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What is a neural network? Layers of simple maths that learn

October 14, 2026

A neural network is a program made of layers of tiny calculations, each taking numbers in, weighting them, and passing a result on. The weights start random. Training shows the network examples, measures how wrong its output is, and adjusts every weight slightly to be less wrong, millions of times. With enough layers and examples, the network learns to recognise a face, transcribe speech or predict the next word, without anyone writing the rules. "Deep learning" just means a network with many layers. The model behind every AI chatbot is one of these, very large.

Forget the brain

The name comes from a loose analogy to neurons, and the analogy stops being useful almost immediately. A neural network is maths: a long chain of multiply-and-add operations with a simple non-linear squash between them. What makes it interesting is not that it resembles a brain but that this particular shape of maths can approximate almost any pattern, if it has enough adjustable numbers and enough examples.

The pieces

  • Inputs. The thing being looked at, as numbers: pixel brightnesses, audio samples, word tokens.
  • Weights. The adjustable numbers. A small network has thousands; the model behind a chatbot has hundreds of billions. These are what "learning" changes.
  • Layers. Each layer takes the previous layer's outputs, multiplies by its weights, adds them up, squashes the result, and passes it on. Early layers end up detecting simple things (edges, letter shapes); later layers combine those into complex things (faces, meanings).
  • Output. A label ("cat"), a number (a price), or a probability for every possible next word.

How it learns

Start with random weights; the network's answers are garbage. Show it an example and compare its answer to the right one; the difference is the error. Then, using a technique called backpropagation, work out for every weight whether nudging it up or down would reduce the error, and nudge each one a tiny amount. Repeat with the next example. After millions of examples the weights have settled into values that produce right answers, not only on the examples it saw but on new ones. Nobody designed those values and nobody can fully read them; the knowledge is spread across all of them at once. That is why a network can be very good at something and still not be able to explain itself.

Why "deep" won

Networks have existed since the 1950s and were mostly a curiosity. Three things changed around 2012: enough labelled data (the internet), enough computing power (graphics chips, built for games, turned out to be perfect for the multiply-and-add), and tricks that let very deep stacks of layers train without the signal vanishing. Deep networks then beat every other method at vision, then speech, then, with a design called the transformer in 2017, language. The history page has the timeline.

Kinds you will hear about

  • Convolutional networks for images: layers that scan for local patterns, the eyes of self-driving cars and photo apps.
  • Recurrent networks for sequences: older speech and text models that read one step at a time.
  • Transformers for language, and now most things: layers that let every token attend to every other, which is what made models large enough to be useful. The LLM page is about the biggest of these.
  • Diffusion models for images and video: networks trained to remove noise, run backwards to create pictures from nothing.

What this means when you use one

The network behind a chatbot is a next-word predictor with hundreds of billions of weights set by reading most of the internet. It is extraordinary at producing plausible text and has no separate store of facts, no memory beyond the conversation window, and no way to know when it is wrong. Everything on the limitations page follows from that shape. One more consequence: the network only learns at training time. Your conversation does not change it, unless the company collects conversations and trains the next version on them. Some do by default. nixm does not: nothing you say is used for training, and no transcript is kept.

frequently asked

What is a neural network in simple terms?

A program made of layers of simple calculations with millions of adjustable numbers, which learns by nudging those numbers toward right answers over many examples. It can learn patterns nobody could write rules for.

How does a neural network learn?

It guesses, measures the error against the right answer, works out which way each weight should move to reduce the error, and nudges them all slightly. Repeated millions of times, this sets the weights to values that generalise to new examples.

What is the difference between a neural network and deep learning?

Deep learning is machine learning using neural networks with many layers. A shallow network with one or two layers is still a neural network but not deep learning.

Is ChatGPT a neural network?

Yes. It is a transformer, a kind of neural network with hundreds of billions of weights, trained to predict the next word and then tuned to answer helpfully.

Why are neural networks called that?

From a loose 1940s analogy to neurons passing signals. The analogy is historical; a modern network is better understood as a very large adjustable formula.

Can a neural network explain its answer?

Not really. Its knowledge is spread across all its weights at once, so it can produce an answer without a readable reason. Explanations a chatbot gives for itself are themselves generated text.

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