Endpoint-Consistent Continual Learning Under Evolving Label Ontologies

Continual learners can reach different endpoint predictors when the same final ontology is revealed through different legal split, merge, and refinement orders. We formulate this path dependence as two coupled failures: historical labels may lack an endpoint-compatible representation, and the resulting update operators may remain functionally noncommutative. ONTOLOGY PATH CONSISTENCY represents every observed label as a marginal constraint over shared latent leaves and penalizes the functional defect between endpoint-equivalent update orders. Across CIFAR-100 superclass/subclass paths, it reaches 73.4% mean leaf accuracy and 72.0% worst-path accuracy with predictive ontology-path variance (OPV) \(2.3\times10^-3\) and path-consistency defect (PCD) \(2.9\times10^-3\). CLEO (MoOn) reaches 72.7%, 69.9%, \(7.1\times10^-3\), and \(9.4\times10^-3\); the latent-leaf-only ablation reaches 73.0%, 70.5%, \(5.9\times10^-3\), and \(7.8\times10^-3\). The paired reductions in PCD and OPV isolate endpoint-order consistency beyond hierarchy-aware representation alone.