Backpropagation Neural Network Training

The Backpropagation (BP) neural network represents one of the most fundamental feedforward neural networks, utilizing the backpropagation algorithm for weight adjustments. Its training process consists of two critical phases: forward propagation and backward propagation.

Network Architecture Analysis This implementation employs a classic three-layer architecture: Input Layer: Receives individual feature values through input nodes Hidden Layer: Performs nonlinear transformations using sigmoid activation function, mapping inputs to the (0,1) range Output Layer: Utilizes linear activation function to maintain numerical continuity, making it suitable for regression tasks

Training Mechanism Explanation Forward Propagation Phase: Input data undergoes layer-by-layer computation, where hidden layer nodes apply sigmoid function after weighted summation, while output layer directly transmits weighted sums Error Calculation: Employs mean squared error to quantify the deviation between predicted values and actual targets Backward Propagation Phase: Output Layer Gradient: Computed directly from error terms using derivative calculations Hidden Layer Gradient: Errors propagate backward from output layer, combined with sigmoid derivative computations Weight Updates: Implements gradient descent optimization with learning rate to adjust layer weights systematically

Key Design Characteristics The hidden layer's sigmoid function introduces nonlinear capabilities, though potential gradient vanishing issues require consideration Output layer's linear activation prevents output range limitations Learning rate selection critically impacts convergence speed and training stability

This architecture effectively addresses simple nonlinear regression problems. In practical applications, performance can be further enhanced by adjusting hidden layer node count, incorporating momentum factors, or implementing advanced optimization techniques. Code implementation typically involves matrix operations for efficient computation, with careful attention to gradient calculation precision and weight initialization strategies.