invariance

A function $f(x)$ is invariant to a transformation $t(x)$ if:

$$f(t(x))=f(x)$$

For example when training an object classifier, it should produce the same outputs, regardless of whether the image has been flipped, rotated, warped, …

Invariance Group

The set of transformations that leave a property/quantity unchanged.

Types of invariances:

• translation invariance
• permutation invariance
• rotation invariance
• …