A Geometric Theory for Binary Classification of Finite Datasets by DNNs with Relu Activations

In this paper we investigate deep neural networks for binary classification of datasets from geometric perspective in order to understand the working mechanism of deep neural networks. First, we establish a geometrical result on injectivity of finite set under a projection from Euclidean space to th...

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Bibliographic Details
Published in:Neural processing letters 2024-04, Vol.56 (3), p.155, Article 155
Main Author: Yang, Xiao-Song
Format: Article
Language:English
Subjects:
Artificial Intelligence
Artificial neural networks
Classification
Complex Systems
Computational Intelligence
Computer Science
Datasets
Euclidean geometry
Euclidean space
Neural networks
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Summary:In this paper we investigate deep neural networks for binary classification of datasets from geometric perspective in order to understand the working mechanism of deep neural networks. First, we establish a geometrical result on injectivity of finite set under a projection from Euclidean space to the real line. Then by introducing notions of alternative points and alternative number, we propose an approach to design DNNs for binary classification of finite labeled points on the real line, thus proving existence of binary classification neural net with its hidden layers of width two and the number of hidden layers not larger than the cardinality of the finite labelled set. We also demonstrate geometrically how the dataset is transformed across every hidden layers in a narrow DNN setting for binary classification task.
ISSN:1573-773X
1370-4621
1573-773X
DOI:10.1007/s11063-024-11612-1