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Lu W, Zhang Z, Qin F, Zhang W, Lu Y, Liu Y, Zheng Y. Analysis on the inherent noise tolerance of feedforward network and one noise-resilient structure. Neural Netw 2023; 165:786-798. [PMID: 37418861 DOI: 10.1016/j.neunet.2023.06.011] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/01/2022] [Revised: 03/11/2023] [Accepted: 06/06/2023] [Indexed: 07/09/2023]
Abstract
In the past few decades, feedforward neural networks have gained much attraction in their hardware implementations. However, when we realize a neural network in analog circuits, the circuit-based model is sensitive to hardware nonidealities. The nonidealities, such as random offset voltage drifts and thermal noise, may lead to variation in hidden neurons and further affect neural behaviors. This paper considers that time-varying noise exists at the input of hidden neurons, with zero-mean Gaussian distribution. First, we derive lower and upper bounds on the mean square error loss to estimate the inherent noise tolerance of a noise-free trained feedforward network. Then, the lower bound is extended for any non-Gaussian noise cases based on the Gaussian mixture model concept. The upper bound is generalized for any non-zero-mean noise case. As the noise could degrade the neural performance, a new network architecture is designed to suppress the noise effect. This noise-resilient design does not require any training process. We also discuss its limitation and give a closed-form expression to describe the noise tolerance when the limitation is exceeded.
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Affiliation(s)
- Wenhao Lu
- School of Electrical and Electronic Engineering, Nanyang Technological University, Nanyang Avenue, 639798, Singapore
| | - Zhengyuan Zhang
- School of Electrical and Electronic Engineering, Nanyang Technological University, Nanyang Avenue, 639798, Singapore
| | - Feng Qin
- School of Electrical and Electronic Engineering, Nanyang Technological University, Nanyang Avenue, 639798, Singapore; State Key Laboratory for Manufacturing Systems Engineering, Xi'an Jiaotong University, No. 99 Yanxiang Road, Yanta District, Xi'an, 710054 Shaanxi, China; International Joint Laboratory for Micro/Nano Manufacturing and Measurement Technologies, Xi'an Jiaotong University, Xi'an, 710049 Shaanxi, China
| | - Wenwen Zhang
- School of Electrical and Electronic Engineering, Nanyang Technological University, Nanyang Avenue, 639798, Singapore
| | - Yuncheng Lu
- School of Electrical and Electronic Engineering, Nanyang Technological University, Nanyang Avenue, 639798, Singapore
| | - Yue Liu
- School of Mechanical Engineering, Shanghai Dianji University, Shanghai, 201306, China.
| | - Yuanjin Zheng
- School of Electrical and Electronic Engineering, Nanyang Technological University, Nanyang Avenue, 639798, Singapore.
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Li K, Yang C, Wang W, Qiao J. An improved stochastic configuration network for concentration prediction in wastewater treatment process. Inf Sci (N Y) 2023. [DOI: 10.1016/j.ins.2022.11.134] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/12/2022]
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Huang C, Wang H, Cao J. Fractional order-induced bifurcations in a delayed neural network with three neurons. CHAOS (WOODBURY, N.Y.) 2023; 33:033143. [PMID: 37003808 DOI: 10.1063/5.0135232] [Citation(s) in RCA: 3] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/17/2022] [Accepted: 02/08/2023] [Indexed: 06/19/2023]
Abstract
This paper reports the novel results on fractional order-induced bifurcation of a tri-neuron fractional-order neural network (FONN) with delays and instantaneous self-connections by the intersection of implicit function curves to solve the bifurcation critical point. Firstly, it considers the distribution of the root of the characteristic equation in depth. Subsequently, it views fractional order as the bifurcation parameter and establishes the transversal condition and stability interval. The main novelties of this paper are to systematically analyze the order as a bifurcation parameter and concretely establish the order critical value through an implicit function array, which is a novel idea to solve the critical value. The derived results exhibit that once the value of the fractional order is greater than the bifurcation critical value, the stability of the system will be smashed and Hopf bifurcation will emerge. Ultimately, the validity of the developed key fruits is elucidated via two numerical experiments.
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Affiliation(s)
- Chengdai Huang
- School of Mathematics and Statistics, Xinyang Normal University, Xinyang 464000, China
| | - Huanan Wang
- School of Mathematics and Statistics, Xinyang Normal University, Xinyang 464000, China
| | - Jinde Cao
- School of Mathematics, Southeast University, Nanjing 210096, China, and Yonsei Frontier Lab, Yonsei University, Seoul 03722, South Korea
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A cooperative genetic algorithm based on extreme learning machine for data classification. Soft comput 2022. [DOI: 10.1007/s00500-022-07202-9] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/26/2022]
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