Neural networks are one of the most important ideas behind modern AI. They power applications such as image recognition, speech assistants, recommendation systems, translation tools, and many generative AI systems.
But despite their impressive capabilities, the basic idea is surprisingly simple. In this article, we'll explore:
The idea behind artificial neural networks was inspired by the human brain. Our brains contain billions of biological neurons. These neurons receive signals, process them, and pass signals to other neurons.
For example, when you see a cat:
Eyes
↓
Visual processing
↓
Features detected
↓
Brain combines the information
↓
"That's a cat!"
The brain doesn't have a single "cat detector."
Instead, many neurons work together to recognize different patterns such as shapes, edges, colors, and textures.
Researchers wondered:
Could we build a mathematical system that learns patterns in a similar way?
This question helped lead to the development of artificial neural networks.
It's important to note that artificial neural networks are not accurate simulations of the human brain. They are mathematical and computational models that were inspired by some aspects of biological neurons.
A neural network is a machine learning model made up of interconnected mathematical units called neurons.
At a high level, it looks something like this:
Input Layer Hidden Layers Output Layer
x₁ ───────┐
├──> ○ ───┐
x₂ ───────┤ │
│ ○ ───┼──> ○
x₃ ───────┤ │
├──> ○ ───┘
x₄ ───────┘
The network receives some information as input, processes it through one or more hidden layers, and produces an output.
For example, suppose we're building a system that determines whether an image contains a cat.
The input could be:
Image → Neural Network → "Cat"
The network doesn't receive the concept of "cat" directly.
It receives numerical data representing the image and learns useful patterns from examples.
A basic neural network consists of layers.
This layer receives data.
For example, if we're predicting whether a student will pass an exam, our inputs might be:
Hours studied
Attendance
Previous test score
These values become the input to the network.
For an image, the inputs might be pixel values.
Between the input and output are the hidden layers. These layers transform the information received from the previous layer.
A network might look like:
Input → Hidden Layer → Hidden Layer → Output
A neural network with many hidden layers is commonly called a deep neural network. That's where the term deep learning comes from.
The output layer produces the final prediction.
For example:
Input:
Hours studied = 8
Attendance = 90%
↓
Neural Network
↓
Output:
Probability of passing = 0.94
The model might interpret 0.94 as a 94% estimated probability of passing.
A neuron is essentially a small mathematical function. It receives several inputs, gives each input a different importance, combines them, and produces an output.
Imagine:
Input 1 ──┐
Input 2 ──┼──> Neuron ──> Output
Input 3 ──┘
A simplified neuron works like this:
output = activation(weighted inputs + bias)
Let's break that down.
A weight controls how strongly an input influences a neuron.
Suppose we're predicting whether someone will buy a product.
We might have:
Age
Income
Previous purchases
The network could assign different weights to these inputs.
For example:
Age × 0.2
Income × 0.7
Previous purchase × 1.1
The actual numbers aren't chosen by us manually. During training, the neural network learns them.
A weight can be thought of as:
"How important is this input for my prediction?"
A large positive weight means an input tends to increase the neuron's result.
A negative weight can decrease it.
Neurons also have something called a bias.
The simplified equation for a neuron is:
z = w₁x₁ + w₂x₂ + w₃x₃ + b
Where:
x = inputw = weightb = biasz = combined result
The bias gives the neuron an additional value that allows it to shift its output.
You can think of it as an adjustable starting point.
Without biases, neural networks would be more limited in the functions they could learn.
After calculating the weighted sum, a neuron usually applies an activation function.
Why?
Because without activation functions, stacking many layers wouldn't give us the powerful nonlinear behavior we want from neural networks.
An activation function takes a number and transforms it.
One popular activation function is ReLU.
ReLU stands for Rectified Linear Unit.
Its rule is simple:
ReLU(x) = max(0, x)
So:
ReLU(-5) = 0
ReLU(-1) = 0
ReLU( 0) = 0
ReLU( 2) = 2
ReLU( 7) = 7
This simple function is widely used in neural networks.
Other activation functions include:
Different architectures and tasks may use different activation functions.
Let's combine everything.
