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$2\% overhead, against data-driven alternatives (SimCLR, SimSiam, DINO, ImageNet transfer, augmentation, learned teachers) under one frozen recipe with fixed subsets: 13 datasets, 9 backbones, 150 to 1.28M images, 32--224\,px, 2.5M--86M parameters ($\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-\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, $Δ= G + \readout(\mathrm{base})$, 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.

Who Should Lead Decoding Now? Tracking Reliable Trajectories for Ensembling Masked Diffusion Language Models

Masked Diffusion Language Models (MDLMs) have emerged as a distinct paradigm for sequence generation. As MDLMs become diverse in capabilities and knowledge coverage, an important question is how to combine their knowledge. Toward this, we first investigate the unique decoding dynamics of MDLMs. We find that successful generations exhibit stable confidence dynamics over answer-relevant positions, while unreliable trajectories can often be corrected by injecting promising intermediate states from other models. Guided by this observation, we propose $\textbf{TIE}$ ($\textbf{T}$rajectory-based $\textbf{I}$terative $\textbf{E}$nsembling), a knowledge fusion framework in which MDLMs iteratively identify reliable decoding trajectories and relay them across models. TIE tracks confidence dynamics over answer-relevant positions to determine which model currently follows a more reliable trajectory and selectively transfers partially denoised sequences across models. As the model on the more promising trajectory often changes across denoising steps, TIE allows different models to contribute complementary strengths at different stages of generation. Strong performance across diverse reasoning tasks, along with our analyses, suggests that TIE offers a practical approach to the underexplored problem of MDLM ensembling.