What is the sigmoid function

・In Japanese
Prerequisite knowledge
・Differential formula

■What is a sigmoid function?

The sigmoid function is a function often used in machine learning, and is expressed as follows.



Graphically, it is as follows.


The advantage of the sigmoid function is that it can be made to operate like a step response. Generally, step responses are often expressed by dividing them into cases as shown below, which makes them nonlinear and difficult to handle, but the sigmoid function can also be differentiated and is easy to handle.

■ Differentiation of the sigmoid function

Since the sigmoid function is a rational function, use the following Differential formula for rational functions.



From the above,


This is the result.

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