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Understanding Activation Functions in Neural Networks

Recently, a colleague of mine asked me a few questions similar "why practise we have so many activation functions?", "why is that one works meliorate than the other?", "how do we know which one to use?", "is it hardcore maths?" and so on. And so I thought, why not write an article on information technology for those who are familiar with neural network only at a bones level and is therefore, wondering most activation functions and their "why-how-mathematics!".

Note: This article assumes that you have a basic knowledge of an artificial "neuron". I would recommend reading up on the basics of neural networks before reading this commodity for improve agreement.

Activation functions

Then what does an artificial neuron practice? But put, information technology calculates a "weighted sum" of its input, adds a bias and then decides whether it should be "fired" or not ( yep correct, an activation part does this, but let'due south go with the menstruum for a moment ).

So consider a neuron.

Now, the value of Y can exist anything ranging from -inf to +inf. The neuron really doesn't know the premises of the value. So how do we make up one's mind whether the neuron should burn down or not ( why this firing pattern? Because we learnt it from biology that's the way brain works and encephalon is a working testimony of an crawly and intelligent system ).

Nosotros decided to add "activation functions" for this purpose. To cheque the Y value produced by a neuron and decide whether outside connections should consider this neuron equally "fired" or not. Or rather allow'south say — "activated" or not.

Step function

The showtime thing that comes to our minds is how about a threshold based activation function? If the value of Y is above a certain value, declare information technology activated. If it'southward less than the threshold, and then say it's non. Hmm keen. This could work!

Activation function A = "activated" if Y > threshold else not

Alternatively, A = 1 if y> threshold, 0 otherwise

Well, what we just did is a "step function", see the below figure.

Its output is one ( activated) when value > 0 (threshold) and outputs a 0 ( not activated) otherwise.

Great. And then this makes an activation function for a neuron. No confusions. However, in that location are certain drawbacks with this. To understand it better, call up about the following.

Suppose you are creating a binary classifier. Something which should say a "yes" or "no" ( activate or not activate ). A Step function could practice that for you! That's exactly what it does, say a 1 or 0. Now, think well-nigh the use case where you would want multiple such neurons to be connected to bring in more classes. Class1, class2, class3 etc. What will happen if more than than one neuron is "activated". All neurons will output a i ( from step office). At present what would you determine? Which class is it? Hmm difficult, complicated.

Yous would want the network to activate but 1 neuron and others should be 0 ( but so would you lot exist able to say information technology classified properly/identified the class ). Ah! This is harder to railroad train and converge this way. It would have been ameliorate if the activation was not binary and it instead would say "50% activated" or "xx% activated" and then on. And then if more than than i neuron activates, you could discover which neuron has the "highest activation" and so on ( better than max, a softmax, but let's leave that for now ).

In this case every bit well, if more than than one neuron says "100% activated", the trouble withal persists.I know! But..since in that location are intermediate activation values for the output, learning can be smoother and easier ( less wiggly ) and chances of more 1 neuron being 100% activated is lesser when compared to footstep function while training ( also depending on what you are grooming and the data ).

Ok, so nosotros want something to give u.s. intermediate ( analog ) activation values rather than proverb "activated" or not ( binary ).

The starting time matter that comes to our minds would exist Linear part.

Linear role

A = cx

A straight line function where activation is proportional to input ( which is the weighted sum from neuron ).

This way, it gives a range of activations, and so it is non binary activation. Nosotros can definitely connect a few neurons together and if more than 1 fires, we could take the max ( or softmax) and decide based on that. And then that is ok as well. Then what is the problem with this?

If yous are familiar with gradient descent for grooming, you would notice that for this function, derivative is a constant.

A = cx, derivative with respect to x is c. That means, the gradient has no relationship with 10. It is a constant gradient and the descent is going to be on constant gradient. If at that place is an error in prediction, the changes made past back propagation is constant and non depending on the change in input delta(x) !!!

This is non that adept! ( not always, simply bear with me ). There is another problem likewise. Call back about connected layers. Each layer is activated by a linear function. That activation in plow goes into the next level equally input and the 2d layer calculates weighted sum on that input and it in turn, fires based on another linear activation part.

No matter how many layers we have, if all are linear in nature, the final activation role of final layer is nothing only merely a linear office of the input of first layer! Pause for a bit and call back about information technology.

That ways these 2 layers ( or N layers ) tin can be replaced by a single layer. Ah! Nosotros but lost the ability of stacking layers this way. No matter how nosotros stack, the whole network is still equivalent to a single layer with linear activation ( a combination of linear functions in a linear fashion is still some other linear office ).

Allow's movement on, shall we?

Sigmoid Function

Well, this looks smoothen and "stride office like". What are the benefits of this? Think about it for a moment. Offset things first, it is nonlinear in nature. Combinations of this role are also nonlinear! Great. Now we can stack layers. What about non binary activations? Yes, that too!. It volition give an analog activation dissimilar step role. It has a smooth gradient also.

And if you notice, between X values -two to 2, Y values are very steep. Which means, any small changes in the values of X in that region will cause values of Y to change significantly. Ah, that means this part has a tendency to bring the Y values to either end of the curve.

