Neural Network Training Based on Kolmogorov's Theorem

Neural network training based on Kolmogorov's theorem provides a mathematical framework for modeling connections similar to those in the human brain. This specific implementation features a three-layer architecture: 14 input nodes corresponding to feature dimensions, 29 hidden layer neurons with hyperbolic tangent sigmoid (tansig) activation functions for nonlinear transformation, and 8 output nodes using log-sigmoid (logsig) functions for final classification or regression. The training process employs the traingdx function, which combines gradient descent with adaptive learning rate and momentum for efficient convergence. During network training, critical implementation considerations include proper weight initialization using methods like Xavier or He initialization, dynamic learning rate adjustment through the traingdx algorithm, and comprehensive data preprocessing including normalization and feature scaling. The training dataset undergoes multiple epochs with batch processing to optimize model performance through backpropagation and gradient computation. In terms of code implementation, the network can be structured using MATLAB's Neural Network Toolbox with layers defined through the network function, where hiddenLayerSize = 29 specifies the architecture. The tansig and logsig functions handle activation computations, while training parameters are configured through net.trainFcn = 'traingdx' and associated property settings. Neural network training represents a sophisticated technical approach with broad applications in computer vision, natural language processing, and predictive analytics. Through continuous optimization of architecture design, hyperparameter tuning, and training methodologies, we can enhance model performance and advance artificial intelligence capabilities. The Kolmogorov theorem-based implementation particularly ensures theoretical foundation for network approximation capabilities while maintaining practical training efficiency.