Suppose we have two inputs:
x₁ = 2
x₂ = 3
And our neuron has:
w₁ = 0.5
w₂ = 0.2
b = 1
First, calculate the weighted sum:
z = (2 × 0.5) + (3 × 0.2) + 1
Which gives:
z = 1 + 0.6 + 1
z = 2.6
Now apply ReLU:
ReLU(2.6) = 2.6
So the neuron outputs:
2.6
That's the basic building block of a neural network.
One neuron isn't very useful for complex problems. The power comes from connecting many neurons together.
For example:
Input Layer
○ ○ ○ ○
\ | / \ |
\ | / \ |
○ ○ ○ ○
\ | /
\|/
○
Each connection has a weight. The neurons in one layer send their outputs to neurons in the next layer.
This allows the network to build increasingly useful representations of the input.
This is where things get interesting. Suppose we want a neural network to recognize cats.
We give it thousands of labeled images:
Image 1 → Cat
Image 2 → Not Cat
Image 3 → Cat
Image 4 → Cat
Image 5 → Not Cat
...
Initially, the network's weights are usually not useful. Its predictions might be terrible:
Correct answer: Cat
Network prediction: Not Cat
The network needs a way to measure how wrong it was.That's the job of a loss function.
A loss function measures the difference between the model's prediction and the desired answer.
Expected: 1.0
Predicted: 0.2
The model is quite wrong.The loss will therefore be relatively high.
If instead:
Expected: 1.0
Predicted: 0.95
the loss should be much smaller.
The general goal of training is:
Minimize the loss.
In simple terms:
Make a prediction
↓
Measure the error
↓
Adjust the network
↓
Make another prediction
↓
Repeat
But how does the network know which weights should change?
This is where backpropagation comes in. Backpropagation calculates how much each parameter contributed to the error.
The process roughly looks like this:
Input
↓
Forward pass
↓
Prediction
↓
Calculate loss
↓
Backpropagation
↓
Calculate gradients
↓
Update weights
The word "backpropagation" can sound intimidating, but the basic idea is straightforward:
Start with the error and work backward through the network to determine how the parameters should change.
Once we know how the parameters should change, we need a method for changing them. One common approach is gradient descent.
Imagine you're standing on a mountain and want to reach the lowest point.
You can't see the entire mountain, but you can determine which direction slopes downward. So you take a small step downhill.
Then another.
And another.
Eventually, you hopefully reach a low point.
Training a neural network works somewhat similarly.
The "height" represents the loss. We want to move toward lower loss.
Loss
^
|\
| \
| \
| \ ●
| \ /
| \ /
| \_/
+----------------> Parameters
The gradient tells us the direction in which the loss changes. The optimizer uses this information to update the weights.
The size of each update is controlled by the learning rate.
A very small learning rate might look like:
Step → Step → Step → Step → Step
Learning can be slow.
A very large learning rate might look like:
↗
↙ ↗
↙
The model could jump around and fail to settle into a good solution.
So choosing an appropriate learning rate is important.
Modern optimizers such as Adam can adapt the updates in useful ways and are widely used in practice.
Putting the pieces together, training often follows this pattern:
┌──────────────┐
│ Training Data│
└──────┬───────┘
↓
Forward Pass
↓
Prediction
↓
Calculate Loss
↓
Backpropagation
↓
Update Parameters
│
└───────────┐
↓
Repeat many times
One complete pass through the training dataset is called an epoch.
A model might train for:
1 epoch
2 epochs
3 epochs
...
50 epochs
The exact number depends on the problem and the training setup.
It's easy to imagine that a neural network "understands" data in the same way humans do.
That's not quite what's happening.
The network is learning numerical parameters that help it make useful predictions.
For example, when training an image classifier, early layers might learn representations related to simple visual patterns, while deeper layers can combine those representations into more complex patterns.
The exact behavior depends heavily on the architecture, training data, objective, and optimization process.
You'll often hear these two terms.
Parameters are values learned by the model during training.
Examples:
Weights
Biases
Hyperparameters are settings chosen by the developer or training process.
Examples include:
Learning rate
Number of layers
Number of neurons
Batch size
Number of training epochs
A simple way to remember it:
Parameters are learned. Hyperparameters configure the learning process.
