“The world is one big data problem.”
As it turns out—
This saying holds true both for our brains as well as machine learning.
Every single moment our brain is trying to segregate the incoming information into the “useful” and “not-so-useful” categories.
A similar process occurs in artificial neural network architectures in deep learning.
The segregation plays a key role in helping a neural network properly function, ensuring that it learns from the useful information rather than get stuck analyzing the not-useful part.
And this is also where activation functions come into the picture.
Sounds a little confusing? Worry not!
Here’s what we’ll cover:
Ready? Let’s get started :)
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An Activation Function decides whether a neuron should be activated or not. This means that it will decide whether the neuron’s input to the network is important or not in the process of prediction using simpler mathematical operations.
The role of the Activation Function is to derive output from a set of input values fed to a node (or a layer).
But—
Let’s take a step back and clarify: What exactly is a node?
Well, if we compare the neural network to our brain, a node is a replica of a neuron that receives a set of input signals—external stimuli.
Depending on the nature and intensity of these input signals, the brain processes them and decides whether the neuron should be activated (“fired”) or not.
In deep learning, this is also the role of the Activation Function—that’s why it’s often referred to as a Transfer Function in Artificial Neural Network.
The primary role of the Activation Function is to transform the summed weighted input from the node into an output value to be fed to the next hidden layer or as output.
Now, let's have a look at the Neural Networks Architecture.
Here’s the thing—
If you don’t understand the concept of neural networks and how they work, diving deeper into the topic of activation functions might be challenging.
That’s why it’s a good idea to refresh your knowledge and take a quick look at the structure of the Neural Networks Architecture and its components. Here it is.
In the image above, you can see a neural network made of interconnected neurons. Each of them is characterized by its weight, bias, and activation function.
Here are other elements of this network.
The input layer takes raw input from the domain. No computation is performed at this layer. Nodes here just pass on the information (features) to the hidden layer.
As the name suggests, the nodes of this layer are not exposed. They provide an abstraction to the neural network.
The hidden layer performs all kinds of computation on the features entered through the input layer and transfers the result to the output layer.
It’s the final layer of the network that brings the information learned through the hidden layer and delivers the final value as a result.
📢 Note: All hidden layers usually use the same activation function. However, the output layer will typically use a different activation function from the hidden layers. The choice depends on the goal or type of prediction made by the model.
When learning about neural networks, you will come across two essential terms describing the movement of information—feedforward and backpropagation.
Let’s explore them.
In the feedforward propagation, the Activation Function is a mathematical “gate” in between the input feeding the current neuron and its output going to the next layer.
To put it simply—backpropagation aims to minimize the cost function by adjusting the network’s weights and biases. The cost function gradients determine the level of adjustment with respect to parameters like activation function, weights, bias, etc.
So we know what Activation Function is and what it does, but—
Why do Neural Networks need it?
Well, the purpose of an activation function is to add non-linearity to the neural network.
Activation functions introduce an additional step at each layer during the forward propagation, but its computation is worth it. Here is why—
Let’s suppose we have a neural network working without the activation functions.
In that case, every neuron will only be performing a linear transformation on the inputs using the weights and biases. It’s because it doesn’t matter how many hidden layers we attach in the neural network; all layers will behave in the same way because the composition of two linear functions is a linear function itself.
Although the neural network becomes simpler, learning any complex task is impossible, and our model would be just a linear regression model.
Now, as we’ve covered the essential concepts, let’s go over the most popular neural networks activation functions.
Binary step function depends on a threshold value that decides whether a neuron should be activated or not.
The input fed to the activation function is compared to a certain threshold; if the input is greater than it, then the neuron is activated, else it is deactivated, meaning that its output is not passed on to the next hidden layer.
Mathematically it can be represented as:
Here are some of the limitations of binary step function:
The linear activation function, also known as "no activation," or "identity function" (multiplied x1.0), is where the activation is proportional to the input.
The function doesn't do anything to the weighted sum of the input, it simply spits out the value it was given.
Mathematically it can be represented as:
However, a linear activation function has two major problems :
The linear activation function shown above is simply a linear regression model.
Because of its limited power, this does not allow the model to create complex mappings between the network’s inputs and outputs.
