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Why Choosing the Right Activation Function is Critical in Machine Learning

Have you ever wondered how a computer is able to recognize a handwritten digit? Or how a machine is able to predict whether an email is spam or not? The answer lies in a crucial component of neural networks called activation functions.

Activation functions are mathematical equations that determine the output of a neural network. They play a critical role in determining how information flows through the network. Conceptually, an activation function takes in a weighted sum of inputs and outputs a value that determines the activation level of a neuron. The output of the activation function is then passed on to the next layer of neurons.

While there are many types of activation functions, some of the most common ones include sigmoid, ReLU, and tanh. Each activation function has its own unique properties that make it suitable for different types of data and network architectures.

## Sigmoid

The sigmoid function is one of the earliest activation functions used in neural networks. Its output ranges from 0 to 1, making it useful for binary classification tasks. The function is defined as follows:

![Sigmoid function](https://miro.medium.com/max/1400/1*5PlJFyojNGIWTP7yMgjr5w.png)

The function is curved and has a maximum slope when the input is close to 0. This means that small changes in the input have a large effect on the output. This property is useful for training neural networks, as it allows the network to update its weights more quickly.

While the sigmoid function was once popular, it has since fallen out of favor due to its tendency to saturate when the input is too large or too small. When this happens, the gradient of the function approaches zero, making it difficult for the network to learn.

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## ReLU

The rectified linear unit (ReLU) function is one of the most popular activation functions used today. Defined as the positive part of the input, the ReLU function is simple and easy to compute:

![ReLU function](https://miro.medium.com/max/1400/1*oePAhrm74RNnNEolprmTaQ.png)

The ReLU function is linear for positive inputs and zero for negative inputs. This makes it useful for deep neural networks, which can suffer from the vanishing gradient problem if the activation functions saturate.

The ReLU function also has a sparsity-inducing effect, as many of its outputs are zero. This property can make the network more efficient by reducing the number of computations that need to be performed.

## Tanh

The hyperbolic tangent (tanh) function is similar to the sigmoid function, but its output ranges from -1 to 1. The function is defined as follows:

![Tanh function](https://miro.medium.com/max/1400/1*y6EhyqP17Mh0v-uwK5ivsg.png)

The tanh function is symmetric around the origin and has a steeper slope than the sigmoid function. This means that the output changes more quickly as the input changes, which can be useful for certain types of data.

The tanh function is also zero-centered, meaning that its output has a mean of zero. This property can help the network converge more quickly during training.

## Choosing an Activation Function

When designing a neural network, choosing the right activation function can be critical to its performance. The choice of activation function depends on the type of data being used and the architecture of the network.

For example, if the data is binary (i.e., either 0 or 1), the sigmoid function may be a good choice. If the data is continuous and the network has many layers, the ReLU function may be a better choice. If the data is centered around zero (e.g., images), the tanh function may be a better choice.

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It’s also possible to use different activation functions for different layers of the network. For example, a network may use the ReLU function for hidden layers and the sigmoid function for the output layer.

## Real-Life Applications

Activation functions are used in a wide range of applications, from image recognition to natural language processing. Here are a few examples of how activation functions are used in real-life scenarios:

* Handwriting Recognition: The MNIST dataset, which consists of handwritten digits, is a common benchmark for testing neural networks. The network takes in an image of a digit and outputs a probability that the digit is a certain number. The sigmoid function is often used for the output layer of the network, as it produces a probability between 0 and 1.

* Speech Recognition: In speech recognition, the network takes in a sequence of audio samples and outputs a sequence of phonemes. The ReLU function is often used for the hidden layers of the network, as it can help prevent the vanishing gradient problem that can occur when training deep neural networks.

* Sentiment Analysis: In sentiment analysis, the network takes in a sequence of words and outputs a sentiment score (e.g., positive or negative). The ReLU function is often used for the hidden layers of the network, while the sigmoid function is often used for the output layer.

## Conclusion

Activation functions are a critical component of neural networks that determine how information flows through the network. While there are many types of activation functions, each with its own unique properties, choosing the right one for the task at hand can be critical to the network’s performance. By understanding activation functions, we can gain a deeper understanding of how neural networks work and how they can be applied to real-life problems.

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