Artificial neural networks are inspired by the structure of the human brain. They're not a perfect replica, but they borrow the core idea of interconnected neurons. In an artificial network, these "neurons" are called nodes, and they're organized into layers.

There are typically three types of layers:

1. Input Layer: This is the network's entry point. It receives the initial data, like the pixels of an image or the words in a sentence.
2. Hidden Layers: These are the intermediate layers between the input and output. This is where most of the computation happens. A network can have one, many, or even zero hidden layers. The more hidden layers, the "deeper" the network.
3. Output Layer: This layer produces the final result, such as a classification (e.g., "cat" or "dog") or a prediction (e.g., the price of a stock).

Information flows from the input layer, through the hidden layers, to the output layer. Each connection between nodes has an associated weight, a number that determines the strength of the connection. The network learns by adjusting these weights.

Each node in the hidden and output layers does a bit of math. It takes all the values from the nodes connected to it, multiplies them by their connection weights, and adds them up. But it doesn't just pass this sum along. First, it runs the sum through an activation function.

Think of an activation function as a gatekeeper. It decides whether the signal from a neuron is important enough to be passed on to the next layer. Without these functions, a neural network would just be a complex linear equation, unable to learn intricate patterns like the nuances of human language or the features in a face.

One of the classic activation functions is the sigmoid function. It takes any real number and squashes it into a value between 0 and 1.

Values close to 1 mean "activate" or "fire," while values close to 0 mean "don't activate." This non-linear behavior is crucial for the network's learning capabilities.

A neural network isn't smart from the start. It begins with random weights and makes terrible predictions. The magic happens during training, where it learns from its mistakes through a process of trial and error.

First, we show the network an example and let it make a prediction. Then, we compare its prediction to the correct answer using a loss function, which calculates how wrong the network was. The goal of training is to minimize this loss. To do this, we use two key techniques: gradient descent and backpropagation.

Imagine you're standing on a foggy mountain and want to get to the lowest valley. You can't see the whole landscape, but you can feel the slope of the ground beneath your feet. To get down, you'd take a step in the steepest downward direction. You'd repeat this process, step by step, until you reach the bottom. Gradient descent works the same way. The "landscape" is the loss function, and the "valley" is the point of minimum error. The algorithm calculates the slope (the gradient) and takes a small step in the opposite direction to reduce the error.

After calculating the total error at the output layer, backpropagation works backward through the network. At each layer, it determines how much each connection contributed to the overall error. It's like a manager tracing a mistake back through a chain of command, figuring out how much responsibility each person holds. Once it knows how much each weight is to "blame," it uses gradient descent to nudge the weight in the right direction to reduce the error next time. This cycle of predicting, calculating error, and adjusting weights is repeated thousands or millions of times until the network becomes accurate.

These core components—layers of nodes, activation functions, and the training loop of gradient descent and backpropagation—are the fundamental building blocks of almost every modern neural network.