## Activation Functions in Neural Networks: Understanding Leaky ReLU

The human brain is one of the most complex and sophisticated organs in the body, capable of processing an enormous amount of information every second. However, the same cannot be said for machines, as they require specific algorithms and functions to understand and process data.

This is where artificial neural networks come in. Neural networks are a set of algorithms that allow machines to learn and make decisions like humans.

In this article, we will focus on one critical component of neural networks, the activation functions. We will discuss what they are, their functions, and introduce one of the most popular activation functions, Leaky ReLU.

### 1. Definition of Activation Function

Activation Functions are mathematical equations that are essential in neural networks. They determine the output of a node or neuron in the network, based on the input received.

This input can come from other neurons in the same layer or inputs from the previous layer. The role of activation functions is to introduce non-linear properties to the network, allowing it to learn and classify input data.

### 2. Examples of Activation Functions

**Sigmoid:**The sigmoid function is one of the first activation functions used in neural networks. It maps any input to a range of 0 to 1.**Step:**The step function is a simple activation function that maps any input to one of two values; 0 or 1.**ReLU:**The Rectified Linear Unit (ReLU) function is currently the most widely used activation function.**Leaky ReLU:**Leaky ReLU is a variation of the ReLU function that overcomes one of its shortcomings.

### 3. Definition and Function of Leaky ReLU

The Leaky ReLU function overcomes the shortcoming of the ReLU function by setting any negative value to a small number instead of zero. In other words, if the input to the function is negative, it will be multiplied by a small constant like 0.01 instead of being set to zero.

This allows for the neuron to learn from negative inputs, and the network to be more accurate.

### 4. Comparison with ReLU

ReLU is faster and more efficient than other activation functions like Sigmoid and Tanh, but it has one major shortcoming. If the input is negative, it will set it to zero, which means that any negative input will not be used in the calculation.

Leaky ReLU overcomes this shortcoming by allowing negative inputs to be used in the calculation. Therefore, Leaky ReLU is a better alternative to ReLU, especially when working with deeper neural networks.

### 5. Determining Use Cases for Activation Functions

The choice of activation function depends on the problem being solved. For example, the Sigmoid function is commonly used in binary classification problems, where the output is either positive or negative, and we want to determine the probability of the output being positive.

The ReLU function is widely used in deep neural networks, as it allows for faster training and convergence of the network. On the other hand, Leaky ReLU is suitable for deeper networks, where large input values push the ReLU activation function to zero.

## Implementing Leaky ReLU in Python

Artificial Neural Networks (ANNs) have been an area of interest in machine learning for quite some time. Amongst the various components that make up ANNs, the activation functions are of significant importance.

One of the popular activation functions today is the Leaky ReLU. In this section, we will see how to implement it in Python.

### 1. Basic Implementation Using Conditional Statement

The basic implementation of the Leaky ReLU function in Python can be done using a simple if-else loop. The implementation is as follows:

def leaky_relu(x):

if x > 0:

return x

else:

return 0.01 * x

Here, the Leaky ReLU activation function is defined with the name `leaky_relu`

.

In this implementation, a constant value of `0.01`

is multiplied with the input value `x`

when it is negative.

### 2. Creating Graphs Using Matplotlib

Now that we have implemented the basic version of Leaky ReLU activation function, we can visualize it using Matplotlib. The following is a code snippet that plots the Leaky ReLU function on a graph.

import matplotlib.pyplot as plt

import numpy as np

x = np.linspace(-10, 10, 100)

y = np.vectorize(leaky_relu)(x)

plt.plot(x, y)

plt.title("Leaky ReLU Function")

plt.xlabel("Input")

plt.ylabel("Output")

plt.show()

The code above creates an array `x`

of values from -10 to 10 in increments of 0.1. The function is then applied to the `x`

array using `np.vectorize()`

and stored in the `y`

array. Finally, the `x`

and `y`

values are plotted using the `plt.plot()`

function from Matplotlib.

### 3. Limitations of Basic Implementation in Keras Neural Networks

Although the basic implementation of the Leaky ReLU function works in Python, it has its limitations when used in larger neural networks. Manually modifying the activation function can be tedious, especially when the network has multiple layers.

This is where deep learning libraries such as Keras can lend a helping hand.

### 4. Leaky ReLU in Keras Python

Let us now implement Leaky ReLU in a simple neural network using Keras. We shall use the popular MNIST dataset as it is easily available and commonly used.

#### Overview of Dataset Used for Demonstration

The MNIST dataset is a collection of 70,000 handwritten digits ranging from 0 to 9. These digits are of size 28 x 28 pixels and are stored in a grayscale format.

This dataset is widely used in computer vision and has been extensively used in image recognition problems.

#### Preprocessing Data for Neural Network

Before we proceed to the neural network model, we need to preprocess the data. We shall use the `Keras.datasets`

API to load MNIST data:

from keras.datasets import mnist

(x_train, y_train), (x_test, y_test) = mnist.load_data()

The above code returns 4 NumPy arrays: `x_train`

, `y_train`

, `x_test`

, and `y_test`

.

These arrays contain the training and testing data. Next, we shall convert the data into a format that can be fed to a neural network.

