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Function of activation function
2022-07-06 06:00:00 【algolearn】
The activation function can introduce non-linear factors into the linear model , So as to solve the problem that linear model is difficult to solve .
Design a classification to separate the triangle and circle above , Take perceptron as an example , Consider a few situations :
Single layer perceptron Multilayer perceptron Single layer perceptron + Activation function Multilayer perceptron + Activation function
1 Single layer perceptron
The expression of single-layer perceptron is , It can draw a line , Divide the plane . For input features And characteristics , If , Prove to be a positive class ; If , Prove to be a negative class . We won't discuss it here In special circumstances . According to this, we can draw the coordinate map on the right .
No matter how the straight line obtained by the perceptron moves, it cannot separate the triangle from the circle .
2 Multilayer perceptron
The expression of multi-layer perceptron is shown in the formula on the right of the above figure , After the expression merges similar items , You can get , It can be found that no matter how it is combined , The final result is about the input linear equation, which can't deal with non-linear classification .
The straight line obtained by the multi-layer perceptron cannot separate the triangle from the circle no matter how it moves .
3 Single layer perceptron + Activation function
Add another one to the output of the sensor sigmoid Activation function , because sigmoid Is a non-linear function , So the output is obviously a nonlinear function , It is possible to solve the non-linear classification problem mentioned above .
Single layer perceptron + The curve obtained by activating the function may separate the triangle from the circle .
4 Multilayer perceptron + Activation function
Add the activation function to the output of the multi-layer perceptron , You can get the expression on the right . Because each layer is a non-linear output , The final output will also be a non-linear function , It is also possible for the non-linear classification problem mentioned above .
Multilayer perceptron + The curve obtained by activating the function may separate the triangle from the circle .
3、4 By constantly optimizing the loss function , Can learn to correctly classify the curves of triangles and circular points , As shown in the figure below 3 Curves .
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