Custom BP Algorithm Implementation

Based on the provided information, I understand that "non-toolbox" refers to achieving tasks or objectives without relying on traditional tools and pre-built libraries. This approach represents an innovative methodology that enables developers to discover unique solutions while enhancing efficiency in daily programming work. In the context of neural network implementation, this means building the backpropagation algorithm from scratch using fundamental mathematical operations and matrix computations rather than depending on high-level frameworks like TensorFlow or PyTorch. The implementation typically involves manually coding the forward propagation phase with weight initialization and activation functions (such as sigmoid or ReLU), followed by the backward propagation phase where gradient calculations and weight updates are performed using chain rule derivatives. This methodology challenges conventional dependency on pre-built libraries, stimulates programming creativity and problem-solving skills, and encourages developers to adopt more flexible approaches when tackling complex machine learning problems. Consequently, non-toolbox implementations are gaining popularity in the programming community, with many companies and organizations adopting this approach to drive innovation and develop customized AI solutions.