Softmax Function

What is Softmax in Machine Learning?

The softmax function reduces K values to real values that add up to 1. The softmax turns these values, which might be negative, zero, positive, or higher than one, to the values 0, 1, and numbers between those two, allowing them to be understood as probabilities.

  • If one of the inputs is tiny or negative, the softmax converts it to a small probability; if one of the inputs is high, it becomes a large probability; nonetheless, it will always be between 0 and 1.

Softargmax, or multi-class logistic regression, is another name for it. It’s because the softmax is a multi-class classification generalization of logistic regression, and its formula is extremely similar to the sigmoid function used in logistic regression. Only when the classes are mutually exclusive can this function be employed in a classifier.

Many multi-layer neural networks conclude with a penultimate layer that produces real-valued scores that are difficult to scale and manipulate. The softmax is particularly beneficial in this situation since it turns the scores to a normalized probability distribution that may be displayed to users or used as input to other systems.

As a result, it’s common to add the softmax classification layer as the neural network’s last layer.

Softmax function in Neural network

The function can be used at the end of a neural network, for example. Consider a convolutional neural network that can determine whether an image is of a human or a dog. It’s worth noting that an image can either be a human or a dog, not both, hence the two groups are mutually exclusive.

In most cases, the network’s last fully connected layer produces data that is not normalized and cannot be understood as probabilities. It is possible to convert the numbers into a probability distribution by adding a softmax layer to the network.

This means that the output can be shown to a user; for example, the app knows that this is a human 90% of the time. It also means that the output does not need to be normalized before being fed into other machine learning algorithms, as it is guaranteed to fall between 0 and 1.

  • When the network is only configured to have two output classes and is classifying images into humans and dogs, it is obliged to categorize every image as either humans or dogs, even if it is neither. If we need to account for this possibility, we’ll need to change the neural network’s configuration to include a third output for miscellaneous.


When we’re training a neural network, the softmax is crucial. Consider a convolutional neural network that is learning to tell the difference between dogs and humans. We assigned the dog to class 1 and the human to class 2.

When we feed our network a dog image in an ideal world, it should return the vector [1, 0]. We want an output [0, 1] when we enter a human image.

The final fully connected layer is when the softmax neural network image processing concludes. This layer generates two non-probabilistic scores for the dog and the human. A softmax layer, which turns the output into a probability distribution, is usually added near the end of the neural network. Weights are randomly formed at the start of training.

  • We may define a loss function for our network that quantifies how far the output probabilities of the network deviate from the desired values. The output vector is closer to the proper class when the loss function is small.

The derivative of the loss function may be calculated concerning every weight in the network, for every image in the training set, because the softmax is a continuously differentiable function.

This attribute allows us to tweak the network’s weights to lower the loss function, bring the output closer to the intended values, and increase the network’s accuracy.

Because the argmax function is not differentiable, the procedure of differentiating the loss function in order to determine how to alter the weights of the network would not have been possible. The softmax function is important for training neural networks because of its differentiability property.

When you’re using the softmax function in a machine learning model, be cautious about interpreting it as a genuine probability because it tends to produce values that are very close to 0 or 1.