• Journal of The Korean Society of Agricultural Engineers
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• v.63 no.1
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• pp.103-116
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• 2021

Analysis of runoff is substantial for effective water management in the watershed. Runoff occurs by reaction of a watershed to the rainfall and has non-linearity and uncertainty due to the complex relation of weather and watershed factors. ANN (Artificial Neural Network), which learns from the data, is one of the machine learning technique known as a proper model to interpret non-linear data. The performance of ANN is affected by the ANN's structure, the number of hidden layer nodes, learning rate, and activation function. Especially, the activation function has a role to deliver the information entered and decides the way of making output. Therefore, It is important to apply appropriate activation functions according to the problem to solve. In this paper, ANN models were constructed to estimate runoff with different activation functions and each model was compared and evaluated. Sigmoid, Hyperbolic tangent, ReLU (Rectified Linear Unit), ELU (Exponential Linear Unit) functions were applied to the hidden layer, and Identity, ReLU, Softplus functions applied to the output layer. The statistical parameters including coefficient of determination, NSE (Nash and Sutcliffe Efficiency), NSEln (modified NSE), and PBIAS (Percent BIAS) were utilized to evaluate the ANN models. From the result, applications of Hyperbolic tangent function and ELU function to the hidden layer and Identity function to the output layer show competent performance rather than other functions which demonstrated the function selection in the ANN structure can affect the performance of ANN.

• The Journal of the Institute of Internet, Broadcasting and Communication
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• v.22 no.6
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• pp.75-81
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• 2022

Autonomous vehicles, which can dramatically solve the lack of parking spaces, are making great progress through deep reinforcement learning. Activation functions are used for deep reinforcement learning, and various activation functions have been proposed, but their performance deviations were large depending on the application environment. Therefore, finding the optimal activation function depending on the environment is important for effective learning. This paper analyzes 12 functions mainly used in reinforcement learning to compare and evaluate which activation function is most effective when autonomous vehicles use deep reinforcement learning to learn parking. To this end, a performance evaluation environment was established, and the average reward of each activation function was compared with the success rate, episode length, and vehicle speed. As a result, the highest reward was the case of using GELU, and the ELU was the lowest. The reward difference between the two activation functions was 35.2%.

• Journal of The Korean Society of Agricultural Engineers
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• v.63 no.1
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• pp.11-25
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• 2021

The objective of this study was to analyze the impact of activation functions on flood forecasting model based on Artificial neural networks (ANNs). The traditional activation functions, the sigmoid and tanh functions, were compared with the functions which have been recently recommended for deep neural networks; the ReLU, leaky ReLU, and ELU functions. The flood forecasting model based on ANNs was designed to predict real-time runoff for 1 to 6-h lead time using the rainfall and runoff data of the past nine hours. The statistical measures such as R2, Nash-Sutcliffe Efficiency (NSE), Root Mean Squared Error (RMSE), the error of peak time (ETp), and the error of peak discharge (EQp) were used to evaluate the model accuracy. The tanh and ELU functions were most accurate with R2=0.97 and RMSE=30.1 (㎥/s) for 1-h lead time and R2=0.56 and RMSE=124.6~124.8 (㎥/s) for 6-h lead time. We also evaluated the learning speed by using the number of epochs that minimizes errors. The sigmoid function had the slowest learning speed due to the 'vanishing gradient problem' and the limited direction of weight update. The learning speed of the ELU function was 1.2 times faster than the tanh function. As a result, the ELU function most effectively improved the accuracy and speed of the ANNs model, so it was determined to be the best activation function for ANNs-based flood forecasting.

• Journal of Applied and Pure Mathematics
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• v.4 no.5_6
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• pp.269-286
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• 2022

In this article we exhibit univariate and multivariate quantitative approximation by Kantorovich-Choquet type quasi-interpolation neural network operators with respect to supremum norm. This is done with rates using the first univariate and multivariate moduli of continuity. We approximate continuous and bounded functions on ℝ^N , N ∈ ℕ. When they are also uniformly continuous we have pointwise and uniform convergences. Our activation functions are induced by the arctangent, algebraic, Gudermannian and generalized symmetrical sigmoid functions.

