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PreprintCC BY 4.0arXiv

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

  • Feliciano Giuseppe Pacifico
  • Duccio Fanelli
  • Lorenzo Buffoni
  • Lorenzo Chicchi
  • Diego Febbe
  • Raffaele Marino
Open at sourcePDFDOICite

Abstract

In this work, Neural ODEs equipped with a curated collection of equilibrium points have been successfully employed for classification tasks. The planted fixed points 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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Cite

BibTeXRIS
BibTeX
@misc{pacifico2026approximating,
  title = {{Approximating velocity fields with planted point attractors via Neural-ODE for classification purposes}},
  author = {Feliciano Giuseppe Pacifico and Duccio Fanelli and Lorenzo Buffoni and Lorenzo Chicchi and Diego Febbe and Raffaele Marino},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2606.23550},
  eprint = {2606.23550},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2606.23550},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Approximating velocity fields with planted point attractors via Neural-ODE for classification purposes
AU  - Feliciano Giuseppe Pacifico
AU  - Duccio Fanelli
AU  - Lorenzo Buffoni
AU  - Lorenzo Chicchi
AU  - Diego Febbe
AU  - Raffaele Marino
PY  - 2026
DA  - 2026/10/23
PB  - arXiv
DO  - 10.48550/arxiv.2606.23550
UR  - https://arxiv.org/abs/2606.23550
AB  - In this work, Neural ODEs equipped with a curated collection of equilibrium points have been successfully employed for classification tasks. The planted fixed points 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.
ER  -