Welcome to the second lesson in our course "Neural Network Fundamentals: Neurons and Layers"! Now that you've been introduced to the basics of neural networks, we're ready to dive deeper into their core components. In this lesson, we'll focus on the fundamental building block of neural networks: the artificial neuron. You'll learn what a neuron is, how it processes information, and implement a simple artificial neuron in Python.

By the end of this lesson, you'll understand how an artificial neuron works, both conceptually and mathematically, and you'll have hands-on experience coding one from scratch using only NumPy. This practical, code-focused approach will give you a much deeper understanding of neural networks than simply using existing libraries.

Before diving into code, let's recap where the concept of an artificial neuron comes from. Artificial neurons are inspired by the biological neurons in our brains.

In your brain, a biological neuron receives signals from other neurons through structures called dendrites. These signals are processed in the cell body, and if the combined signal is strong enough, the neuron "fires," sending a signal through its axon to other neurons.

An artificial neuron mimics this behavior in a simplified way:

• Inputs represent the signals received from other neurons (like dendrites);
• Weights represent the strength of each connection;
• Bias represents the neuron's tendency to fire regardless of inputs;
• Activation function (which we'll cover in future lessons) mimics the "firing" behavior.

This simple model, when combined with many other neurons, forms the basis of neural networks that can learn complex patterns and make predictions. The beauty of this approach is that even though individual neurons perform very simple operations, their collective behavior can solve incredibly complex problems — from recognizing faces to translating languages.

Let's formalize the mathematical model of an artificial neuron. A neuron takes multiple inputs, multiplies each by a corresponding weight, sums these weighted inputs, adds a bias, and produces an output.

Mathematically, for a neuron with $n$ inputs ($x_1, x_2, \ldots, x_n$), we calculate the output as:

Where:

• $x_1, x_2, \ldots, x_n$ are the input values
• $w_1, w_2, \ldots, w_n$ are the weights for each input
• $b$ is the bias

This calculation is also known as a weighted sum plus bias. We can express this more concisely using vector notation:

Where $\mathbf{w} \cdot \mathbf{x}$ represents the dot product of the weight vector and the input vector. This compact notation highlights why tools like NumPy are so useful — they're optimized for these vector operations that are central to neural network calculations.

Think of the weights as importance factors — they determine how much attention the neuron pays to each input. The bias acts like a threshold adjustment that makes it easier or harder for the neuron to produce a high output regardless of the inputs.

Now that you understand the concept, let's start implementing an artificial neuron in Python. First, let's import NumPy and create a simple Neuron class:

This code defines the structure of our neuron. When you create a new neuron, you specify how many inputs it will accept. The __init__ method initializes two important properties:

1. weights: A random array with one value per input, scaled to be small (0.1 times a random number between 0 and 1)
2. bias: A single value, starting at 0.0

We use small random values for weights rather than zeros because if all weights were identical, all neurons in a network would learn the same features during training. This randomness gives each neuron a unique starting point, which is crucial for the learning process later on.

The "forward pass" refers to the process of calculating the neuron's output given a set of inputs. This is where we implement the mathematical model we discussed earlier:

This forward method is the heart of our neuron. It takes an array of inputs and performs these steps:

1. First, it validates that the input array has the correct number of elements.
2. Then it calculates the weighted sum using np.dot(), which efficiently computes the dot product.
3. Finally, it adds the bias to get the final output value.

The use of NumPy's dot() function is much more efficient than writing a loop to multiply and sum each input-weight pair, especially when dealing with larger networks later on.

Now that you've implemented a neuron, let's test it with some sample inputs to see how it works in practice:

When you run this code, you'll see:

1. The neuron's initialization information, including the random weights it generated
2. The input values you're providing: [1.0, 2.0, 3.0]
3. The resulting output calculation (which will vary depending on the random weights)

This simple test demonstrates how a single artificial neuron processes input data. In a real application, these inputs might represent features like temperature, pressure, or pixel values in an image, and the neuron's job would be to learn which features are important for a specific task.

Congratulations! You've just implemented your first artificial neuron from scratch using Python and NumPy. You've learned how neurons are inspired by biology, understood their mathematical representation, and coded a working implementation that can process inputs and produce outputs. This seemingly simple weighted sum operation forms the foundation for even the most sophisticated neural networks used in modern AI systems.

In the upcoming practice exercises, you'll get hands-on experience working with your neuron implementation. You'll explore how changing weights and biases affect outputs and gain intuition about how neural networks begin to learn patterns in data. This practical understanding will prepare you for our next lessons, where we'll add activation functions and combine multiple neurons into layers to build more powerful networks.