamical systems. By embedding predefined stable equilibrium points—each representing a distinct class—as attractors within a Neural Ordinary Differential Equation (Neural ODE), the approach constructs a velocity field with well-defined basins of attraction. Input data, treated as initial conditions, evolve along this vector field and converge to the attractor corresponding to their class label. This is the first method to integrate prespecified attractors with Neural ODEs for classification, leveraging the universal approximation capacity of deep networks to learn appropriate dynamics that render the decision process interpretable through the lens of dynamical systems theory. Experiments demonstrate that the model reliably guides inputs to their target attractors, achieving competitive performance while offering a transparent and mechanistically clear classification framework.

Abstract

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.

Problem

• Neural ODEs
• attractors
• classification
• velocity fields
• basins of attraction

Innovation

• Neural ODEs
• planted attractors
• classification
• velocity field
• basins of attraction