The Softmax function is a commonly used activation function, which is mainly used for the output layer in multi-classification problems. The Softmax function converts each element of the input vector into a real number between 0 and 1, so that the sum of all elements is equal to 1, representing the probability distribution of each category. The formula of the Softmax function is as follows:
scss
softmax(x_i) = exp(x_i) / sum(exp(x_j)) for j = 1 to n
Among them, x_i represents the i-th element in the input vector, and n represents the length of the vector.
The following is a Python sample code using the Softmax function:
python
import numpy as np
def softmax(x):
e_x = np.exp(x - np.max(x)) # prevent exponent overflow
return e_x / np.sum(e_x)
# Example using NumPy arrays
x = np.array([2, 1, 0.5])
result = softmax(x)
print(result) # Output: [0.65223987 0.23994563 0.1078145 ]
In the above example, we defined a softmax function that takes an input vector x and returns the computed result. We first process the input vector, use the np.exp function to calculate the index of each element, and perform a normalization operation so that the sum of all elements is equal to 1. Then we used a NumPy array as an example, calculated the result of the Softmax function, and printed the output.
The Softmax function is often used in the output layer in multi-classification problems to convert the original output of the model into a probability distribution. It allows the model to output the probability of each class to make classification decisions. During training, the Softmax function is usually used in conjunction with the cross-entropy loss function to calculate the difference between the model output and the true label.
It should be noted that the Softmax function may have a numerical overflow problem during exponential calculation. In order to solve this problem, some preprocessing is often performed on the input vector, such as subtracting the maximum value. This maintains computational stability and does not change the nature of the probability distribution.