## 2 Materials and Methods  
This study included several stages. The first stage involved the evaluation of the antiradical activity of food products. For this, the photocolorimetric method was used [31]. ARP was determined from the difference between the detected extinction values of mixtures of alcoholic solutions of the stable colored radical DPPH and extracts of food products according to the previously published method [28; 29; 32]. In total, about 100 types of products,food components and types of agricultural raw materials were analyzed. For antiradical values, a 95% confidence interval (hereinafter CI) was calculated, which was used to train the ANN. After analyzing the data, a comparison was made of those products that were presented in the FNDDS database and those that were analyzed by us. Twenty-nine indisputably coinciding positions were singled out: wheat and rye bread; milk and dairy products; seafood, fish and products of its processing; cereals; frozen and fresh vegetables; fruits; eggs; can molasses. For selected positions, the chemical composition of products and the concentration of components were used from the FNDDS database, and the ARP values were substituted according to our own experimental data. Thus, a mixed table was formed, simultaneously containing both the data obtained by us and the values of the chemical composition. At the second stage, using the data, optimization (training) of the neural network was carried out. The level of deviation from the model values was \(\approx\)0.005 (or half a percent). NeuroXL Predictor (v. 3.1.2; OLSOFT software development; Russia, Uzbekistan) program was used to create the ANN structure, which was used in the study (a schematic representation is given at the center of Figure 1). Since in our work the goal was only to obtain two estimates (without complex transformations), we used a neural network built according to the \"perceptron\" type (with one layer of hidden neurons). The choice of such a structure was justified by the simplicity of calculations, and the use of MLP has been repeatedly justified in the literature and was often used earlier to study problems of similar complexity [1; 9; 10; 33; 34; 35]. At this stage, we empirically selected ANN parameters according to the number of hidden neurons (structures from 2 to 20 neurons were tested). Preference was given to such an ANN structure, with the use of which it was possible to obtain the best approximation with the least number of training epochs. The schematic diagram of the internal structure of the ANN used by us to calculate the ARP of food systems is shown schematically in Figure 1. The number of input neurons was equal to the number of cells in the FNDDS database (with the exception of three, which were removed from the calculation, since these substances were not present in the products we studied: alcohol content, and specially added vitamins B\({}_{12}\) and tocopherols. All input neurons are schematically combined for visual convenience in one rectangle (see Figure 1) Hyperbolic tangent (Tanh) was used as the activation function of latent neurons. Figure 1: The scheme of a neural network with the structure of an MLP, with highlighted stages of the study [29]. Antifradical activity values within the 95% CI for the output neurons were designated by the term ARP (max-min). In addition to the number of neurons, the applicability of several activation functions was tested--threshold (Thd), logarithmic (Log), hyperbolic tangent (Tanh), sigmoid (Sig). As in the first case, preference was given to those configurations that had the fewest training epochs. For different configurations, the number of epochs varied from 5.5 to 80 thousand. The training curves for different functions are shown in Figure 2.  
In the upper right corner of Figure 2 (inset), there is a fragment of the curve obtained for a neural network with a threshold activation function (Thd) in the hidden layer of neurons.