Notice of Retraction: An Efficient High-Speed Channel Modeling Method Based on Optimized Design-of-Experiment (DoE) for Artificial Neural Network Training

Kim, Heegon; Sui, Chunchun; Cai, Kevin; Sen, Bidyut; Fan, Jun

doi:10.1109/temc.2018.2796091

Cited by 12 publications

(15 citation statements)

References 8 publications

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“…where ( ) ( ) = ( ) −1 ( ) . Solving 1 = ( 1 ) (( ) (1) , ( ) (2) , ⋅ ⋅ ⋅ , ( ) ( ) ) is equivalent to solving equation (34). Because ( ) ( ) = ( ) −1 ( ) is equivalent to ( ) ( ) = ( ) , the calculation formula for the element (V ) ( ) of ( ) ( ) can be obtained by comparing the elements on both sides of the equation…”

Section: Process Of Matrices Decomposition For Fc-imrelmmentioning

confidence: 99%

“…where = ( ) , ( +1) * = (((( ) + ) ) (1) , ((( ) + ) ) (2) , ⋅ ⋅ ⋅ , ((( ) + ) ) ( ) ) . Therefore, the process of solving ( +1) * can be transformed into solving linear equations in the form of equation (37), or solving linear equations in the form of equation 38, is the number of hidden nodes, and is the dimension of the observation vector.…”

Section: ( )mentioning

confidence: 99%

“…Mathematical Problems in Engineering where = 1, 2, ⋅ ⋅ ⋅ , , = 1, 2, ⋅ ⋅ ⋅ , , ( ) + = ((( ) + ) (1) , (( ) + ) (2) , ⋅ ⋅ ⋅ , (( ) + ) ( ) ); consequently, we can get ( +1) * = ((( ) + ) (1) , (( ) + ) (2) , ⋅ ⋅ ⋅ , (( ) + ) ( ) ).…”

Section: (( )mentioning

confidence: 99%

“…where = ( ) , ( ) = (( ) (1) , ( ) (2) , ⋅ ⋅ ⋅ , ( ) ( ) ) ( ) . If ( ) is nonsingular, then let ( ) + = ( ) ( ( ) ) −1 and substitute it into (8) and 13:…”

Section: ((( )mentioning

confidence: 99%

“…The neural network is a complex nonlinear system interconnected by a large number of neurons, and it is based on the research of human brain information processing ability by modern neurobiology and cognitive science. The neural network is also a mathematical simulation form of human brain physiological structure, with strong adaptability, selflearning ability, and nonlinear mapping, and it has been widely used by researchers in many scientific fields [1][2][3]. However, the above prediction models are all based on the traditional neural networks, and the network training process needs to modify the network weights repeatedly according to the training objectives and gradient information.…”

Section: Introductionmentioning

confidence: 99%

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Incremental Multiple Hidden Layers Regularized Extreme Learning Machine Based on Forced Positive‐Definite Cholesky Factorization

Liu

2019

Mathematical Problems in Engineering

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The theory and implementation of extreme learning machine (ELM) prove that it is a simple, efficient, and accurate machine learning method. Compared with other single hidden layer feedforward neural network algorithms, ELM is characterized by simpler parameter selection rules, faster convergence speed, and less human intervention. The multiple hidden layer regularized extreme learning machine (MRELM) inherits these advantages of ELM and has higher prediction accuracy. In the MRELM model, the number of hidden layers is randomly initiated and fixed, and there is no iterative tuning process. However, the optimal number of hidden layers is the key factor to determine the generalization ability of MRELM. Given this situation, it is obviously unreasonable to determine this number by trial and random initialization. In this paper, an incremental MRELM training algorithm (FC-IMRELM) based on forced positive-definite Cholesky factorization is put forward to solve the network structure design problem of MRELM. First, an MRELM-based prediction model with one hidden layer is constructed, and then a new hidden layer is added to the prediction model in each training step until the generalization performance of the prediction model reaches its peak value. Thus, the optimal network structure of the prediction model is determined. In the training procedure, forced positive-definite Cholesky factorization is used to calculate the output weights of MRELM, which avoids the calculation of the inverse matrix and Moore-Penrose generalized inverse of matrix involved in the training process of hidden layer parameters. Therefore, FC-IMRELM prediction model can effectively reduce the computational cost brought by the process of increasing the number of hidden layers. Experiments on classification and regression problems indicate that the algorithm can be effectively used to determine the optimal network structure of MRELM, and the prediction model training by the algorithm has excellent performance in prediction accuracy and computational cost.

