OBRABOTKAMETALLOV MATERIAL SCIENCE Том 23 № 3 2021 EQUIPMEN . INSTRUM TS Vol. 7 No. 2 2025 To function effectively, neural models use a vast network of simple computing processors known as “neurons.” Neural networks are often used to solve complex problems in which the behavior of variables is not well known. One of their fundamental characteristics is the ability to learn from examples and apply this knowledge in a generalized way, which allows the creation of nonlinear models. This ability makes the use of ANN in multicriteria analysis very effective [7, 8]. The configuration of a neural network requires the definition of several important parameters: the number of nodes in the input layer, the number of hidden layers, the number of neurons in each hidden layer, and the number of neurons in the output layer. The state of neuron k is determined by the equation: 1 ( ) i = , n k i ki k S x w b where xi is the output signal calculated by a neuron i; wki is the synaptic weight between i and bk neurons; k is a weight associated with a constant, non–zero value known as the neuron’s bias. To use ANN, it is necessary to calculate synaptic weights and biases. The process of determining these parameters is called training and occurs iteratively, where the initial parameters are updated until the process reaches sufficient convergence. The activation function f describes how the internal input and the current activation state influence the determination of the next state of the block. The most commonly used types of activation functions can be identified as follows: Threshold function: 1, 0 ( ) . 0, 0 k k k if S f S if S A unit step function, or threshold function, is a mathematical function that takes the value 1 if its argument is greater than or equal to some threshold, and 0 otherwise. Piecewise linear function, an example of which can be represented as: , ; ( ) , , k k k k k aS d if S c f S eS g if S c where a, c, d, e, g are constants. A piecewise linear function consists of several linear sections, each defined on its own interval. The linear sections are connected to form a continuous function, although the derivative of such a function may be discontinuous at the junctions between sections. Sigmoidal function: 1 ( ) , 1 exp( ) k f S aµ where a is the slope parameter of the sigmoidal function. This function is the most commonly used and is characterized as an increasing function that balances linear and nonlinear behavior while maintaining its value within the range from 0 to 1. The choice of activation function can significantly impact network performance. The rectified linear unit (ReLU), defined as ReLU(X) = max{X, 0}, is currently the most widely used activation function and is popular in neural networks due to its non-saturation and non-linearity [9]. Compared to activation functions that exhibit saturation, such as the sigmoidal function, ReLU combined with gradient descent has superior performance. Gradient descent is a method used to minimize the loss function by adjusting the weights. In neural network training, the objective function is the output error of the network. The minima of the function form troughs, and the maxima form hills [10, 11].
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