Definition
Plain language
A simple logic operation where the output is true only when exactly one input is true — the classic test case that can't be solved by a straight line.
As stated in the literature
Exclusive-or, the canonical non-linearly-separable binary function used to demonstrate the need for nonlinear or pairwise features in classifiers.
Why it matters: It is the textbook example that motivated multi-layer neural networks, since a single linear layer fundamentally cannot learn it.
For example, XOR returns 1 for inputs (0,1) and (1,0) but 0 for (0,0) and (1,1), which no single straight line can separate.