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    Comparison of Activation Functions in the KarciFANN Method
    (Institute of Electrical and Electronics Engineers Inc., 2024) Karakurt, Meral; Saygili, Hulya; Karci, Ali
    The lack of a certain standard in modeling Artificial Neural Networks (ANNs) sometimes provides successful results while sometimes it causes unsuccessful results depending on the changes in the selected hyper parameters. The optimization method is a hyper parameter that significantly affects the performance of ANNs. If the learning coefficient parameter used in the SGD optimization method, which is a fixed number, is chosen too small, the solution takes a long time; if it is chosen too large, it causes problems such as getting stuck in local minima and moving away from the solution. In the Karci Fractional Neural Network (KarciFANN) method proposed in this article, the learning of the network is performed by using the fractional derivative instead of the learning coefficient parameter. Thanks to the KarciFANN method, the weights are updated with a fractional derivative that changes according to the value of the error function obtained at each iteration and external intervention to the network is minimized. Activation function is another hyperparameter that affects the performance of ANNs. Activation function determines whether the output value of a neuron will be produced or not, that is, whether the neuron will be active or not. In this study, Gina_Prior2 data set was classified using KarciFANN method using sigmoid, hyperbolic tangent (tanh) and hyperbolic tangent sigmoid (tansig) activation functions and the effects of these activation functions on performance were compared. As a result of the experiments performed on the designed model, it was seen that the most successful activation function was the sigmoid function, which produced accuracy values over 99%. © 2024 IEEE.
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    Comparison of Loss Functions in the KarciFANN Method
    (Institute of Electrical and Electronics Engineers Inc., 2024) Saygili, Hulya; Karakurt, Meral; Karci, Ali
    Various hyperparameters are used in the design phase of artificial neural networks (ANNs). One of the hyperparameters that significantly affects the performance of ANNs is the optimization method. In this paper, the Karci Fractional-Order Artificial Neural Network (KarciFANN) method is proposed, where learning is performed using fractional-order derivatives instead of a fixed learning rate parameter used in the SGD optimization method. Thus, in the KarciFANN method, an external intervention to the network is minimized by using a fractional-order derivative that changes according to the value of the loss function obtained at each iteration. The loss function is another hyperparameter that affects the performance of ANNs. It is a mathematical function that measures the difference between the expected true value and the predicted value produced by the network. The loss function indicates how effectively the ANN has learned. In backpropagation-based ANNs, the value of the loss function is propagated backward from the network output to the input layer to update the weights, aiming to minimize this loss value and improve the network's performance. In this study, the performance of the mean squared error (MSE), mean absolute error (MAE), and root mean squared error (RMSE) loss functions was compared using the KarciFANN method for classifying the Gina_Prior2 dataset. As a result of the experiments performed on the designed model, it was seen that the most successful loss function was MSE, which produced accuracy values over 99%. © 2024 IEEE.
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    Karcı fractional artificial neural networks (KarcıFANN): anew artificial neural networks model without learning rate and its problems
    (Tubitak Scientific & Technological Research Council Turkey, 2025) Karakurt, Meral; Saygili, Hulya; Karci, Ali
    The learning rate parameter used in classical artificial neural networks (ANNs) designed with stochastic gradient descent causes problems such as failure to learn, getting stuck in local minima, memorization, and long training times (divergence problem). To address these issues, this paper proposes a novel ANN method that uses a fractional derivative instead of Newton's derivative. This method is referred to as Karc & imath; fractional ANN (Karc & imath;FANN). In classical ANNs, the weight update is done by assigning the same constant value to the learning rate in each iteration or for a set number of iterations. In contrast, in Karc & imath;FANNs, the weight update process is carried out by calculating the fractional derivative based on the error value in each iteration. Thus, in Karc & imath;FANN, external intervention in the network is minimized compared to that of classical ANNs. Karc & imath;FANN and classical ANN methods were compared for the classification of MNIST and fashion-MNIST datasets. The Karc & imath;FANN method produces successful results for fractional derivative orders between 0.8 and 1.8. The highest accuracy values obtained in the classification of the MNIST dataset were 99.39% for Karc & imath;FANN and 99.43% for classical ANN in the training phase, and 96.76% for Karc & imath;FANN and 96.72% for classical ANN in the validation phase. The highest accuracy values obtained in the classification of the Fashion-MNIST dataset were 98.10% for Karc & imath;FANN and 98.11% for classical ANN in the training phase, and 88.56% for Karc & imath;FANN and 88.54% for classical ANN in the validation phase. The experimental studies show that Karc & imath;FANN is a competitive alternative to classical ANN. Karc & imath;FANN learns faster than classical ANN and eliminates the learning coefficient problem. Additionally, it is seen that the Karc & imath;FANN method is more successful in global modeling. However, achieving the optimal model in Karc & imath;FANN depends on the dataset and hyperparameters.
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    Karcı fractional order neural network (KarcıFANN): solving learning rate, overfitting and underfitting problems
    (Gazi Univ, Fac Engineering Architecture, 2025) Saygili, Hulya; Karakurt, Meral; Karci, Ali
    The performance of artificial neural networks (ANN) is affected by the selection of hyperparameters. Learning coefficient is a hyperparameter that significantly affects this performance. Choosing the right learning coefficient to achieve optimum success with different models and datasets is a difficult and time-consuming process. Inappropriate learning coefficient can cause problems such as network failure to learn, memorization, gradient explosion and loss. In the Karc & imath; Fractional Neural Network (Karc & imath;FANN) method proposed in this article, the weight update process is performed by using the fractional derivative instead of the learning coefficient, which is a fixed number in Classical ANNs where the Stochastic Gradient Descent (SGD) method is used. Thus, in the Karc & imath;FANN method, a fractional derivative that changes according to the error value obtained in each iteration will be used and thus external intervention to the network will be minimized, thus contributing to the literature. In the study, the results of the Classical ANN and Karc & imath;FANN methods with the same initial and parameter values were compared in order to classify the Kuzushiji_MNIST, GinaPrior2 and SignMnist data sets. In the experimental studies conducted by giving values between 0.1-5.0 to the alpha parameter, which is the fractional order of the fractional derivative, and to the learning coefficient in Classical ANN, it was observed that the Karc & imath;FANN method performed better than the Classical ANN in the classification of Kuzushiji-Mnist and GinaPrior2 data sets, especially between 3.0-5.0. It was observed that the problems of memorization and learning that were encountered in Classical ANN were eliminated in the Karc & imath;FANN method. In addition, the generalizability of the Karc & imath;FANN method was experienced by running it on multiple data sets.