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

Feliciano Giuseppe Pacifico; Duccio Fanelli; Lorenzo Buffoni; Lorenzo Chicchi; Diego Febbe; Raffaele Marino

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arXiv · 2606.23550

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

Feliciano Giuseppe Pacifico·Duccio Fanelli·Lorenzo Buffoni·Lorenzo Chicchi·Diego Febbe·Raffaele Marino

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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.

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cond-mat.dis-nn cs.LG

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Feliciano Giuseppe Pacifico, Duccio Fanelli, Lorenzo Buffoni, Lorenzo Chicchi, Diego Febbe, Raffaele Marino. 2026-06-22. Approximating velocity fields with planted attractors via Neural-ODEs for classification purposes. https://arxiv.org/abs/2606.23550

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