How Neural Networks Work: A Simple Explanation

The idea in two paragraphs

A neural network is a function that turns input numbers (pixels, words, prices) into output numbers (a class, the next word, a forecast). Inside, it is made of many small units called neurons, each holding adjustable numbers called weights.

At first the weights are random and the network answers badly. Training means showing it many examples with correct answers and, after every mistake, slightly adjusting the weights. Nobody writes the rules by hand: the rules end up stored in the weights.

What a single neuron does

A neuron takes several inputs, multiplies each by its weight, adds them up, adds a bias and passes the result through an activation function, a simple non-linear function that, for example, turns negative values into zero.

Analogy: you are deciding whether to take an umbrella. Inputs are cloud cover, the forecast and humidity. Weights are how much you trust each signal. If the total is above a threshold, you take the umbrella.

One neuron can do little. Stack many into layers (input, several hidden, output) and the network starts capturing complex patterns: early layers notice simple features, later layers combine them into more complex ones.

How a network learns: a tiny example

Let the network be one neuron with no activation: output = w × x. We want it to learn to double a number, without telling it so.

1. Starting weight w = 0.5. Example: x = 3, correct answer 6.
2. The network outputs 0.5 × 3 = 1.5. Error: 1.5 − 6 = −4.5.
3. We work out which way to move the weight. For squared error the slope is 2 × (−4.5) × 3 = −27.
4. We take a small step against the slope with a learning rate of 0.01: w = 0.5 + 0.27 = 0.77.
5. New output: 0.77 × 3 = 2.31, already closer to 6.

Repeat this over thousands of examples and w approaches 2. A real network has millions of weights or more, and backpropagation is the method that efficiently computes this slope for every weight, moving from the output back to the input.

Overfitting: when the network memorizes

Overfitting means the network does great on training examples but poorly on new ones. Like a student who memorized the exam answers without understanding the subject.

How to spot and fight it:

• Hold-out data. Keep part of the data away from training and measure quality on it. If training error falls while validation error rises, you are overfitting.
• More and more varied data. Harder to memorize, easier to learn the real pattern.
• Early stopping. Stop training when validation quality stops improving.
• Regularization and dropout. Techniques that stop the network from relying on random details.
• A simpler model. With little data, a huge network will almost certainly overfit.

What this means for a business

• A neural network does not know rules; it reflects data. Poor or biased data gives a poor model.
• Quality must be checked on new examples, not on the ones used for training.
• Ready-made models (LLMs, image recognition) often already solve the task, so training your own from scratch is needed less often than it seems.