Training a model on millions of examples at once can be expensive.
Instead, training data is usually divided into smaller groups called batches.
Dataset = 10,000 examples
Batch 1 → 64 examples
Batch 2 → 64 examples
Batch 3 → 64 examples
...
The model processes a batch, calculates the loss, and updates its parameters.
The number of examples in each batch is called the batch size.
Neural networks involve a huge number of mathematical operations.
Many of these operations can be performed in parallel.
GPUs are particularly good at this type of computation.
That's why modern deep learning often relies on GPUs or other specialized accelerators.
A simplified comparison is:
CPU
Good at many different types of tasks
GPU
Excellent at performing many similar numerical operations in parallel
This makes GPUs extremely useful for training large neural networks.
"Neural network" is a broad term. There are many architectures designed for different kinds of problems.
Information generally moves from input toward output without recurrent connections.
They're useful for many basic prediction tasks.
CNNs became especially important for computer vision.
They are designed to work effectively with spatial patterns such as those found in images.
They can learn features such as:
Edges
↓
Shapes
↓
Object parts
↓
Objects
RNNs were designed for sequential data.
Examples include:
Text
Speech
Time series
They process information while maintaining a form of state from previous steps.
While important historically, many modern language applications use transformer-based architectures instead.
Transformers have become one of the most influential neural network architectures in modern AI.
They are heavily used in:
A key idea behind transformers is attention, which allows the model to determine which parts of the input are especially relevant when processing information.
Modern language models are built using neural networks, particularly transformer architectures.
Suppose you type:
The sky is usually
A language model processes the context and estimates likely continuations.
For example:
blue
The model doesn't simply retrieve a sentence from a database. During training, it learns statistical patterns and representations from enormous amounts of data. At inference time, it uses those learned parameters to generate predictions.
If you're just starting, you can think about a neural network like this:
Neural Network
Input ──> Process patterns ──> Prediction
↑
│
Learned weights
│
↑
Training adjusts
those weights
The most important concepts are:
| Concept | Simple meaning |
|---|---|
| Neuron | Small mathematical processing unit |
| Weight | Controls the influence of an input |
| Bias | Additional adjustable value |
| Layer | Group of neurons |
| Activation | Adds nonlinear behavior |
| Loss | Measures prediction error |
| Gradient | Indicates how parameters affect loss |
| Optimizer | Updates parameters during training |
| Epoch | One pass through the training dataset |
| Batch | Small group of training examples |
| Parameter | Value learned during training |
The real power comes from combining many simple operations.
A single neuron can perform a relatively simple calculation. Millions or billions of parameters arranged in layers can represent much more complicated relationships. This gives neural networks the ability to learn patterns that would be extremely difficult to program manually.
Instead of writing:
IF this condition
AND this condition
AND that condition
THEN predict X
we can provide data and an objective and allow the model to learn useful parameters.
A neural network can perform extremely well while still making mistakes.
Problems can include:
A model is only as reliable as the problem setup, data, evaluation, and deployment practices surrounding it.
Let's summarize the complete process.
TRAINING
Training Data
↓
Neural Network
↓
Prediction
↓
Compare with expected answer
↓
Loss
↓
Backpropagation
↓
Gradients
↓
Optimizer
↓
Update weights
↓
Repeat
After training, we can use the learned model on new data:
New Data
↓
Trained Neural Network
↓
Prediction
That's the core idea behind many neural-network-based machine learning systems.
Neural networks can seem complicated because modern AI systems contain enormous numbers of parameters and sophisticated architectures.
But the fundamental ideas are approachable.
A neural network:
The result is a system that can learn useful patterns from data rather than requiring every rule to be explicitly programmed.
And that's the central idea behind neural networks:
Give a model data, define what you want it to optimize, and use optimization to learn parameters that make useful predictions.
Once these fundamentals make sense, topics like CNNs, transformers, attention mechanisms, embeddings, and large language models become much easier to understand.
If you're learning neural networks for the first time, a good progression is:
Machine Learning Basics
↓
Neural Networks
↓
Backpropagation
↓
PyTorch / TensorFlow
↓
CNNs
↓
Transformers
↓
Large Language Models