What is a vector in deep learning?

A vector is an ordered list of numbers. In deep learning, every example — a flattened image, a sentence turned into token indices, or three spam indicators — is stored as a vector $\mathbf{x} \in \mathbb{R}^d$.

Concrete case: an email has $x_1 = 2$ promotional words, $x_2 = 0$ links, and $x_3 = 1$ for an unknown sender. Pack them as $\mathbf{x} = (2,\,0,\,1)$ with fixed length $d = 3$. The network always expects exactly three numbers in the same order; permuting the entries changes the meaning.

In Python:

x = [2, 0, 1]
assert len(x) == 3

Matrix multiplication — a Linear layer in PyTorch — is defined on this column vector: $\mathbf{z} = \mathbf{W}\mathbf{x} + \mathbf{b}$. Without vectorization, heterogeneous form fields force hand-written loops per feature, which wastes GPUs and breaks batch training.

So a vector is not decorative jargon. It is the standard way to turn every input into one mathematical object so a neural net can process thousands of examples in parallel.