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Optimized classification with neural ODEs via separability

Alvarez-Lopez A, Rafael OI, Zuazua Iriondo E (2024)

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Publication Language: English

Publication Status: Submitted

Publication Type: Unpublished / Preprint

Future Publication Type: Journal article

Publication year: 2024

DOI: 10.48550/arXiv.2312.13807

Open Access Link: https://doi.org/10.48550/arXiv.2312.13807

Abstract

Classification of N points becomes a simultaneous control problem when viewed through the lens of neural ordinary differential equations (neural ODEs), which represent the time-continuous limit of residual networks. For the narrow model, with one neuron per hidden layer, it has been shown that the task can be achieved using O(N) neurons. In this study, we focus on estimating the number of neurons required for efficient clusterbased classification, particularly in the worst-case scenario where points are independently and uniformly distributed in [0, 1]d . Our analysis provides a novel method for quantifying the probability of requiring fewer than O(N) neurons, emphasizing the asymptotic behavior as both d and N increase. Additionally, under the sole assumption that the data are in general position, we propose a new constructive algorithm that simultaneously classifies clusters of d points from any initial configuration, effectively reducing the maximal complexity to O(N/d) neurons.

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How to cite

APA:

Alvarez-Lopez, A., Rafael, O.-I., & Zuazua Iriondo, E. (2024). Optimized classification with neural ODEs via separability. (Unpublished, Submitted).

MLA:

Alvarez-Lopez, Antonio, Orive-Illera Rafael, and Enrique Zuazua Iriondo. Optimized classification with neural ODEs via separability. Unpublished, Submitted. 2024.

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