The input images shall be normalized and flattened:

x_train = x_train.reshape(x_train.shape[0], 28*28)

x_test = x_test.reshape(x_test.shape[0], 28*28)

x_train = x_train.astype('float32')

x_test = x_test.astype('float32')

x_train /= 255

x_test /= 255

Here, we reshape the input images from a 2D matrix of size 28 x 28 to a 1D array of size 784. We also normalize the input pixel values to a range of 0 to 1.

#### Creating Neural Network with Leaky ReLU Activation Function

Now that the data has been preprocessed, we can proceed with the creation of the neural network model. The model architecture is defined as follows:

from keras.models import Sequential

from keras.layers import Dense

from keras.layers import LeakyReLU

model = Sequential()

model.add(Dense(256, input_shape=(784,)))

model.add(LeakyReLU(alpha=0.1))

model.add(Dense(128))

model.add(LeakyReLU(alpha=0.1))

model.add(Dense(10, activation='softmax'))

model.summary()

Here, we define a sequential model that consists of 3 layers:

- a hidden layer with 256 neurons,
- a hidden layer with 128 neurons, and
- an output layer with 10 neurons representing the digits 0-9.

In the hidden layers, Leaky ReLU is used as the activation function. The slope of the negative part of the function is set to 0.1 using the `alpha`

argument.

#### Compiling and Running Neural Network Model

After creating the neural network model, we need to compile it before we can train and evaluate it. We shall use the `categorical_crossentropy`

loss function, as this is a multi-class classification problem:

model.compile(loss='categorical_crossentropy',

metrics=['accuracy'],

optimizer='adam')

Now, we can train the model using the training data:

history = model.fit(x_train, y_train,

epochs=10,

batch_size=128,

validation_data=(x_test, y_test))

After training the model, we can evaluate its performance on the test data:

score = model.evaluate(x_test, y_test, verbose=0)

print('Test loss:', score[0])

print('Test accuracy:', score[1])

The above code outputs the loss and accuracy of the model on the test data.

## Conclusion

In conclusion, we have learned how to implement the Leaky ReLU activation function in Python using both the basic implementation method and using the popular deep learning library Keras. The Leaky ReLU activation function overcomes the shortcoming of the ReLU activation function in larger neural networks.

With the implementation in Keras, we also saw how to preprocess data and create a simple neural network for image classification using the MNIST dataset.

## Advantages of Leaky ReLU as an Activation Function

One of the significant advantages of Leaky ReLU over other activation functions is that it prevents the issue of “dead” neurons. In neural networks, neurons that do not activate or learn from the data inputs are called “dead” neurons.

Since Leaky ReLU allows some input values to pass through even when the input is negative, it prevents the “dead” neuron issue and allows for the neural network to learn effectively. Additionally, the use of Leaky ReLU activation function helps in preventing vanishing gradients.

In deep neural networks, there is a chance of the gradients becoming very small, known as the vanishing gradient problem. Leaky ReLU helps in preventing this problem, as it utilizes a non-zero slope for negative input values.

## Choosing the Correct Activation Function Based on Dataset Analysis

Choosing the correct activation function is critical in determining the performance of the neural network. The choice of activation function depends on the data being used and the problem being solved.

For instance, the Sigmoid function works well in binary classification problems, while Softmax is suitable for multi-class classification problems. ReLU, on the other hand, is commonly used in deep neural networks, while Leaky ReLU is suitable for deeper networks, where a large input value can push the ReLU activation function to zero.

Therefore, it is necessary to thoroughly analyze the data before choosing an activation function. One must determine the range of input values, the number of hidden layers, the problem being solved, and the type of activation that would best suit the model.

This will help in selecting the right activation function to build an efficient and effective neural network model.

## How to Implement Leaky ReLU in Python and Keras

In this article, we have discussed two methods to implement Leaky ReLU in Python: a basic implementation using conditional statements and a more advanced implementation using the deep learning library Keras. The Keras implementation makes it easier to use Leaky ReLU in larger neural networks, as it automatically modifies the activation function of multiple layers.

To implement Leaky ReLU using Keras, one just needs to use the `LeakyReLU`

function from the `keras.layers`

module. It takes an optional argument, `alpha`

, which sets the slope of the negative part of the function.

In summary, understanding activation functions and their roles in neural networks is crucial in building effective and efficient models for solving real-world problems. Leaky ReLU is a popular activation function that provides many advantages, such as preventing the vanishing gradient problem and the issue of dead neurons.

Choosing the correct activation function through careful data analysis can be the key to achieving optimal results. With the availability of deep learning libraries such as Keras, implementing Leaky ReLU has never been easier.

Activation Functions are a fundamental component of neural networks and play a crucial role in enabling machines to make decisions like humans. In this article, we explored different activation functions, focusing on Leaky ReLU, which has proven effective in preventing dead neurons and vanishing gradients.

We discussed how choosing the right activation function for a neural network depends on the problem being solved and the dataset. We learned how to implement Leaky ReLU in Python using conditional statements and advanced methods using the Keras library.

In conclusion, understanding activation functions’ importance can help build efficient and accurate machine learning models.