Artificial neural networks sit behind many of the AI systems people now use every day. They help models recognise images, interpret speech, detect patterns, make predictions and generate language. The mathematics can become sophisticated, but the basic idea is surprisingly approachable: take numbers in, transform them through layers of learned parameters, and produce an output.
Neural networks are often introduced using the human brain as a metaphor. That comparison can be useful at a very high level, but it should not be taken literally. Artificial neural networks are not digital copies of biological brains. They are mathematical systems made from layers of computational units whose parameters are adjusted during training.
A neural network learns by adjusting many small numerical settings so that a useful pattern of inputs produces a useful output.
Where the idea came from
The terminology of neural networks comes from biology. A biological neuron receives signals from other cells and may produce an output depending on its state and incoming activity.
Artificial neural networks borrow only a simplified conceptual idea from this: many small processing units can be connected together so that information is transformed as it moves through the system.
A living cell that receives and transmits electrochemical signals within a nervous system.
A mathematical function that combines numerical inputs and produces a numerical output.
Neurons communicate through complex biological structures and processes.
Numerical parameters determine how strongly one input influences a computational unit.
Neural networks were historically inspired by ideas from neuroscience, but modern ANNs should be understood primarily as mathematical models rather than simplified digital brains.
What is an artificial neural network?
An artificial neural network, or ANN, is a model made from connected layers of computational units. Each layer transforms the numerical information it receives and passes a new representation onwards.
A simple network is often described as having three broad parts:
The term hidden layer simply means an internal layer between the input and output. It does not mean the layer is mysterious or inaccessible. It is “hidden” because its internal activations are not the original inputs or the final prediction.
The input layer: turning the world into numbers
Neural networks operate on numerical data.
That means the real-world information we care about must first be represented as numbers.
An image can be represented as arrays of numerical colour and intensity values.
Language is broken into tokens and converted into numerical vectors.
Sound can be represented through sampled waveforms or transformed frequency features.
Age, price, location, account activity and other measurable values can become numerical inputs.
The network does not receive a “cat”, a “house” or a “sentence” in the human sense. It receives numerical representations from which useful patterns may be learned.
What does a single artificial neuron do?
A simplified artificial neuron performs three main operations:
- multiply each input by a weight;
- add the weighted values together with a bias;
- pass the result through an activation function.
A compact form of that calculation is:
This article stays conceptual. The detailed mathematics behind this expression is covered in the companion DigiFixIT Insight on the maths behind neural networks.
Weights: how strongly should an input matter?
Weights are learned numerical parameters that influence how strongly one input contributes to a neuron’s result.
Imagine a very simple system trying to predict whether someone might enjoy a film. It receives three inputs:
- whether the film is a comedy;
- whether a favourite actor appears in it;
- how positively the film has been reviewed.
If the training data suggests that a favourite actor is particularly influential for this prediction, the model may learn a stronger weight for that input.
A change in the input has a smaller effect on the neuron’s weighted total.
A change in the input contributes more strongly to the neuron’s weighted total.
Weights help the network learn which relationships matter for the task it is trying to perform.
Bias: giving the neuron flexibility
The bias is another learned parameter. It allows the neuron to shift its response rather than being entirely constrained by the weighted inputs.
A useful conceptual analogy is to think of the bias as a baseline adjustment.
The weight changes how strongly inputs matter. The bias helps shift the neuron’s response so the network can represent a wider range of patterns.
Activation functions: adding non-linearity
After calculating a weighted total, a neuron usually passes that value through an activation function.
Activation functions are important because they introduce non-linearity. Without non-linear transformations, stacking many layers would not give the network the same ability to represent complex relationships.
Returns zero for negative inputs and the input itself for positive values. Widely used in many hidden layers.
Compresses a value into the range between 0 and 1 and can be useful for some probability outputs.
Compresses values into the range between −1 and 1 and is centred around zero.
Modern architectures use several activation functions depending on the model design and task.
Hidden layers: where representations are transformed
Hidden layers repeatedly transform the data.
It is tempting to say that “learning happens in the hidden layers”, but a more accurate description is that learning changes parameters throughout the trainable network. Hidden layers are where many of the useful internal representations are constructed.
In an image-recognition system, internal layers may gradually become useful for representing increasingly complex visual patterns. In a language model, internal layers transform token representations according to linguistic and contextual relationships.
The output layer: turning internal representations into a result
The final layer depends on the task.
For example: cat, dog or horse.
For example: price, demand or a continuous risk score.
Generate scores for possible next tokens in a sequence.
