Trainable Topology Supervision under Structurally Unreliable Pseudo Supervision

Topology supervision relies on meaningful structural targets, yet this assumption can fail under structurally unreliable pseudo supervision. In pseudo-label learning, the topology induced by pseudo masks may already contain distorted components, broken connections, or spurious holes, making direct supervision-side topology fitting unreliable and potentially propagating structural errors. We address this problem by reformulating topology supervision as trainable topology-side correction. Specifically, we propose a differentiable persistent-homology proxy loss that derives topology signals from a soft Euler-characteristic trajectory and threshold-wise structural variation, without computing or matching persistence barcodes. We further introduce a conservative topology-consistency injection mechanism that regulates when, how strongly, and in which direction these signals enter optimization. We validate the proposed reformulation in unsupervised camouflaged object detection, a challenging setting where pseudo masks often contain severe structural distortions. Experiments under controlled same-carrier comparisons show consistent improvements in both task-level detection performance and topology-level structural reliability. These results suggest that, under structurally unreliable pseudo supervision, topology supervision is more effective when derived as trainable proxy signals and introduced into optimization conservatively. Code is available at https://anonymous.4open.science/r/LPHP/.