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Activation functions for neural networks are an essential part of deep learning since they decide the accuracy and efficiency of the training model used to create or split a large-scale neural network and the output of deep learning models. The Activation Function is a valuable tool for neural networks since it allows them to focus on relevant data while discarding the rest. As with any other function, the Activation Function (the Transfer Function) takes an input and returns an output proportional to that input. The activation function of a node in a neural network specifies the node’s output in response to a particular input or group of inputs.

They effectively choose which neurons to activate or deactivate to achieve the intended result. The input is also nonlinearly transformed to improve performance on a sophisticated neural network. Any information in the 1 to -1 can have its output normalized with the activation function. Since neural networks are often trained on millions of data points, it is essential that the activation function be fast and that it minimizes the amount of time needed to calculate results.

Let’s check out the structure of Neural Networks now and look at how Neural Networks Architecture is put together and what elements are present in Neural Networks.

An artificial neural network contains a large number of linked individual neurons. The activation function, bias, and weight of each are specified.

Input layer – The domain’s raw data is sent into the input layer. This layer is the lowest level where any calculation takes place. The only thing these nodes do is relay data to the next secret layer.

Hidden layer – Upon receiving features from the input layer, the hidden layer performs various computations before passing the result on to the output layer. Layer 2 nodes are hidden from view, providing a layer of abstraction for the underlying neural network.

Output layer – The output of the network’s hidden layer is brought together at this layer, which provides the network’s ultimate value.

Importance of Activation Functions

Since a linear equation is a polynomial of just one degree, a neural network without an activation function is merely a linear regression model. It is easy to solve but restricted in its capacity to tackle complicated problems or higher-degree polynomials.

An activation function is used in a neural network to provide non-linearity. Although the activation function’s computation adds an extra step at each layer during forward propagation, it is well worth the effort.

In the absence, every neuron will be doing a linear transformation on the inputs using the weights and biases. The composite of two linear functions is a linear function itself; hence the total number of hidden layers in the neural network does not affect its behavior.

Types of Activation Function

Neural Network is classified mainly into three parts under which different Activation Functions are used.

Binary step function

Linear function

Non-linear activation function

Binary Step Neural Network Activation Function

Binary Step Function

This activation function is quite simplistic, serving primarily as a threshold-based classifier in which we set a threshold value to determine whether a particular neuron’s output is activated. If the value of the input to the activation function is more significant than a certain threshold, the neuron is activated, and its output is passed on to the next hidden layer; otherwise, the neuron is deactivated.

Limitations:

It is unsuitable for issues requiring multiple values, such as multi-class classification, because it only provides single-valued results.

Since the step function has no gradient, backpropagation encounters difficulty.

Linear Neural Network Action Function

Linear Function

An activation function where the output is equal to the input is called a linear activation function. This function is also called “no activation” or the “identity function” (x1.0). The function takes the weighted sum of the input and spits out the value without changing it. In other words, our function is proportional to the total of neurons or input. Therefore we have a straight-line activation function. Generating a broad range of activations is more efficient using linear activation functions. A line with a positive slope may increase the firing rate in response to an increase in the input rate.

Limitations:

Backpropagation cannot be used since the function’s derivative is a constant with no bearing on the input x.

The neural network’s last layer is always a linear function of the first layer. A linear activation function eliminates all of its layers to reduce the neural network to its simplest form. When a linear activation function is applied to a neural network, all layers will effectively merge into a single super layer.

Non-Linear Neural Network Activation Function

Sigmoid Activation Function

This function accepts real numbers as input and returns integers between 0 and 1. The output value will be closer to 1.0 the bigger (more positive) the input is and will be closer to 0.0 the smaller (more negative) the input is. As a result, it finds its most common application in models whose output requires probability prediction. A sigmoid distribution is appropriate since all probabilities lie between 0 and 1. It’s also called a Logistics Function.

Limitations:

Logistic functions do not produce symmetrical results near zero. This ensures that all neuron outputs share the same sign. This complicates the inherently unstable training of the neural network.

2. ReLU (Rectified Linear unit) Activation Function

Nowadays, the ReLU is the most popular activation function. Since this is a crucial component of any deep learning or convolutional neural network system. While the function’s 0–infinity range presents some challenges, the fact that negative values are converted to zero at such a high rate means that it neither maps nor fits into data correctly. The critical hitch is that the ReLU function does not activate all neurons simultaneously. The neurons are turned off when the linear transformation yields a value less than 0. Since ReLU is linear and non-saturating, it speeds up the gradient descent’s approach to the global minimum of the loss function.

