# Invariance

I have been hearing about this term in various contexts.

- CS138: Representation Invariant, Representation Invariant, Loop Invariant
- Lidar: PointPillars permutation invariance, maybe even PointPillars permutation invariance, maybe even Distance Metric where they talk about the importance of symmetry
- SE212: Implicit Invariant
- STAT206: Property 3 of MLE

### SE212

“An invariant is a formula stating what must be true in every state of the execution.”

The invariant is a formalization of the programmer’s intention for what the loop should accomplish.

`Inv`

is usually an assertion that the intended computation of the loop is correct up to the current step in execution. In general, `Inv`

expresses a relationship between the variables manipulated by the body of the loop.

**The variable values may change in each iteration of the loop, but the relationship holds**.

If we choose the wrong invariant, we won’t be able to prove the VC’s.