Softmax function

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Softmax function

What is the softmax function?

The softmax function is a function that converts a vector of K real values into a vector of K real values that add up to 1. The input values could be positive, negative, zero, or even greater than one, but the softmax transforms them into values between 0 and 1 which makes it possible for them to be interpreted as probabilities. 

Sometimes, the softmax function is referred to as the Softargmax function or multi-class logistic regression. This is due to the fact that softmax is a generalization of logistic regression that can be employed to carry out multi-class classification, and its formula very closely resembles that of the sigmoid function that is used for logistic regression.

Basically, the Softmax regression is a type of logistic regression that normalizes an input value into a vector of values that follows a probability distribution whose total adds up to 1. ​​Softmax is sometimes known as a multinomial logistic regression. Yet another name for softmax regression is the Maximum Entropy (MaxEnt) Classifier.

You can only really use the softmax function n a classifier only when the classes are mutually exclusive. 

A lot of multi-layer neural networks end in a penultimate layer which generates real-valued scores that are not conveniently scaled and which may be rather troublesome to work with. While working with this multi-layer neural networks, the softmax is highly useful due to the fact that it converts the scores to a normalized probability distribution, which can be displayed to a user or fed as input to other systems. Because of this reason, it is quite common to append a softmax function as the final layer of the neural network.

What does Softmax function do?

The softmax function acts as the  activation function in the output layer of neural network models that predict a multinomial probability distribution. To simplify this, let’s just say that the softmax function works as the activation function for multi-class classification problems in which class membership is needed on upwards of two class labels.

If you want to represent a probability distribution over a discrete variable with n possible values, you can make use of the softmax function. It is essentially a generalization of the sigmoid function which was used to represent a probability distribution over a binary variable.

You could also use the softmax function as an activation function for a hidden layer in a neural network, although this is not done very commonly. It could be used when the model internally needs to choose or weigh several different inputs at a bottleneck or concatenation layer.

Softmax units represent a probability distribution over a discrete variable with k possible values, so they could be used as a switch of some sort.

The softmax formula computes the exponential (e-power) the given input value and the total of exponential values of all the values in the inputs. After that, the ratio of the exponential of the input value and the sum of exponential values will be the output of the softmax function.

Why is it called softmax?

The softmax function can be seen as a probabilistic or “softer” version of the argmax function. It is known as the softmax function because it represents a smooth version of the winner-takes-all activation model where the unit that has the largest input has output +1 while all other units have output 0.

So basically, the softmax function is a softened version of the argmax function that returns the index of the largest value in a list.

How does the softmax layer work?

The softmax layer works like this: 

It assigns decimal probabilities to each class in a multi-class problem. Those decimal probabilities need to add up to 1.0. This additional constraint helps speed up the convergence of training. 

The Softmax gets implemented through a neural network layer right before the output layer. The Softmax layer needs to have the same number of nodes as the output layer.

The softmax function works on the assumption that every example is a member of exactly one class. However, there are examples that could be members of several classes simultaneously. When you are dealing with such examples you cannot make use of the softmax function. You will have to rely on multiple logistic regressions.

How do you calculate softmax? 

Softmax function
Source: Deep AI

If you want to calculate the softmax, you’re going to need to use the formula. Here is the softmax formula.

p(y=j|x) = e(wjtx + bj)kKe(wkTx + bk)

This formula essentially extends the formula for logistic regression into multiple classes.

What are the types of softmax?

What are the types of softmax?

The variants or types of softmax include:

Full Softmax 

This is the type of softmax that we have been talking about all along. Full softmax calculates a probability for every possible class.

Candidate sampling

In candidate sampling, Softmax calculates a probability for all the positive labels but only calculates probabilities for a random sample of negative labels. As an example, if you’re trying to figure out whether an input image is an apple or an orange, you wouldn’t have to calculate probabilities for every non-fruit example.

Full softmax can be quite cheap when there is a rather small number of classes, but it can become far too expensive when the number of classes climbs. In such problems where there is an extremely large number of classes, candidate sampling can be used to improve the efficiency.

​​What is the advantage of softmax?

The most significant advantage of making use of the softmax function is the output probabilities range. The range will be from 0 to 1 and the total of all the probabilities will sum up to 1. When the softmax function is employed for a multi-classification model it will return the probabilities of each class and the target class will have the high probability. 

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