# Stable Attractors for Neural networks classification via Ordinary Differential Equations (SA-nODE)

arXiv: https://arxiv.org/abs/2311.10387 · HTML: https://mlsanity.com/paper/2311.10387/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 11 of its 40 references that are in the map.
- First posted on arXiv 17 Nov 2023.

## Builds on (most cited first, 11 of 11)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [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)
- [Solving high-dimensional partial differential equations using deep learning](https://mlsanity.com/paper/1707.02568/) (2017)
- [Financial Time Series Forecasting with Deep Learning : A Systematic Literature Review: 2005-2019](https://mlsanity.com/paper/1911.13288/) (2019)
- [Liquid Time-constant Networks](https://mlsanity.com/paper/2006.04439/) (2020)
- [Machine learning in spectral domain](https://mlsanity.com/paper/2005.14436/) (2020)
- [Learning from Survey Propagation: a Neural Network for MAX-E-3-SAT](https://mlsanity.com/paper/2012.06344/) (2020)
- [Solving non-linear Kolmogorov equations in large dimensions by using deep learning: a numerical comparison of discretization schemes](https://mlsanity.com/paper/2012.07747/) (2020)
- [Hard Optimization Problems have Soft Edges](https://mlsanity.com/paper/2209.04824/) (2022)

## Built on by (most cited first, 5 of 5)

- [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)
- [Engineered Ordinary Differential Equations as Classification Algorithm (EODECA): thorough characterization and testing](https://mlsanity.com/paper/2312.14681/) (2023)
- [Approximating velocity fields with planted attractors via Neural-ODEs for classification purposes](https://mlsanity.com/paper/2606.23550/) (2026)
- [Multiplicity of Stable Attractors in Disordered Neural Models](https://mlsanity.com/paper/2607.22047/) (2026)

## Abstract (arXiv)

A novel approach for supervised classification is presented which sits at the intersection of machine learning and dynamical systems theory. At variance with other methodologies that employ ordinary differential equations for classification purposes, the untrained model is a priori constructed to accommodate for a set of pre-assigned stationary stable attractors. Classifying amounts to steer the dynamics towards one of the planted attractors, depending on the specificity of the processed item supplied as an input. Asymptotically the system will hence converge on a specific point of the explored multi-dimensional space, flagging the category of the object to be eventually classified. Working in this context, the inherent ability to perform classification, as acquired ex post by the trained model, is ultimately reflected in the shaped basin of attractions associated to each of the target stable attractors. The performance of the proposed method is here challenged against simple toy models crafted for the purpose, as well as by resorting to well established reference standards. Although this method does not reach the performance of state-of-the-art deep learning algorithms, it illustrates that continuous dynamical systems with closed analytical interaction terms can serve as high-performance classifiers.