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Section: Process Of Matrices Decomposition For Fc-imrelmmentioning

confidence: 99%

Section: ( )mentioning

confidence: 99%

Section: (( )mentioning

confidence: 99%

“…where = ( ) , ( ) = (( ) (1) , ( ) (2) , ⋅ ⋅ ⋅ , ( ) ( ) ) ( ) . If ( ) is nonsingular, then let ( ) + = ( ) ( ( ) ) −1 and substitute it into (8) and 13:…”

Section: ((( )mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Incremental Multiple Hidden Layers Regularized Extreme Learning Machine Based on Forced Positive‐Definite Cholesky Factorization

Liu

2019

Mathematical Problems in Engineering

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A modified model of conductor roughness for manufacturing copper lines of printedcircuit board

Wang

Adi

et al. 2021

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Purpose The purpose of this paper is to establish an accurate model to quantify the effect of conductor roughness on insertion loss (IL) and provide improved measurements and suggestions for manufacturing good conductive copper lines of printed circuit board. Design/methodology/approach To practically investigates the modified model of conductor roughness, three different kinds of alternate oxidation treatments were used to provide transmission lines with different roughness. The IL results were measured by a vector net analyzer for comparisons with the modified model results. Findings An accurate model, with only a 1.8% deviation on average from the measured values, is established. Compared with other models, the modified model is more reliable in industrial manufacturing. Originality/value This paper introduces the influence of tiny roughness structures on IL. Besides, this paper discusses the effect of current distribution on IL.

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Transient Simulations of High-Speed Channels Using CNN-LSTM With an Adaptive Successive Halving Algorithm for Automated Hyperparameter Optimizations

Goay

Ahmad

Goh³

2021

IEEE Access

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Transient simulations of high-speed channels can be very time intensive. Recurrent neural network (RNN) based methods can be used to speed up the process by training a RNN model on a relatively short bit sequence, and then using a multi-steps rolling forecast method to predict subsequent bits. However, the performance of the RNN model is highly affected by its hyperparameters. We propose an algorithm named adaptive successive halving automated hyperparameter optimization (ASH-HPO) which combines successive halving, Bayesian optimization (BO), and progressive sampling to tune the hyperparameters of the RNN models. Modifications are proposed to the successive halving and progressive sampling algorithms for better efficiency on time series data. The ASH-HPO algorithm trains on smaller dataset subsets initially, then expands the training dataset progressively and adaptively adds or removes models along the process. In this paper, we use the ASH-HPO algorithm to optimize the hyperparameters of convolutional neural networks (CNNs), long short-term memory (LSTM) networks, and CNN-LSTM networks. We demonstrate the effectiveness of the ASH-HPO algorithm using a PCIe Gen 2 channel, a PCIe Gen 5 channel, and a PAM4 differential channel. We also investigate the effects of several settings and tunable variables of the ASH-HPO algorithm on its convergence speed. As a benchmark, we compared the ASH-HPO algorithm to three state-of-the-art HPO methods: BO, successive halving, and hyperband. The results show that the ASH-HPO algorithm converges faster than the other HPO methods on transient simulation problems.INDEX TERMS Automated hyperparameter optimization, convolutional neural network (CNN), highspeed channel, long short-term memory (LSTM) network, progressive sampling, transient simulation.

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Notice of Retraction: An Efficient High-Speed Channel Modeling Method Based on Optimized Design-of-Experiment (DoE) for Artificial Neural Network Training

Cited by 12 publications

References 8 publications

Incremental Multiple Hidden Layers Regularized Extreme Learning Machine Based on Forced Positive‐Definite Cholesky Factorization

Incremental Multiple Hidden Layers Regularized Extreme Learning Machine Based on Forced Positive‐Definite Cholesky Factorization

A modified model of conductor roughness for manufacturing copper lines of printedcircuit board

Transient Simulations of High-Speed Channels Using CNN-LSTM With an Adaptive Successive Halving Algorithm for Automated Hyperparameter Optimizations

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