2026-09-19T15:25:04Zhttps://dspace.mit.edu/server/oai/requestoai:dspace.mit.edu:1721.1/1222412022-01-13T07:55:19Zcom_1721.1_7582com_1721.1_7581col_1721.1_131023
Robert Freund.
Ang, Jun Siong.
Massachusetts Institute of Technology. Engineering and Management Program.
System Design and Management Program.
Massachusetts Institute of Technology. Engineering and Management Program
2019-09-17T19:49:40Z
2019-09-17T19:49:40Z
2019
2019
https://hdl.handle.net/1721.1/122241
1119537063
Thesis: S.M. in Engineering and Management, Massachusetts Institute of Technology, System Design and Management Program, 2019
Cataloged from PDF version of thesis.
Includes bibliographical references (pages R-1 to R-2).
With vast improvements in computational power, increased accessibility to big data, and rapid innovations in computing algorithms, the use of neural networks for both engineering and business purposes was met with a renewed interest beginning in early 2000s. Amidst substantial development, the Softplus and Rectified Linear Unit (ReLU) activation functions were introduced in 2000 and 2001 respectively, with the latter emerging as the more popular choice of activation function in neural networks. Notably, the ReLU activation function maintains a high degree of gradient propagation while presenting greater model sparsity and computational efficiency over Softplus. As an alternative to the ReLU, a family of a modified Softplus activation function - the "Smoothing" activation function of the form g(z) = [mu] log(1 + e[superscript z/[mu]) has been proposed. Theoretically, the Smoothing activation function will leverage the high degree of gradient propagation and model simplicity characteristic of the ReLU function, while eliminating possible issues associated with the non-differentiability of ReLU about the origin. In this research, the performance of the Smoothing family of activation functions vis-à-vis the ReLU activation function will be examined.
by Jun Siong Ang.
S.M. in Engineering and Management
S.M.inEngineeringandManagement Massachusetts Institute of Technology, System Design and Management Program
78, A-1 to A-26, B-1 to B-10, R-1 to R-2 pages
eng
Massachusetts Institute of Technology
MIT theses are protected by copyright. They may be viewed, downloaded, or printed from this source but further reproduction or distribution in any format is prohibited without written permission.
http://dspace.mit.edu/handle/1721.1/7582
Engineering and Management Program.
System Design and Management Program.
Evaluation of the smoothing activation function in neural networks for business applications
Thesis
application/pdf
2019-09-17T19:49:38Z
Publication
Master
SysDes
unknown
unknown
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<Abstract>With vast improvements in computational power, increased accessibility to big data, and rapid innovations in computing algorithms, the use of neural networks for both engineering and business purposes was met with a renewed interest beginning in early 2000s. Amidst substantial development, the Softplus and Rectified Linear Unit (ReLU) activation functions were introduced in 2000 and 2001 respectively, with the latter emerging as the more popular choice of activation function in neural networks. Notably, the ReLU activation function maintains a high degree of gradient propagation while presenting greater model sparsity and computational efficiency over Softplus. As an alternative to the ReLU, a family of a modified Softplus activation function - the "Smoothing" activation function of the form g(z) = [mu] log(1 + e[superscript z/[mu]) has been proposed. Theoretically, the Smoothing activation function will leverage the high degree of gradient propagation and model simplicity characteristic of the ReLU function, while eliminating possible issues associated with the non-differentiability of ReLU about the origin. In this research, the performance of the Smoothing family of activation functions vis-à-vis the ReLU activation function will be examined.</Abstract>
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