Softmax and Python Implementation

Softmax is an activation function used primarily in the output layer of multi-class classification neural networks. It takes a vector of raw, unnormalized scores and converts them into a probability distribution over the different classes. The output of the softmax function can be interpreted as the likelihood or probability of each class being the correct one.

The softmax function is defined as follows:

Given an input vector z = [z1, z2, ..., zn], the softmax function calculates the probability p_i for each element z_i as:

p_i = exp(z_i) / (exp(z1) + exp(z2) + ... + exp(zn))

Where:

exp is the exponential function, which raises the mathematical constant "e" (approximately 2.71828) to the power of the argument.

z_i represents the raw score or logit for the i-th class.

Key characteristics of the softmax function:

1. Probability distribution: The sum of all probabilities p_i will be equal to 1, ensuring that the output forms a valid probability distribution over the classes.
2. Amplifies differences: Softmax amplifies the differences between the scores, converting them into probabilities that emphasize the differences between classes. Higher scores will have correspondingly higher probabilities.
3. Output interpretation: The class with the highest probability is typically chosen as the predicted class by the model.

The softmax activation is particularly useful in multi-class classification tasks, where the neural network needs to predict a single class out of multiple possible classes. It is commonly used in conjunction with the cross-entropy loss function to train the neural network in such scenarios.

However, it is worth noting that softmax is not typically used in the hidden layers of the neural network, as it can make the model more susceptible to vanishing and exploding gradients during training. In the hidden layers, ReLU and its variants are commonly used for their ability to mitigate such issues.

In summary, softmax is a crucial activation function in multi-class classification neural networks, as it converts raw scores into meaningful class probabilities, allowing the model to make accurate predictions among multiple classes.

Python Implementation

To implement the softmax function in the python programming language, all you have to do is write the following code.

The result of running this code is shown in the original image at the top of the article. You can run the code in the following colab notebook: softmax activation function