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

arXiv: https://arxiv.org/abs/2606.23550 · HTML: https://mlsanity.com/paper/2606.23550/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 8 of its 16 references that are in the map.
- First posted on arXiv 22 Jun 2026.

## Builds on (most cited first, 8 of 8)

- [Fashion-MNIST: a Novel Image Dataset for Benchmarking Machine Learning Algorithms](https://mlsanity.com/paper/1708.07747/) (2017)
- [Neural Ordinary Differential Equations](https://mlsanity.com/paper/1806.07366/) (2018)
- [Universal Approximation Property of Neural Ordinary Differential Equations](https://mlsanity.com/paper/2012.02414/) (2020)
- [Universal approximation property of invertible neural networks](https://mlsanity.com/paper/2204.07415/) (2022)
- [Stable Attractors for Neural networks classification via Ordinary Differential Equations (SA-nODE)](https://mlsanity.com/paper/2311.10387/) (2023)
- [Deterministic versus stochastic dynamical classifiers: opposing random adversarial attacks with noise](https://mlsanity.com/paper/2409.13470/) (2024)
- [Learning in Wilson-Cowan model for metapopulation](https://mlsanity.com/paper/2406.16453/) (2024)
- [Exact Fixed-Point Constraints in Neural-ODEs with Provable Universality](https://mlsanity.com/paper/2605.10613/) (2026)

## Abstract (arXiv)

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.