Generate a vector that can be used for comparison, retrieval or downstream tasks.
How does the network learn?
At the beginning of training, a neural network’s parameters are not yet tuned to the task.
The training process repeatedly:
This cycle is repeated many times across training examples.
The model makes a prediction, measures how wrong it was, works out which parameters contributed to the error, adjusts them and tries again.
Loss: how the network knows it was wrong
A network needs an objective that tells the training process whether its predictions are improving.
A loss function converts the difference between the model’s output and the desired result into a number.
Lower loss generally means the model’s predictions are closer to the training objective, although good training performance alone does not guarantee good real-world performance.
Backpropagation: tracing the error backwards
Backpropagation calculates how sensitive the loss is to the network’s trainable parameters.
The underlying mathematics uses derivatives and the chain rule, but the conceptual idea is simpler:
Work backwards through the calculation to estimate how changing each parameter would affect the error.
An optimiser then uses those gradients to update the weights and biases.
Why layers make neural networks powerful
A single neuron is extremely limited.
The power comes from combining large numbers of computational units across multiple layers. Each layer can build on representations produced by earlier layers.
This layered representation learning is one of the reasons deep neural networks can handle tasks that would be extremely difficult to describe using manually written rules.
What does “deep” mean in deep learning?
In this context, deep generally refers to neural networks with multiple layers of trainable computation between the input and output.
Modern deep-learning systems can contain many layers and very large numbers of learned parameters.
Can still solve useful problems, particularly where relationships are relatively simple.
Can construct increasingly rich internal representations when architecture, data and training support it.
What is linear algebra doing behind the scenes?
Neural networks perform the same basic operations across many neurons and layers. Writing every multiplication separately would be inefficient.
Linear algebra allows inputs and weights to be organised into vectors and matrices, so large groups of calculations can be performed together.
This compact expression can represent a large number of individual calculations.
If you want the mathematical version of the story, the companion article The Maths Behind Neural Networks: How Machines Learn Using Numbers explains these operations in more detail.
What kinds of neural networks exist?
“Neural network” describes a broad family rather than one single architecture.
Information moves from input towards output through one or more layers.
Designed to exploit spatial structure and historically important in computer vision.
Use recurrent connections so earlier sequence information can influence later processing.
Gated recurrent architectures designed to handle longer-range dependencies more effectively.
Use attention-based mechanisms and underpin many modern language and multimodal models.
Neural-network design continues to evolve across generative, scientific and control applications.
Neural networks do not “know” in the human sense
Neural networks can learn extremely useful internal representations, but it is important not to overstate what that means.
The network learns parameters that make it better at its training objective and, ideally, at related tasks on new data.
That is not the same as possessing human experience, intent or conscious understanding.
The model is trained using numerical representations of data.
Weights and biases encode useful statistical relationships.
The model can classify, predict or generate without necessarily possessing human-like comprehension.
Why this matters for real AI services
Understanding neural networks is useful because their limitations shape the services built around them.
A model that performs well statistically may still fail in ways that matter operationally.
- The data may not represent the people affected by the service.
- The model may be uncertain when the interface presents an answer confidently.
- An incorrect prediction may create significant consequences.
- The service may not provide an appropriate human review path.
- Teams may not know how to monitor model performance after deployment.
- A decision may be technically generated by a model but operationally owned by a person or organisation.
Inputs, architecture, weights, training objective, performance and limitations.
User journeys, workflows, exceptions, hand-offs and human intervention.
Purpose, risk, accountability, monitoring, evidence, logs and challenge.
The power of simple operations at enormous scale
The most surprising thing about neural networks is how much can emerge from repeated combinations of relatively simple mathematical operations.
Training repeatedly adjusts the parameters inside this system until its outputs better match the objective it is being trained to achieve.
At small scale, this sounds like little more than arithmetic. At large scale, with many layers, huge datasets and substantial compute, neural networks can learn representations powerful enough to recognise objects, transcribe speech, model language and support generative AI.
Final reflections
Artificial neural networks are powerful precisely because they combine simple ideas in scalable ways.
Inputs become numbers. Weights control influence. Biases add flexibility. Activation functions introduce non-linearity. Layers repeatedly transform the representation. Training adjusts the parameters according to error.
A neural network is not a digital brain. It is a trainable mathematical system whose many small numerical adjustments can collectively produce remarkably sophisticated behaviour.
Understanding that conceptual foundation makes the rest of modern AI much easier to approach — from deep learning and computer vision to transformers and large language models.
Continue reading
This article is part of the DigiFixIT AI learning series. Continue with: