Advantages and disadvantages of sigmoid function

The advantages and disadvantages of sigmoid function are as follows:

Advantages:

1. Nonlinear mapping: sigmoid function maps the input to a continuous value between 0 and 1, which can handle nonlinear relations and is suitable for various nonlinear problems.

2. Derivability: sigmoid function can be derived on the definition domain, which makes it possible to use gradient descent algorithm to optimize when training neural network.

3. Interpretation of output probability: The output of sigmoid function can be interpreted as probability, which can be used for binary classification problems. An output value close to 0 indicates a low probability of belonging to a certain category, and a value close to 1 indicates a high probability of belonging to this category.

4. output range limitation: the output range of sigmoid function is bounded, which can avoid the problem that the output value is too large or too small.

Disadvantages:

1. gradient vanishing problem: when the input value is large or small, the derivative of sigmoid function tends to zero, which leads to the disappearance of gradient and makes the training of neural network difficult.

2. The output is not zero center: the output of sigmoid function is not centered on 0, which may lead to the deviation of neural network in training.

3. High calculation cost: The calculation of sigmoid function is relatively complicated, including exponential operation, and the calculation cost is high.

4. Easily saturated: When the input value is large or small, the output of sigmoid function is close to 0 or 1, which leads to neuron saturation and slow gradient update.

To sum up, sigmoid function has advantages in dealing with nonlinear problems and explaining output probability, but it has some disadvantages in gradient disappearance, output is not zero center, calculation cost and saturation. In practical application, it needs to be based on the requirements and characteristics of specific problems.

Sigmoid function

Sigmoid function is a commonly used mathematical function, which is often used in machine learning and neural network. The definition of sigmoid function is as follows: f (x) =1(1+e (-x)), where e stands for the base of natural logarithm. The value range of sigmoid function is between 0 and 1, which has the characteristics of S-shaped curve.