Invariance Is Sample-Conditional: Risk-Controlled Consistency for Transformation–Example Pairs

A transformation family is not uniformly label preserving: the same crop, occlusion, or attribute edit can preserve one example and remove the defining evidence from another. Always-on consistency therefore injects incorrect invariance gradients for semantically invalid example–transformation pairs. We formulate invariance validity as a sample–transformation relation and introduce SELECTIVE INVARIANCE, a compatibility gate whose threshold controls false acceptance on a held-out audit split. Accepted pairs receive consistency supervision; rejected pairs retain the clean supervised objective without being forced invariant. On CIFAR-100, SELECTIVE INVARIANCE reaches 79.1% clean accuracy and 69.4% shift accuracy with 4.8% false acceptance and an invalid invariance gradient ratio (IIGR) of 8.6 at 74.6% coverage. AROID reaches 77.8%, 67.2%, 15.4%, and 21.0 at 75.2% coverage, while a matched random gate reaches 77.0%, 65.7%, 22.7%, and 28.9 at the same 74.6% coverage. The matched-coverage control shows that semantic compatibility, rather than reduced regularization mass alone, drives the improvement.