When does fusing hand-crafted knowledge with learned representations pay? A cost-normalized benchmark of stacking, substitution, and interference

Fusing prior knowledge with data-driven learning is attractive where data is scarce, yet no controlled account says when it helps, is redundant, or harms. We benchmark one fixed hand-crafted knowledge source, a pinned bank of Gabor targets injected only during training at ~2% overhead, against data-driven alternatives (SimCLR, SimSiam, DINO, ImageNet transfer, augmentation, learned teachers) under one frozen recipe with fixed subsets: 13 datasets, 9 backbones, 150 to 1.28M images, 32--224,px, 2.5M--86M parameters (computeCells classification configurations over computeRuns runs, plus segmentation and detection transplants). Across the training-time combinations we measure, three outcomes recur (decision-level fusion differs). Different-currency sources can stack: the prior composes with DeiT augmentation on attention backbones and is worth +26 points to ViT-B/16 at 224,px, +6.7 at twice that budget. Same-currency sources substitute: against effective self-supervised pretraining, the combination never usefully exceeds the better single source. Fusing at full strength into an already-informed initialization interferes in proportion to what it carries: ImageNet transfer, -15 to -17 points, removed by a weaker auxiliary weight. Frozen-feature diagnostics measured on each source alone separate these outcomes retrospectively but do not predict them: a rule built on them calls one of nine unseen pairs. At a practitioner's own label budget, the frozen-feature gain predicts the end-to-end gain to within 0.17 points across 30 cells and seven datasets; the underlying decomposition, Delta = G + readout(base), holds in sign on auditRate% of testable cells and is called an unseen backbone family's feature gain in advance. The project page is https://amughrabi.github.io/MomentAux.