Non-linear activation functions solve the following limitations of linear activation functions:
Now, let’s have a look at ten different non-linear neural networks activation functions and their characteristics.
This function takes any real value as input and outputs values in the range of 0 to 1.
The larger the input (more positive), the closer the output value will be to 1.0, whereas the smaller the input (more negative), the closer the output will be to 0.0, as shown below.
Mathematically it can be represented as:
Here’s why sigmoid/logistic activation function is one of the most widely used functions:
The limitations of sigmoid function are discussed below:
As we can see from the above Figure, the gradient values are only significant for range -3 to 3, and the graph gets much flatter in other regions.
It implies that for values greater than 3 or less than -3, the function will have very small gradients. As the gradient value approaches zero, the network ceases to learn and suffers from the Vanishing gradient problem.
Tanh function is very similar to the sigmoid/logistic activation function, and even has the same S-shape with the difference in output range of -1 to 1. In Tanh, the larger the input (more positive), the closer the output value will be to 1.0, whereas the smaller the input (more negative), the closer the output will be to -1.0.
Mathematically it can be represented as:
Advantages of using this activation function are:
Have a look at the gradient of the tanh activation function to understand its limitations.
As you can see— it also faces the problem of vanishing gradients similar to the sigmoid activation function. Plus the gradient of the tanh function is much steeper as compared to the sigmoid function.
ReLU stands for Rectified Linear Unit.
Although it gives an impression of a linear function, ReLU has a derivative function and allows for backpropagation while simultaneously making it computationally efficient.
The main catch here is that the ReLU function does not activate all the neurons at the same time.
The neurons will only be deactivated if the output of the linear transformation is less than 0.
Mathematically it can be represented as:
The advantages of using ReLU as an activation function are as follows:
The limitations faced by this function are:
The negative side of the graph makes the gradient value zero. Due to this reason, during the backpropagation process, the weights and biases for some neurons are not updated. This can create dead neurons which never get activated.
Note: For building the most reliable ML models, split your data into train, validation, and test sets.
Leaky ReLU is an improved version of ReLU function to solve the Dying ReLU problem as it has a small positive slope in the negative area.
Mathematically it can be represented as:
The advantages of Leaky ReLU are same as that of ReLU, in addition to the fact that it does enable backpropagation, even for negative input values.
By making this minor modification for negative input values, the gradient of the left side of the graph comes out to be a non-zero value. Therefore, we would no longer encounter dead neurons in that region.
Here is the derivative of the Leaky ReLU function.
The limitations that this function faces include:
Parametric ReLU is another variant of ReLU that aims to solve the problem of gradient’s becoming zero for the left half of the axis.
This function provides the slope of the negative part of the function as an argument a. By performing backpropagation, the most appropriate value of a is learnt.
Mathematically it can be represented as:
Where "a" is the slope parameter for negative values.
The parameterized ReLU function is used when the leaky ReLU function still fails at solving the problem of dead neurons, and the relevant information is not successfully passed to the next layer.
This function’s limitation is that it may perform differently for different problems depending upon the value of slope parameter a.
Exponential Linear Unit, or ELU for short, is also a variant of ReLU that modifies the slope of the negative part of the function.
ELU uses a log curve to define the negativ values unlike the leaky ReLU and Parametric ReLU functions with a straight line.
Mathematically it can be represented as:
ELU is a strong alternative for f ReLU because of the following advantages:
The limitations of the ELU function are as follow:
Mathematically it can be represented as:
Before exploring the ins and outs of the Softmax activation function, we should focus on its building block—the sigmoid/logistic activation function that works on calculating probability values.
The output of the sigmoid function was in the range of 0 to 1, which can be thought of as probability.
But—
This function faces certain problems.
Let’s suppose we have five output values of 0.8, 0.9, 0.7, 0.8, and 0.6, respectively. How can we move forward with it?
The answer is: We can’t.
The above values don’t make sense as the sum of all the classes/output probabilities should be equal to 1.
You see, the Softmax function is described as a combination of multiple sigmoids.
It calculates the relative probabilities. Similar to the sigmoid/logistic activation function, the SoftMax function returns the probability of each class.
