GLADE: Adaptive Structural Transfer for Powerful Out-of-Distribution Testing

Auxiliary labeled data from historical records, related domains, or synthetic sources can be leveraged to improve the power of out-of-distribution testing. However, differences between auxiliary and current anomaly distributions can make directly transferred detection scores ineffective or even harmful. The challenge is to turn auxiliary category information into detection power while controlling false discoveries and guarding against negative transfer. We propose GLADE, an adaptive structural-transfer procedure that uses auxiliary category labels to guide local score learning from current unlabeled data and reference inliers. GLADE further combines these local scores with a global anchor and selects their contribution according to estimated discovery utility. A symmetric learning-and-selection construction ensures finite-sample false discovery rate (FDR) control under exchangeability conditions. Our theory characterizes the potential power gains from structural transfer, the costs of learning and selection, and conditions for protection against negative transfer. Experiments on synthetic and real datasets demonstrate power improvements over matched global baselines, with empirical FDR below the nominal level. Together, these results establish a principled approach to exploiting auxiliary structure for out-of-distribution detection with rigorous control of false discoveries.