Neural Network

A neural network is a mathematical model used to learn patterns from data. It is built by connecting many small computational units called neurons. Each neuron performs a simple calculation, and when many neurons are combined in layers, they can represent complex relationships between inputs and outputs. Despite the large size of modern neural networks, the entire system is constructed from one basic equation:

y = f(∑(wi xi) + b)

y = f( w₁x₁ + w₂x₂ + ... + wₙxₙ + b )

In this expression, 'xi' represents the inputs. These are numerical values provided to the neuron, such as measurements, features, or signals. The neuron processes all these inputs together.

The terms 'wi' are the weights. Each weight controls how strongly its corresponding input affects the result. Larger weights increase influence, smaller weights reduce influence, and a zero weight removes influence completely.

The symbol 'b' represents the bias. It is a constant added to the weighted sum. The bias shifts the result and allows the neuron to adjust its activation threshold.

The function 'f' is called the activation function. The expression inside the brackets is linear, but the activation function transforms it into a possibly nonlinear output. This nonlinearity allows neural networks to model complex patterns instead of only straight-line relationships.

Finally, 'y' is the output of the neuron. It is the final computed value after combining inputs, weights, bias, and applying the activation function.

A neural network is formed by connecting many such neurons together. Although large networks may contain thousands or millions of parameters, every part of the system follows this same fundamental equation.