Alvarez-Lopez A, Rafael OI, Zuazua Iriondo E (2024)
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Publication Type: Unpublished / Preprint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
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.
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 (Unpublished, Submitted).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 Unpublished, Submitted. 2024.
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