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 $\sim$2% overhead, against data-driven alternatives (SimCLR, SimSiam, DINO, ImageNet transfer, augmentation, learned teachers) under one frozen recipe with fixed subsets: 13 datasets, 9 backbones, 150 to 1.28M images, 32–224,px, 2.5M–86M parameters ($\text{computeCells}$ classification configurations over $\text{computeRuns}$ runs, plus segmentation and detection transplants). Across the training-time combinations we measure, three outcomes recur (decision-level fusion differs). Different-\emph{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, $\mathrm{\Delta }=G+\text{readout}(\mathrm{b}\mathrm{a}\mathrm{s}\mathrm{e})$, holds in sign on $\text{auditRate}\mathrm{\%}$ of testable cells and is called an unseen backbone family’s feature gain in advance. The project page is https://amughrabi.github.io/MomentAux.