Abstract
Mixture-of-experts (MoE) networks pursue specialization through learned routers, gates, and load-balancing losses, yet at matched total-parameter budgets learned routers can underperform equal-weight No-Routing baselines. Is the bottleneck the routing algorithm, or the alignment between training-signal granularity and the target categories? We probe the question with SpecDrop, a fixed parameter-free routing scheme: each of branches receives weight for its assigned category and a small leakage otherwise, merged through a category-independent fixed denominator, with no learned routing parameters and no auxiliary losses; the category label is required at inference. On vision tasks where each image has one superclass label (CIFAR-100 on ResNet-110; ImageNet-1K on ViT-S/16), SpecDrop reaches 79.23% on CIFAR-100 and 79.89% on ImageNet-1K, exceeding parameter-matched baselines that do not use the label (+4.75 over dense on CIFAR-100; +6.53 over the No-Routing+SE control on ImageNet-1K). These gains quantify what category supervision buys when deployed through routing -- not an advantage over label-aware deployments of the baselines: given the same label, masking a dense model's outputs is stronger for accuracy alone (85.2 / 83.7). SpecDrop's contribution is converting the label into trained-in modular structure: 58%/100% branch-category alignment, and masking gains of 0.00 (CIFAR) / +1.06 (ImageNet) -- the output-space restriction is largely internalized during training. On fuzzy partitions, where training units span multiple categories (SlimPajama-6B language modeling with a 30M Transformer; SuperNI instruction tuning over Llama-3.2-1B with LoRA), the routing mechanism reduces to the matched No-Routing controls within seed noise, the null our thesis predicts. Granularity alignment, not algorithm choice, localizes when routing helps. Code: https://github.com/Beryex/SpecDrop