How Can Deep Neural Networks Fail Even with Global Optima?
Year: 2024
Author: Qingguang Guan
International Journal of Numerical Analysis and Modeling, Vol. 21 (2024), Iss. 5 : pp. 674–696
Abstract
Fully connected deep neural networks are successfully applied to classification and function approximation problems. By minimizing the cost function, i.e., finding the proper weights and biases, models can be built for accurate predictions. The ideal optimization process can achieve global optima. However, do global optima always perform well? If not, how bad can it be? In this work, we aim to: 1) extend the expressive power of shallow neural networks to networks of any depth using a simple trick, 2) construct extremely overfitting deep neural networks that, despite having global optima, still fail to perform well on classification and function approximation problems. Different types of activation functions are considered, including ReLU, Parametric ReLU, and Sigmoid functions. Extensive theoretical analysis has been conducted, ranging from one-dimensional models to models of any dimensionality. Numerical results illustrate our theoretical findings.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/ijnam2024-1027
International Journal of Numerical Analysis and Modeling, Vol. 21 (2024), Iss. 5 : pp. 674–696
Published online: 2024-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 23
Keywords: Deep neural network global optima binary classification function approximation overfitting.
Author Details
Qingguang Guan Email