MATHEMATICAL MODELING OF MACHINE LEARNING PROCESSES IN IMAGE RECOGNITION TASKS

Abstract

The relevance of this study is driven by the need to develop mathematically grounded approaches to optimizing machine learning algorithms applied in image recognition tasks. The rapid growth in visual information volumes, the complexity of its structure, and the requirements for algorithm accuracy and performance determine the necessity of finding universal methods capable of enhancing the reliability and practical effectiveness of computer vision systems. It is shown that traditional algorithmic solutions do not provide sufficient transparency in learning processes and often require complete retraining when environmental conditions change, which limits their applied use. The aim of this article is to develop conceptually and practically justified approaches to mathematical modeling of machine learning processes in the field of image recognition, which ensure improved accuracy, robustness, and adaptability of algorithms to real-world application conditions. The research methodology is based on combining systematic analysis of data properties, formalization of learning process patterns, and the use of statistical, optimization, and geometric methods. A multilevel modeling approach is employed, allowing simultaneous description of internal parametric changes in algorithm architectures and external characteristics of their functioning. The application of tools such as Scikit-learn, TensorFlow, PyTorch, OpenCV, and ResNet is proposed to ensure practical model implementation. The results of this work consist of investigating key complexity factors in mathematical modeling, including data multidimensionality and stochasticity, learning process nonlinearity, and hardware resource constraints. It is established that the application of formalized models ensures control over learning processes, increases algorithm accuracy, enhances robustness to noise and incomplete data, and opens opportunities for predicting results and adapting systems without the need for complete retraining. It is proven that integrating models into applied technologies in medicine, transportation, security, and industry enables error reduction, performance enhancement, and cost optimization. The conclusions confirm that mathematical modeling of machine learning processes is an effective tool for improving image recognition quality. Barriers to its application are identified, including high computational complexity, insufficient generalizability, and sensitivity to data quality. It is proven that overcoming these barriers is possible through implementing energy-efficient and modular architectures, adaptive mechanisms, and explainable AI methods. Prospects for further research are associated with improving simulation environments for model validation under realistic conditions, creating industry-specific annotated datasets, developing digital twins to reproduce learning processes, and integrating hybrid methods that combine statistical, geometric, and neural network approaches.