• The Journal of the Institute of Internet, Broadcasting and Communication
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• v.19 no.2
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• pp.135-141
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• 2019

Recently, there has been active researches about building an artificial intelligence agent that can learn how to play a game by using re-enforcement learning. The performance of the learning can be diverse according to what kinds of deep learning activation functions they used when they train the agent. This paper compares the activation functions when we train our agent for learning how to play a 2D shooting game by using re-enforcement learning. We defined performance metrics to analyze the results and plotted them along a training time. As a result, we found ELU (Exponential Linear Unit) with a parameter 1.0 achieved best rewards than other activation functions. There was 23.6% gap between the best activation function and the worst activation function.

• Communications for Statistical Applications and Methods
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• v.28 no.3
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• pp.281-294
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• 2021

In this paper, we propose an adaptive regression method based on the single-layer neural network structure. We adopt a symmetric activation function as units of the structure. The activation function has a flexibility of its form with a parametrization and has a localizing property that is useful to improve the quality of estimation. In order to provide a spatially adaptive estimator, we regularize coefficients of the activation functions via ℓ₁-penalization, through which the activation functions to be regarded as unnecessary are removed. In implementation, an efficient coordinate descent algorithm is applied for the proposed estimator. To obtain the stable results of estimation, we present an initialization scheme suited for our structure. Model selection procedure based on the Akaike information criterion is described. The simulation results show that the proposed estimator performs favorably in relation to existing methods and recovers the local structure of the underlying function based on the sample.

• Proceedings of the IEEK Conference
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• 2008.06a
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• pp.679-680
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• 2008

When we apply the neural networks to applications, we need to select proper architecture of the network and the activation function of the network is one of most important characteristics. In this research, we propose a method to make a network using multiple activation functions. The performance of the proposed method is investigated through the computer simulations on various regression problems.

• ETRI Journal
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• v.15 no.2
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• pp.35-51
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• 1993

This paper presents function approximation based on nonparametric estimation. As an estimation model of function approximation, a three layered network composed of input, hidden and output layers is considered. The input and output layers have linear activation units while the hidden layer has nonlinear activation units or kernel functions which have the characteristics of bounds and locality. Using this type of network, a many-to-one function is synthesized over the domain of the input space by a number of kernel functions. In this network, we have to estimate the necessary number of kernel functions as well as the parameters associated with kernel functions. For this purpose, a new method of parameter estimation in which linear learning rule is applied between hidden and output layers while nonlinear (piecewise-linear) learning rule is applied between input and hidden layers, is considered. The linear learning rule updates the output weights between hidden and output layers based on the Linear Minimization of Mean Square Error (LMMSE) sense in the space of kernel functions while the nonlinear learning rule updates the parameters of kernel functions based on the gradient of the actual output of network with respect to the parameters (especially, the shape) of kernel functions. This approach of parameter adaptation provides near optimal values of the parameters associated with kernel functions in the sense of minimizing mean square error. As a result, the suggested nonparametric estimation provides an efficient way of function approximation from the view point of the number of kernel functions as well as learning speed.

• The Journal of the Institute of Internet, Broadcasting and Communication
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• v.21 no.6
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• pp.117-122
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• 2021

Autonomous driving allows cars to drive without people and is being studied very actively thanks to the recent development of artificial intelligence technology. Among artificial intelligence technologies, deep reinforcement learning is used most effectively. Deep reinforcement learning requires us to build a neural network using an appropriate activation function. So far, many activation functions have been suggested, but different performances have been shown depending on the field of application. This paper compares and evaluates the performance of which activation function is effective when using deep reinforcement learning to learn autonomous driving on highways. To this end, the performance metrics to be used in the evaluation were defined and the values of the metrics according to each activation function were compared in graphs. As a result, when Mish was used, the reward was higher on average than other activation functions, and the difference from the activation function with the lowest reward was 9.8%.

• Journal of the Institute of Electronics Engineers of Korea CI
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• v.49 no.2
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• pp.115-122
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• 2012

We present here a new class of activation functions for neural networks, which herein will be called CosGauss function. This function is a cosine-modulated gaussian function. In contrast to the sigmoidal-, hyperbolic tangent- and gaussian activation functions, more ridges can be obtained by the CosGauss function. It will be proven that this function can be used to aproximate polynomials and step functions. The CosGauss function was tested with a Cascade-Correlation-Network of the multilayer structure on the Tic-Tac-Toe game and iris plants problems, and results are compared with those obtained with other activation functions.