PHASED INTEGRATION OF NEURAL NETWORKS OF DIFFERENT ARCHITECTURES IN MATHEMATICAL COMPUTING SYSTEMS

Background. The development of modern mathematical computing systems requires the effective implementation of machine learning algorithms while maintaining a balance between prediction accuracy and computational resources. Particular attention should be given to the phased integration of neural networks of varying complexity with minimized risks for production systems and investigation of the saturation effect when increasing architectural depth. Materials and Methods. This article aims to develop a methodology for evolutionary integration of neural networks from simple perceptrons to ultra-deep architectures in mathematical computing systems, with detailed comparative analysis of four architectural types and mathematical modeling of the accuracy saturation effect. Results and Discussion. For this purpose, four neural network architectures were investigated: a single-layer perceptron, a four-layer network (128→64→32), a ten-layer network (128→96→64→48→32→24→16→12), and a twenty-layer architecture with gradual dimensionality reduction. Experiments were conducted on a dataset from mathematical modeling results containing 45,000 samples with 24 characteristics. A comprehensive system of metrics was used to evaluate accuracy, processing speed, resource consumption, and model stability. The experimental design included stratified data splitting and cross-validation to ensure statistical reliability of the obtained results across different architectural configurations. Conclusion. As a result, the single-layer perceptron demonstrated baseline accuracy of 78.3% with minimal resource consumption (45 MB RAM, 15 ms latency). The four-layer network achieved 94.1% accuracy with a moderate increase in resource costs. The ten-layer architecture showed 95.6% accuracy, demonstrating the beginning of the saturation effect. The twenty-layer network achieved only 96.8% accuracy with disproportionate growth in resource consumption (1024 MB RAM, 270 ms latency). Mathematical modeling confirmed the logistic nature of the relationship between accuracy and architectural complexity . The findings provide practical guidelines for selecting optimal neural network architectures in resource-constrained production environments, establishing clear thresholds beyond which increased complexity yields diminishing returns. Keywords : Neural networks, evolutionary integration, mathematical computing, deep learning, saturation effect, architecture optimization