Popular Activation Functions In Neural Networks


Activation functions in neural networks

Within the neural network introduction article, we’ve mentioned the fundamentals of neural networks. This text focus is on differing types of activation features utilizing in constructing neural networks. 

Within the deep studying literate or in neural network online courses, these activation features are popularly referred to as switch features.

The primary focus of this text is to offer you an entire overview of assorted activation features and their properties. We’ll additionally see learn how to implement them in python.

Standard activation features in neural networks.

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Earlier than we drive additional, Let’s see the subject you will study on this article.

So let’s start with understanding what’s the activation operate. In the event you bear in mind choice tree, at every node the decision tree algorithm must take choice to separate the additional information, we will associated this to know about activation features.

What’s Activation Perform?

The title activation is self explainable. Because the title suggests, the activation operate is to alert or fireplace the neurons/node in neural networks.

If we deal with these features as a black field, like we deal with many classifiction algorihtms , these features will take enter and return output, which helps the neural community to cross the worth to the subsequent nodes of the community.

Activation features are very important parts within the neural networks, which helps the community to study the intricate patterns in practice information, which helps in predicting the long run.

In mathematical phrases, activation features are utilized in neural networks to compute the weighted sum of enter and biases, which is used to determine if a neuron might be fired or not. 

We are able to associated the computing the weighted sum with the linear regression concept.

It manipulates the introduced information by way of some gradient processing, often gradient descent, and afterward produces an output for the neural community that accommodates the parameters within the information. 

Activation features are also known as a switch operate in deep studying analysis papers literature. These activation features are having a set of properties to observe. 

Let’s talk about this.

Properties of activation features

Properties of activation functions

Properties of activation features

These features having the set of properties to observe,

  • Computational Cheap
  • Differentiable
  • Zero Centered

Computational Cheap

The activation operate computation must be very minimal, as this impacts the neural community coaching interval/time. 

For the sophisticated neural community architectures such because the Convolutional neural community (CNN), Recurrent Neural Community (RNN) wants many parameters to optimize. 

This optimization must compute the activation features at every layer. If the activation features are computational excessive, it can take a hell lot of time for getting the optimized weights at every layer within the community. 

So the important thing properties activation operate ought to observe computational inexpensiveness.


The second elementary property is differentiable.

Activation features need to be differentiable, regardless that we’re having linear features that are non-differentiable, to study the advanced patterns within the coaching information, the activation features should be differentiable. 

Now raised the opposite questions 

why the activation features have to differentiable?

In the event you bear in mind within the neural networks introduction article we defined the idea name backpropagation. Utilizing the backpropagation the networks calculate the errors it’ made beforehand and utilizing this info, it updates the weights accordingly to scale back the general community error. 

To carry out this the community makes use of the gradient descent method which wants the differential of the activation features.

Zero Centered

The output of the activation features must be zero centered, So this can assist in the calculated gradients to be within the similar course and shifting throughout. 

We mentioned the important thing properties of the activation features, now let’s talk about varied classes of those features.

Activation Perform Classes

Activation Function Categories

Activation Perform Classes

At a excessive stage, the activation operate categorized into 3 sorts.

  • Binary step features
  • Linear activation features
  • Nonlinear activation features

Binary step features

The less complicated activation operate is a step operate. The output worth will depend on the threshold worth we’re contemplating. If the enter worth is bigger than the edge worth the output might be 1, else the output might be 0.

This implies if the enter worth is greater than the edge worth which implies the node has to fireside, else no.

That is much like the way in which how logistic regression predicts the binary goal class.

Within the above graph, we’re contemplating the threshold worth as zero. If the graph will not be seen, scroll the code, you will discover the graph. 

This activation operate can be utilized in binary classifications because the title says, nonetheless, it cannot be utilized in a state of affairs the place you may have a number of courses to take care of.

Why is it used?

Some circumstances name for a operate which applies a exhausting threshold: both the output is exactly a single worth, or not. 

The opposite features we’ve checked out have an intrinsic probabilistic output to them i.e. a better output in decimal format implying a better likelihood of being 1 (or excessive output).

The step operate does away with this choosing a particular excessive or low output relying on some threshold on the enter  T. 

Nevertheless, the step-function is discontinuous and subsequently non-differentiable. Subsequently the usage of this operate in apply will not be finished with back-propagation.

Linear activation features

The linear activation operate is the only type of activation. In the event you use a linear activation operate the flawed method, your entire neural community finally ends up being a regression.

Undecided about that,

Simply suppose

How the community might be if we easy use the linear activation features?

Ultimately, we have to add all of the nodes activation features, if we’re utilizing the linear activation operate we might be including all of the linear features. So the sum of all of the linear features is a linear operate. 

This makes the community a regression equation.

Linear activations are solely wanted if you’re contemplating a regression problem, because the final layer.

Why is it used?

If there’s a state of affairs the place we wish a node to offer its output with out making use of any thresholds, then the id or linear operate is the way in which to go. 

The linear operate is not used within the hidden layers. We should use non-linear switch features within the hidden layer nodes or else output will solely ever find yourself being a linearly separable operate.


  • The output worth will not be binary.

  • Can join a number of neurons collectively, if anybody fires, we will take the utmost on to take the choice.


  • Derivate is fixed, which implies no use with the gradient descent.

  • Modifications within the backpropagation will depend upon the fixed derivate however not on the precise variable.

