Hello, and welcome to the journey of understanding and implementing neural networks using R! Neural networks are a cornerstone of machine learning and AI, enabling innovative solutions across many domains. In this lesson, you will learn how to create and define a simple neural network using the keras3 package in R. You will also gain an understanding of the components of a neural network, including layers, weights, biases, and activation functions.

Neural networks are computational systems inspired by the human brain. They consist of neurons (the most basic unit), which are assembled in layers to make the network. Each neuron in one layer is connected to neurons in the next layer through synaptic weights. Moreover, each neuron has a bias that allows shifting the neuron's activation threshold.

An activation function regulates the output of a neuron given a set of inputs and the weights associated with them. One popular activation function is the ReLU (Rectified Linear Unit) activation function. Neurons and layers play essential roles in neural networks, and understanding them is key to building effective models.

Visualizing a simple neural network with an input layer, a hidden layer, and an output layer:

In the above image, the input layer receives the data, the hidden layer processes it, and the output layer provides the final result. The hidden layer is where the magic happens, as it transforms the input data into a form that can be used to make predictions.

In the graphical representation, each circle represents a neuron, and the lines connecting them represent the weights. The weights are adjusted during the training process to minimize the error in the model's predictions.

Such a network can be used for various real-world applications, such as image recognition, natural language processing, and more — for example, predicting the price of a house based on its features or classifying an image as a cat or a dog.

We will build a neural network using the powerful keras3 package in R. Let's start by setting the backend and loading the required library:

Now that we have our library, we will accomplish the following steps:

1. Initialize a Sequential Neural Network.
2. Add an input and hidden layer.
3. Add an output layer.
4. Compile the model.
5. Train and evaluate the model.

A neural network can be thought of as a sequence of layers. In R, we can define this using the keras_model_sequential() function from the keras3 package.

The input layer forms the starting point of our network. It's where we feed in our data. For this model, we assume that we have 20 input features. In Sequential models, we typically specify the input_shape in the first dense layer.

This hidden layer with 64 neurons uses the ReLU activation function to introduce non-linearity.

The output layer provides the final prediction. For classification into 10 categories, we use 10 neurons and the softmax activation function.

The number of neurons in the output layer typically corresponds to the number of classes in a classification problem.

Now, we will compile the model. This step involves defining the loss function and optimizer. Since this is a classification problem, we use categorical crossentropy as the loss function.

Let’s print the summary of our model:

The output of the above code will look like:

This summary showcases the architecture of the neural network we just created. It includes the layer types, output shapes, and the number of parameters at each layer and in total. Observing this summary helps in understanding the model's complexity and its learning capacity.

To demonstrate training, let’s create some random input data and labels:

This shows how the model learns by adjusting its weights during training.

That's a wrap for this lesson! You've learned about neural networks, their components, and their architecture. You've also implemented a neural network using keras3 in R, defined layers, compiled the model, trained it with example data, and interpreted its summary.

As you move forward, you will encounter exercises reinforcing these concepts and providing hands-on experience with R and keras3. Remember, becoming proficient takes practice and persistence, so keep experimenting and coding!