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29.09.2020

Therefore, this function can be used as the loss function of logistic regression classifier. If the calculated value is closer to 1, then it means that it is closer to the world result, otherwise, it is farther away. If there is a three-layer neural network with input layer, hidden layer and output layer, we can calculate the partial derivative of the weight of the loss function. If we first calculate the partial derivative of the weight of the first layer, and then calculate the partial derivative of the weight of the second layer, we will find that there are some problems A lot of repeated calculation steps, like the example of simple function above, so, in order to avoid this kind of consumption, we use to find the partial derivative from the back to the front, find out the function value of each unit, find out the partial derivative of the corresponding unit, save it, multiply it all the time, and input the layer. The essence of calculation is from top to bottom. How can we only calculate the derivative once? If the equation is particularly complex, then the amount of calculation becomes very large. If all the results are close to the result value, then The closer it is to 0. Therefore, this function can be used as the loss function of logistic regression classifier. It is a complex composite function. One idea is that if the result is closer, the difference will be smaller, otherwise, it will be larger. Derivation of neural network loss function The loss function of neural network can be understood as a multi-level composite function, and the chain rule is used for derivation. The essence of calculation is from top to bottom. If we first calculate the partial derivative of the weight of the first layer, and then calculate the partial derivative of the weight of the second layer, we will find that there are some problems A lot of repeated calculation steps, like the example of simple function above, so, in order to avoid this kind of consumption, we use to find the partial derivative from the back to the front, find out the function value of each unit, find out the partial derivative of the corresponding unit, save it, multiply it all the time, and input the layer. This function provides such an idea. Therefore, this function can be used as the loss function of logistic regression classifier. Then there is a good feature, that is, no matter what x We can get the value between 0,1 for whatever it is; 1. If the calculated value is closer to 1, then it means that it is closer to the world result, otherwise, it is farther away. Then there is a good feature, that is, no matter what x We can get the value between 0,1 for whatever it is; 1. When calculating, save the value and multiply it to the following unit, so that the partial derivatives of each path only need to be calculated once, from top to bottom All the partial derivatives are obtained by calculating them from top to bottom. Derivation of neural network loss function The loss function of neural network can be understood as a multi-level composite function, and the chain rule is used for derivation. C is a function of a and E is a function of C. The essence of calculation is from top to bottom. When calculating, save the value and multiply it to the following unit, so that the partial derivatives of each path only need to be calculated once, from top to bottom All the partial derivatives are obtained by calculating them from top to bottom. 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