Each the binary step operate and the linear activation features are not so well-known when it comes to deep studying advanced and fashionable architectures. The nonlinear activation features are principally used. 

So let’s talk about varied nonlinear activation features.

Nonlinear activation features

We’re having quite a few non-linear activation features, on this article we’re primarily focussing on the beneath features.

  • Sigmoid Perform
  • Tanh Perform
  • Gaussian
  • Relu
  • Leaky Relu

Let’s begin with the sigmoid operate.

Sigmoid operate

The sigmoid activation function  is typically known as the logistic operate or squashing operate in some literature. 

Why it’s used?

This operate maps the enter to a worth between Zero and 1 (however not equal to Zero or 1). This implies the output from the node might be a excessive sign (if the enter is optimistic) or a low one (if the enter is destructive). 

The simplicity of its by-product permits us to effectively carry out backpropagation with out utilizing any fancy packages or approximations. The truth that this operate is easy, steady, monotonic, and bounded signifies that backpropagation will work nicely. 

The sigmoid’s pure threshold is 0.5, which means that any enter that maps to a worth above 0.5 might be thought of excessive (or 1) in binary phrases.

Similary to this we’ve the softwax operate which might used for multi classification problems. You may take a look on the key distinction by studying the softmax Vs sigmod article.


  • Interpretability of the output mapped between Zero and 1.

  • Compute gradient rapidly.
  • It’s has a easy gradient.


  • On the finish of the sigmoid operate, the Y values have a tendency to reply very much less to adjustments in X, this is called the Vanishing gradient downside.

  • Sigmoids saturate and kill gradients.
  • The optimization turns into exhausting when the output will not be zero centered.

Hyperbolic Tangent operate

The hyperbolic tangent operate generally known as the tanh operate is a smoother zero-entered operate whose vary lies between -1 to 1.

Why is it used?

It is a very related operate to the earlier sigmoid operate and has a lot of the identical properties, even its by-product is straight ahead to compute. Nevertheless, this operate permits us to map the enter to any worth between -1 and 1 (however not inclusive of these). 

In impact, this enables us to use a penalty to the node (destructive) reasonably than simply have the node not fireplace in any respect. 

This operate has a pure threshold of 0, which means that any enter worth better than Zero is taken into account excessive (or 1) in binary phrases. 

Once more, the truth that this operate is easy, steady, monotonic, and bounded signifies that backpropagation will work nicely. 

The next features don’t have all these properties which makes them tougher to make use of in backpropagation.


  • Environment friendly because it has imply Zero within the center layers between -1 and 1.

Now the query is

what’s the distinction between sigmoid and hyperbolic tangent?

They each obtain the same mapping, each are steady, easy, monotonic, and differentiable, however give out totally different values.

For a sigmoid operate, a bigger destructive enter generates an virtually zero output. This lack of output will have an effect on all subsequent weights within the community which will not be fascinating – successfully stopping the subsequent nodes from studying.

In distinction, the tanh operate provides -1 for destructive values, sustaining the output of the node, and permitting subsequent nodes to study from it. 

Gaussian Perform

Why is it used?

The Gaussian operate is a fair operate, thus it provides the identical output for equally optimistic and destructive values of enter. It provides its maximal output when there isn’t a enter and has reducing output with growing distance from zero. 

We are able to maybe think about this operate is utilized in a node the place the enter characteristic is much less more likely to contribute to the ultimate consequence. 

Rectified Linear Unit (ReLU)

This Relu is extensively utilized in Convolutional Neural networks. Because the operate is simply the max of enter and nil, It so is straightforward to compute and doesn’t saturate and does not trigger the Vanishing Gradient Downside.

You could got here accross these activation operate in extracting the text from the hand written images.

Why is it used?

The ReLU represents an almost linear operate and subsequently preserves the properties of linear fashions that made them straightforward to optimize, with gradient-descent strategies.

This operate rectifies the values of the inputs lower than zero thereby forcing them to zero and eliminating the vanishing gradient downside noticed within the earlier varieties of the activation operate.


  • Simple to implement and fast to compute.

  • It avoids and rectifies the vanishing gradient downside.


  • Problematic when we’ve plenty of destructive values because the final result is at all times Zero and results in the demise of the neuron.

  • It has only one concern of not being zero centered. It suffers from the “dying ReLU” downside


The LeakyRelu is a variant of ReLU. As an alternative of being Zero when 𝑧<Zero z<0, a leaky ReLU permits a small, non-zero, fixed gradient.

Why is it used?

As mentioned earlier than leakyRelu is a variant of Relu. Right here alpha is a hyperparameter typically set to 0.01. Leaky ReLU solves the “dying ReLU” downside to some extent. 

In the event you observe if we set α as 1 then Leaky ReLU will develop into a linear operate f(x) = x and might be of no use. Therefore, the worth of alpha isn’t set near 1. If we set alpha as a hyperparameter for every neuron individually, we get parametric ReLU or PReLU.

The activations features are not restricted to those however we’ve mentioned extensively used activation features within the trade.

The beneath determine exhibits the differing types of activation features.

Different activation functions

Completely different activation features (Supply: wikipedia)


To conclude, we supplied a complete abstract of the activation features utilized in deep studying.

The activation features have the potential to enhance the educational of the patterns in information there by automating the method of characteristic detection and justifying their use within the hidden layers of the neural networks.

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