Limitations:

Because of the potential for the weights to go negative at a high Learning Rate, the output term could also be harmful. Reducing the learning rate is one possible solution for the same.

The model’s capacity to appropriately fit or learn from the data is impaired since all negative input values are instantly set to zero.

3. Tanh Function

Tanh function is also called as Hyperbolic function. The tanh is an improved version of the logistic Sigmoid. The tanh function has the range of (-1 to 1). Tanh is sigmoidal as well (s-shaped). The negative inputs are mapped strongly negatively, whereas the zero inputs are mapped near zero, which is an advantage when plotting a tanh graph. We can differentiate the function. While the function itself is monotonic, its derivative is not.

Limitations:

Similar to the sigmoid activation function, it suffers from the issue of vanishing gradients. And the tanh function’s gradient is much steeper than the Sigmoid’s.

4. Leaky ReLU Function

Because of its slight positive slope in the negative area, Leaky ReLU is an enhanced variant of the ReLU function that can be used to circumvent the Dying ReLU problem. Consequently, the nodes are not turned off, and the ReLU problem of dying nodes is avoided since negative values are not converted to 0.

Limitations:

Learning model parameters can be tedious when the gradient is minimal for negative values.

5. Parametric ReLU Function

The P-ReLU or Parametric Since negative values do not reach 0, the nodes are not turned off, and the dying ReLU problem does not arise, ReLU is a variant of the Leaky ReLU variate that seeks to replace the negative half of ReLU with a line of a slope.

Limitations:

Depending on the value of the slope parameter, it may yield varying results for various issues.

6. Exponential Linear Units Function

The ELU activation function is another option, and it is well-known for its rapid convergence and high-quality output. A modified exponential function is substituted for the negative terminal. Unfortunately, there is a growing computational overhead, but at least the ReLU problem is no longer terminal. It reduces the likelihood of the “dead” ReLU issue by providing a “log” curve for negative input values. It aids the network in adjusting its biases and weights appropriately.

Limitations:

The inclusion of an exponential operation causes a rise in processing time.

The value of ‘a’ is not acquired in any way, and the Gradient explosion issue is one of the main limitations.

7. Scaled Exponential Linear Units Function

Internal normalization is handled by SELU, which was developed for self-normalizing networks and ensures that the mean and variance of each layer are maintained. By modifying the mean and variance, SELU makes this normalization possible. Because the ReLU activation function cannot produce negative values, SELU may move the mean in previously impossible ways. The variance may be modified with the use of gradients.

To be amplified, the SELU activation function requires an area with a gradient greater than one. Network convergence occurs more quickly when internal normalization is used more than external normalizing.

8. Gaussian Error Linear Unit Function

Many of the most popular NLP models, including BERT, ROBERTa, and ALBERT, are compatible with the GELU activation function. Dropout, zoneout, and ReLUs qualities are combined to inspire this activation function. Across all tasks in computer vision, NLP, and speech recognition, GELU non-linearity improves performance more than ReLU and ELU activations.

9. Softmax Activation Function

In the same way that sigmoid activation assigns a value to each input variable based on its weight, softmax assigns a value to each input variable based on the sum of these weights, which is ultimately one. This is why softmax is typically used at the output layer, the final layer used for decision-making.

Conclusion

To better comprehend and carry out increasingly complicated tasks, the input is often subjected to a non-linear transformation, and activation functions like these play a crucial role in this process. A neural network’s hidden layers will typically have the same activation function. As the network’s parameters may be learned by backpropagation, this activation function has to be differentiable. We have covered the most common activation functions, their limitations (if any), and how they are employed.

Despite the widespread familiarity with the “Activation Function,” few like to contemplate its effects. Why they’re utilized, how they contribute, what has to be said, etc. Although the issues may appear straightforward, the underlying dynamics may be rather complicated.

References:

https://www.analyticssteps.com/blogs/7-types-activation-functions-neural-network

https://towardsdatascience.com/activation-functions-neural-networks-1cbd9f8d91d6

https://thehackweekly.com/8-most-popular-types-of-activation-functions-in-neural-networks/

https://www.v7labs.com/blog/neural-networks-activation-functions

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