Introduction

Softmax  Functional activation theory of the softmax The activation function is essential for the operation of neural networks. Without the activation function, a linear regression model is just another name for a neural network. This is due to the fact that neural networks exhibit non-linear behaviour as a result of the activation function.

If you learn best when you see and hear something, please check out the video explanation down below. 

If you want to find out more, you should read this article.

For what purposes do activation functions serve in Deep Learning?

This paper discusses the SoftMax activation function. It is useful for many classification problems. As a first step, let's find out how neural networks work, and more specifically, why different activation functions can't be used for a multi-class classification task.

Example

So, let's imagine we have a dataset like this one, where each observation is accompanied by five features (FeatureX1 through FeatureX5) and the target variable can take on one of three values.

Create a simple neural network to analyse 

The data and find the answer. To account for the five distinct features in this data set, the Input layer consists of five neurons. A single hidden layer of four neurons follows. This is a network of neurons, and the Zij value is the sum of the calculations made by each neuron with the inputs, weights, and biases displayed.

Z11 stands for the first neuron in the initial layer of the neural network. The second neuron in the initial layer also uses the same nomenclature (Z12).

After that, we use the activation function on top of those numbers. To illustrate, we could use the activation function tanh to transform the input values before sending them on to the output layer.

The output layer's 

Neurons are normalised by the dataset's class dimension. To accommodate the three classes present in the training data, the output layer will consist of three distinct populations of neurons. It is the job of these neurons to determine the probabilities associated with distinct classes. In other words, the first neuron will indicate the probability that a data point belongs to class 1. The second neuron will yield the probability that the data point is related with class 2, and so on.

What's the harm in that, Sigmoid?

Let's say that the Z value is calculated using the weights and biases of this layer, and then the sigmoid activation function is applied. It is common knowledge that the range of a sigmoid activation function lies between 0 and 1. Let's imagine the end outcome looks like this for the moment.

To begin, while using a 0.5 threshold, this network states that the input data point belongs to two classes. Second, none of these possibilities have any relationship with one another. That's because the chances of the data item belonging to classes 2 and 3 aren't factored into the probability that it belongs to class 1.

Because of this, the sigmoid activation function is not recommended for dealing with problems involving more than one class.

Softmax's Turning On

In the final layer, Softmax will replace sigmoid as the activation function of choice. The Softmax activation function is used to calculate the probabilities. This signifies that the likelihood is computed taking into account Z21, Z22, and Z23.

Let's have a look at the practical application of the softmax activation function. The SoftMax function, which is similar to the sigmoid activation function, is used to determine the probability of the various classes. 

The SoftMax activation function is represented here by the following equation.

In this scenario, Z represents the numerical values that are reported by the layer's neurons. The exponential function is used to introduce non-linearity. These numbers are then normalised by dividing by the total of exponential values after being converted to probabilities.

Always keep in mind that the sigmoid activation function is used instead when there are just two classes. Since the Softmax function is more general, it follows that the sigmoid function is just a specific case of it. If you're curious about this concept any more, here's a link for more reading.

To begin, let's examine a simple case study to better understand the softmax,

We have access to the following neural network:

The results Z21 = 2.33, Z22 = -1.46, and Z23 = 0.56 are looked at here. The following results are obtained by applying the SoftMax activation function to each of these neurons. Here, it's crystal clear that the input is in Category 1. So, if the chance of any of these classes changed, the value of the probability of the first class would change as well.

Considerations for the Future

In this article, we will examine the SoftMax activation function in detail. Here, we saw why activation functions like sigmoid and tanh shouldn't be used for multiclass classification and how the softmax function can help.

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