Welcome back to our course "Neural Network Fundamentals: Neurons and Layers"! You've made excellent progress so far. In the previous lessons, we built a single artificial neuron and then enhanced it with the sigmoid activation function to introduce nonlinearity.

Today, we're taking a significant step forward in our neural networks journey. Rather than working with individual neurons, we'll learn how to group neurons together into layers — the fundamental building blocks of neural network architectures. Specifically, we'll implement a Dense Layer (also called a fully connected layer), which is one of the most common types of layers in neural networks.

By the end of this lesson, we'll have built a layer that can process multiple inputs through multiple neurons simultaneously, bringing us closer to implementing a complete neural network!

While a single neuron, as we've built, performs a basic computation, real-world problems demand more processing power. This is where layers come into play. A layer is essentially a group of neurons working in parallel, with each neuron in the layer processing the same input data independently. For instance, if a single neuron with 3 inputs produces 1 output, a layer of 5 such neurons, each receiving those same 3 inputs, would collectively produce 5 outputs.

This layered approach offers significant advantages:

• Increased Computational Power: Multiple neurons can learn diverse patterns from the data.
• Parallelism: All neurons in a layer compute their outputs simultaneously.
• Efficiency: Enables the use of vectorized operations (like matrix math) for faster computations.
• Hierarchical Learning: When layers are stacked, the network can learn increasingly complex features from the input.

This organization, inspired by how our brains process information, allows us to build more powerful and expressive neural network models.