Approximating velocity fields with planted attractors via Neural-ODEs for classification purposes
2026-06-22 • Machine Learning
Machine Learning
AI summaryⓘ
The authors use a special type of neural network called Neural ODEs that can model continuous changes over time. They add specific stable points called attractors that represent different classes to help the model decide what category an input belongs to. The underlying system moves inputs toward these attractors, effectively sorting them into groups based on where they end up. This approach leverages both the stability of attractors and the flexibility of Neural ODEs for classification.
Neural ODEsEquilibrium PointsAttractorsVelocity FieldBasins of AttractionClassificationDynamical SystemsUniversal ApproximationInitial Conditions
Authors
Feliciano Giuseppe Pacifico, Duccio Fanelli, Lorenzo Buffoni, Lorenzo Chicchi, Diego Febbe, Raffaele Marino
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.