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Left-sorted Bongard Problems have the keyword "invariance" on the OEBP.
Bongard Problems labelled "invariance" are usually (but not always) about transformations that can be undone by other transformations of the same class. (The technical term for this kind of transformation is an "isomorphism".)
When the transformations used in a "invariance" Bongard Problem vary continuously, there could usually be made a corresponding stability Bongard Problem. Stability Bongard Problems are like "invariance" Bongard Problems but for arbitrarily small applications of [transformation] affecting examples' sorting.
Potentially, stability Bongard Problems could be considered "invariance" Bongard Problems. On one hand, they are different, since checking whether arbitrarily small transformations switch an example's sorting is different from checking whether a particular transformation switches an example's sorting; the former is infinitely many conditions. On the other hand, there is actually only finitely much detail in any of the examples, and in practice a stability Bongard Problem generally just amounts to "a small application of [transformation] switches an example's sorting vs. not".
(The keyword gap is another example of a Bongard Problem currently labelled with "invariance" that arguably does not technically fit.)
Also, dependence Bongard Problems could be considered "invariance" Bongard Problems, where the relevant kind of transformation is swapping the example out for any other example that shares the relevant property. | 
