The BP algorithm (back propagation algorithm) is a basic algorithm used for neural network training. It iteratively adjusts the weights and biases of the neural network layer by layer to make the output of the network as close as possible to the desired output. The reason why the BP algorithm can train neural networks is that it is based on the idea of gradient descent and optimizes network parameters by minimizing the loss function.
The principle of BP algorithm is as follows:
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Forward Propagation: Starting from the input layer, the input signal is calculated through the weight and activation function of each layer to obtain the output result of the network.
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Loss Calculation: Compare the output of the network with the expected output and calculate the error (loss) of the network.
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Backward Propagation: Starting from the output layer, calculate the gradient (derivative) of each layer based on the loss value, and then pass the gradient forward to the input layer. The chain rule is used here to calculate the gradient of each layer and back-propagate the loss along the network.
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Update weights and biases (Weight and Bias Update): Use the idea of gradient descent to update the weights and biases of each layer according to the magnitude of the gradient and learning rate, so that the loss function continues to decrease.
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Repeat the above steps: through multiple iterations, continuously adjust the weights and biases of the network until the set training stop condition is reached (such as reaching the maximum number of iterations or the loss function converges).
The principle of the BP algorithm can be better understood by comparing it to the temperature regulation of a shower. Suppose we want to adjust the temperature of the shower so that the output temperature is as close as possible to the desired temperature. We can think of the shower as a neural network and the thermostat as the weights and biases of the network. Initially, there is a certain gap between the shower temperature and the desired temperature, which is a loss. By adjusting the parameters of the thermostat (weights and biases) we can gradually reduce the losses so that the shower temperature gets closer and closer to the desired temperature.
In this analogy, the process of adjusting the temperature is similar to forward propagation, the process of calculating losses is similar to calculating losses, and adjusting the parameters of the thermostat is similar to back propagation and parameter updating. Through multiple iterations and constant adjustments to the parameters of the thermostat, the desired temperature can eventually be achieved. Similarly, through multiple iterations, the BP algorithm can continuously adjust the weights and biases of the neural network so that the output of the network gradually approaches the desired output.
To sum up, the BP algorithm uses the idea of gradient descent and uses backpropagation and parameter updating to gradually optimize the weights and biases of the neural network, thereby achieving network training and learning.