Neural Network Forward Propagation

Hello, and welcome to today's exciting lesson! We will delve into the world of neural networks, focusing on a technique called forward propagation, or the data flow from input to output in a neural network.

Neural networks are a variety of machine learning models inspired by the human brain. They draw upon the idea of having neurons interconnected in a net-like structure to process and learn from information, similar to how our brain learns from the data fed into it by our senses. One basic and essential step in how a neural network processes and learns from information is termed forward propagation.

As the name suggests, forward propagation involves moving forward through the network. Each node in the network receives inputs from the nodes in the previous layer, multiplies them by their weights, adds a bias, and then "fires" that through an activation function. The result is then passed on as input to the nodes in the next layer. This process is repeated layer after layer until we reach the output layer, giving us the predicted output.

But what if the predicted output is far from the actual result? That's when backpropagation comes into play. In simple terms, backpropagation is the method used to update the weights of our neural network based on error correction. The less the error, the better our model's predictions.

The entity that quantifies the error between predicted and actual outputs is the loss function. To minimize this loss and hence the prediction error, we use optimization algorithms like gradient descent. In this lesson, we focus on understanding forward propagation, setting a solid foundation for learning more intricate neural network operations such as backpropagation in future lessons.

Now, let's get our hands on practical implementation. We'll use the built-in iris dataset in R for our demonstration:

# Load required libraries
library(keras3)
library(dplyr)
library(ggplot2)

set.seed(42)

# Load the iris dataset
data(iris)

# Only use the first two features and first two classes
iris_binary <- iris %>%
  filter(Species %in% c("setosa", "versicolor")) %>%
  mutate(Species = as.numeric(Species == "versicolor")) # 0 for setosa, 1 for versicolor

X <- as.matrix(iris_binary[, 1:2]) # Sepal.Length and Sepal.Width
y <- iris_binary$Species

We start by loading the iris dataset, which is a classic dataset in statistics and machine learning. For this task, we only consider the first two features: sepal length and sepal width. We also convert the problem into a binary classification problem by selecting only the "setosa" and "versicolor" classes.