Looks like it's good for a classifier considering its belongings? Yes ! It indeed is. It tends to bring the activations to either side of the curve ( above ten = two and below x = -two for case). Making clear distinctions on prediction.

Another advantage of this activation function is, unlike linear function, the output of the activation function is always going to exist in range (0,1) compared to (-inf, inf) of linear office. Then we take our activations bound in a range. Nice, it won't blow up the activations then.

This is great. Sigmoid functions are ane of the most widely used activation functions today. Then what are the problems with this?

If you find, towards either terminate of the sigmoid role, the Y values tend to answer very less to changes in 10. What does that mean? The gradient at that region is going to be small-scale. It gives rise to a problem of "vanishing gradients". Hmm. Then what happens when the activations reach almost the "nearly-horizontal" function of the bend on either sides?

Gradient is small or has vanished ( cannot make significant alter because of the extremely pocket-size value ). The network refuses to larn further or is drastically boring ( depending on use case and until gradient /computation gets hit by floating point value limits ). There are means to work around this problem and sigmoid is still very popular in classification issues.

Tanh Function

Another activation office that is used is the tanh function.

Hm. This looks very similar to sigmoid. In fact, information technology is a scaled sigmoid function!

Ok, now this has characteristics similar to sigmoid that we discussed in a higher place. Information technology is nonlinear in nature, so great we tin can stack layers! Information technology is bound to range (-1, 1) so no worries of activations blowing upward. 1 point to mention is that the gradient is stronger for tanh than sigmoid ( derivatives are steeper). Deciding between the sigmoid or tanh will depend on your requirement of gradient force. Like sigmoid, tanh also has the vanishing slope problem.

Tanh is also a very pop and widely used activation office.

ReLu

After, comes the ReLu function,

A(ten) = max(0,x)

The ReLu function is equally shown above. It gives an output x if x is positive and 0 otherwise.

At kickoff expect this would look like having the same problems of linear function, every bit it is linear in positive axis. Get-go of all, ReLu is nonlinear in nature. And combinations of ReLu are also non linear! ( in fact information technology is a good approximator. Any function can be approximated with combinations of ReLu). Bully, so this means we tin can stack layers. Information technology is not spring though. The range of ReLu is [0, inf). This ways information technology tin blow upwards the activation.

Another point that I would like to talk over hither is the sparsity of the activation. Imagine a large neural network with a lot of neurons. Using a sigmoid or tanh will crusade most all neurons to burn down in an analog way ( remember? ). That ways nearly all activations volition be processed to describe the output of a network. In other words the activation is dense. This is plush. Nosotros would ideally want a few neurons in the network to non activate and thereby making the activations sparse and efficient.

ReLu give us this benefit. Imagine a network with random initialized weights ( or normalised ) and about 50% of the network yields 0 activation because of the characteristic of ReLu ( output 0 for negative values of x ). This means a fewer neurons are firing ( thin activation ) and the network is lighter. Woah, nice! ReLu seems to be awesome! Yes it is, just nothing is flawless.. Non even ReLu.

Considering of the horizontal line in ReLu( for negative X ), the gradient can go towards 0. For activations in that region of ReLu, gradient will be 0 because of which the weights will not get adapted during descent. That means, those neurons which go into that country volition end responding to variations in fault/ input ( merely considering gradient is 0, nothing changes ). This is chosen dying ReLu problem. This problem can crusade several neurons to just die and not respond making a substantial part of the network passive. There are variations in ReLu to mitigate this issue by simply making the horizontal line into non-horizontal component . for example y = 0.01x for 10<0 will make it a slightly inclined line rather than horizontal line. This is leaky ReLu. At that place are other variations as well. The master idea is to let the gradient be not nada and recover during preparation somewhen.

ReLu is less computationally expensive than tanh and sigmoid because information technology involves simpler mathematical operations. That is a good betoken to consider when nosotros are designing deep neural nets.

Ok, at present which one exercise we use?

At present, which activation functions to utilise. Does that mean nosotros just use ReLu for everything we do? Or sigmoid or tanh? Well, yes and no. When yous know the function y'all are trying to approximate has certain characteristics, y'all tin can choose an activation office which volition approximate the function faster leading to faster training procedure. For example, a sigmoid works well for a classifier ( run across the graph of sigmoid, doesn't it bear witness the backdrop of an ideal classifier? ) because approximating a classifier function as combinations of sigmoid is easier than peradventure ReLu, for instance. Which will lead to faster grooming process and convergence. You tin use your own custom functions as well!. If you don't know the nature of the function you are trying to learn, then maybe i would suggest offset with ReLu, and and then work backwards. ReLu works well-nigh of the time equally a general approximator!

In this article, I tried to describe a few activation functions used commonly. There are other activation functions also, but the full general idea remains the same. Research for ameliorate activation functions is still ongoing. Promise you got the thought backside activation function, why they are used and how do nosotros decide which i to apply.

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Source: https://medium.com/the-theory-of-everything/understanding-activation-functions-in-neural-networks-9491262884e0

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