Artificial Neural Network

machine-learning deep-learning

Definition

Artificial Neural Network

An artificial neural network (ANN) is a computational model inspired by biological neural systems, structured as a directed graph of interconnected processing units termed neurons. Formally, an ANN represents a function $f:\mathcal{X}\to \mathcal{Y}$ composed of layers of affine transformations followed by non-linear activation functions.

For a single neuron, the output $y$ is given by:
$y=\sigma ({\mathbf{w}}^{\top }\mathbf{x}+b)$
where $\mathbf{x}$ is the input, $\mathbf{w}$ the weight vector, $b$ the bias, and $\sigma (\cdot )$ a non-linear activation function.

Architecture

Deep networks are constructed by stacking multiple layers of neurons, where the output of one layer serves as the input to the next. This hierarchy allows for the approximation of highly complex, high-dimensional non-linear mappings.