SymSelect: Recovering Symmetry Alignment When Validity Depends on the Sample

Candidate transformations can provide useful structural supervision even when their validity varies across samples. When pair validity is unobserved, aligning every candidate can impose invalid constraints, while discarding transformed pairs loses the benefit carried by valid relations. We study how much of the benefit of supervised valid-pair alignment can be recovered without observing pair validity. We introduce SymSelect, which ranks candidate relations by representation similarity and aligns only the most similar pairs. On MNS and I-RAVEN, SymSelect recovers 77%–92% of the accuracy gain from supervised valid-pair alignment across the evaluated backbones. Our analysis shows that selecting mostly valid pairs is not sufficient to inherit the oracle benefit: the retained valid subset must also preserve a useful alignment update. Local and finite-batch results separate invalid-pair contamination from bias among the retained valid pairs and characterize the effects of retention and contribution variability. Matched controls show that aggregate validity enrichment alone does not explain SymSelect's recovery, while checkpoint measurements on I-RAVEN show increasing batch precision, decreasing selected-valid gradient discrepancy, and positive local alignment effects. These results characterize selective symmetry alignment when transformation validity is available structurally but hidden at the level of individual applications.