It is most commonly used as an activation function for the last layer of the neural network in the case of multi-class classification.
Mathematically it can be represented as:
Let’s go over a simple example together.
Assume that you have three classes, meaning that there would be three neurons in the output layer. Now, suppose that your output from the neurons is [1.8, 0.9, 0.68].
Applying the softmax function over these values to give a probabilistic view will result in the following outcome: [0.58, 0.23, 0.19].
The function returns 1 for the largest probability index while it returns 0 for the other two array indexes. Here, giving full weight to index 0 and no weight to index 1 and index 2. So the output would be the class corresponding to the 1st neuron(index 0) out of three.
You can see now how softmax activation function make things easy for multi-class classification problems.
It is a self-gated activation function developed by researchers at Google.
Swish consistently matches or outperforms ReLU activation function on deep networks applied to various challenging domains such as image classification, machine translation etc.
This function is bounded below but unbounded above i.e. Y approaches to a constant value as X approaches negative infinity but Y approaches to infinity as X approaches infinity.
Mathematically it can be represented as:
Here are a few advantages of the Swish activation function over ReLU:
The Gaussian Error Linear Unit (GELU) activation function is compatible with BERT, ROBERTa, ALBERT, and other top NLP models. This activation function is motivated by combining properties from dropout, zoneout, and ReLUs.
ReLU and dropout together yield a neuron’s output. ReLU does it deterministically by multiplying the input by zero or one (depending upon the input value being positive or negative) and dropout stochastically multiplying by zero.
RNN regularizer called zoneout stochastically multiplies inputs by one.
We merge this functionality by multiplying the input by either zero or one which is stochastically determined and is dependent upon the input. We multiply the neuron input x by
m ∼ Bernoulli(Φ(x)), where Φ(x) = P(X ≤x), X ∼ N (0, 1) is the cumulative distribution function of the standard normal distribution.
This distribution is chosen since neuron inputs tend to follow a normal distribution, especially with Batch Normalization.
Mathematically it can be represented as:
GELU nonlinearity is better than ReLU and ELU activations and finds performance improvements across all tasks in domains of computer vision, natural language processing, and speech recognition.
SELU was defined in self-normalizing networks and takes care of internal normalization which means each layer preserves the mean and variance from the previous layers. SELU enables this normalization by adjusting the mean and variance.
SELU has both positive and negative values to shift the mean, which was impossible for ReLU activation function as it cannot output negative values.
Gradients can be used to adjust the variance. The activation function needs a region with a gradient larger than one to increase it.
Mathematically it can be represented as:
SELU has values of alpha α and lambda λ predefined.
Here’s the main advantage of SELU over ReLU:
SELU is a relatively newer activation function and needs more papers on architectures such as CNNs and RNNs, where it is comparatively explored.
There are two challenges you might encounter when training your deep neural networks.
Let's discuss them in more detail.
Like the sigmoid function, certain activation functions squish an ample input space into a small output space between 0 and 1.
Therefore, a large change in the input of the sigmoid function will cause a small change in the output. Hence, the derivative becomes small. For shallow networks with only a few layers that use these activations, this isn’t a big problem.
However, when more layers are used, it can cause the gradient to be too small for training to work effectively.
Exploding gradients are problems where significant error gradients accumulate and result in very large updates to neural network model weights during training.
An unstable network can result when there are exploding gradients, and the learning cannot be completed.
The values of the weights can also become so large as to overflow and result in something called NaN values.
You need to match your activation function for your output layer based on the type of prediction problem that you are solving—specifically, the type of predicted variable.
Here’s what you should keep in mind.
As a rule of thumb, you can begin with using the ReLU activation function and then move over to other activation functions if ReLU doesn’t provide optimum results.
And here are a few other guidelines to help you out.
Finally, a few rules for choosing the activation function for your output layer based on the type of prediction problem that you are solving:
The activation function used in hidden layers is typically chosen based on the type of neural network architecture.
And hey—use this cheatsheet to consolidate all the knowledge on the Neural Network Activation Functions that you've just acquired :)
Well done!
You’ve made it this far ;-) Now, let’s have a quick recap of everything you’ve learnt in this tutorial:
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