Home Publications Research Grants Inventions & Patents Awards Additional Research Activities Faculties & Institutions Research Areas

Cluster-based classification with neural ODEs via control

Álvarez López A, Orive-Illera R, Zuazua Iriondo E (2025)

---

Publication Language: English

Publication Status: Accepted

Publication Type: Unpublished / Preprint

Future Publication Type: Journal article

Publication year: 2025

Publisher: Journal of Machine Learning

DOI: 10.4208/jml.241114

Open Access Link: https://arxiv.org/abs/2312.13807

Abstract

We address binary classification using neural ordinary differential equations from the perspective of simultaneous control of N data points. We consider a single-neuron architecture with parameters fixed as piecewise constant functions of time. In this setting, the model complexity can be quantified by the number of control switches. Previous work has shown that classification can be achieved using a point-by-point strategy that requires O(N) switches. We propose a new control method that classifies any arbitrary dataset by se- quentially steering clusters of d points, thereby reducing the complexity to O(N/d) switches. The optimality of this result, particularly in high dimensions, is supported by some numerical experiments. Our complexity bound is sufficient but often conservative because same-class points tend to appear in larger clusters, simpli- fying classification. This motivates studying the probability distribution of the number of switches required. We introduce a simple control method that imposes a collinearity constraint on the parameters, and analyze a worst-case scenario where both classes have the same size and all points are i.i.d. Our results highlight the benefits of high-dimensional spaces, showing that classification using constant controls becomes more probable as d increases. 

Authors with CRIS profile

Involved external institutions

How to cite

APA:

Álvarez López, A., Orive-Illera, R., & Zuazua Iriondo, E. (2025). Cluster-based classification with neural ODEs via control. (Unpublished, Accepted).

MLA:

Álvarez López, Antonio, Rafael Orive-Illera, and Enrique Zuazua Iriondo. Cluster-based classification with neural ODEs via control. Unpublished, Accepted. 2025.

BibTeX: Download