Softmax function activation hypothesis To function properly, neural networks depend on the activation function. To put it simply, a linear regression model is merely a neural network with a different label attached to it if the activation function is absent. This is because of the activation function’s role in producing non-linear behaviour in neural networks.
If you’re more of a visual and auditory learner, the video breakdown is provided below.
The softmax function activation function is the topic of this article. Before attempting a multi-class classification problem, it is important to understand how neural networks function, and more especially, why alternative activation functions cannot be employed.
So, let’s pretend we have a dataset like this one, where the target variable can take on one of three values and there are a total of five features associated with each observation (FeatureX1 through FeatureX5).
Construct a basic neural network for evaluation.
The information and locate the solution. With five distinct characteristics in this dataset, the Input layer has been designed with five neurons. Thereafter, there is just one covert layer of four neurons. We can see that the Zij value is the sum of the computations performed by each neuron using the inputs, weights, and biases shown.
The starting neuron in the neural network is denoted by the symbol Z11. Same terminology is used for the second neuron in the first layer (Z12).
The activation function is then applied to those values. As an example, we could apply the activation function tanh on the input values before passing them on to the output layer.
The class dimension of the dataset is used to standardise the neurons. The output layer will have three sets of neurons to account for the three categories found in the training data. These neurons are responsible for assigning probability to various categories. Simply put, the first neuron will represent the likelihood that a given data item belongs to class 1. The output of the second neuron will indicate the likeliness that the data point is associated with class 2, and so on.
So what if you do that, Sigmoid?
The Z value is computed using the weights and biases of this layer, and then the sigmoid activation function is applied, for example. Everyone knows that a sigmoid activation function has a domain between zero and one. For the time being, let’s pretend the final product looks like this.
As a first step, this network claims that the input data point is split evenly between two categories when employing a 0.5 threshold. Second, there is no connection between any of these alternatives. This is because the probability that the data item belongs to class 1 does not take into account the likelihood that it belongs to classes 2 and 3.
This is why the sigmoid activation function is not advised for dealing with multi-class situations.
The Switch to Softmax
Softmax will replace sigmoid as the preferred activation function in the last hidden layer. Probabilities are determined using the softmax function activation function. Meaning Z21, Z22, and Z23 are factored into the likelihood calculation.
First, let’s have a look at how the softmax function activation function can be used in the real world. The probabilities of the various classes are calculated using the SoftMax function, which is analogous to the sigmoid activation function.
This is an equation for the SoftMax activation function.
In this case, Z stands for the reported numbers from the layer’s neurons. As a means of introducing non-linearity, the exponential function is used. When the numbers have been transformed into probabilities, they are normalised by dividing by the sum of the exponential values.
In the case of a binary classification problem, you should always utilise the sigmoid activation function. The sigmoid function can be thought of as a special case of the more general softmax function. Here’s a link to further reading if you’re interested in learning more about this idea.
So that we can get a feel for how the softmax works, let’s start with a concrete example.
The following artificial neural network is available to us:
Here, we have a look at the outcomes with Z21 = 2.33, Z22 = -1.46, and Z23 = 0.56. Applying the SoftMax activation function to each of these neurons yields the subsequent outcomes. In this case, it’s abundantly obvious that the input belongs in Class 1. Hence, the value of the likelihood of the first class would change if the probability of any of the other classes changed.
Factors to Think About
The SoftMax activation function will be dissected in this article. In this article, we learned why sigmoid and tanh activation functions aren’t optimal for multiclass classification and how the softmax function can be utilised instead.
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