Upper-shadow mask augmentation

1. Integration point: use this in a mask-augmentation layer before the encoder, or in a sparse MoE router whose route is a binary subset of n features or experts. Fix a base cardinality k and an augmentation cardinality l>k. Maintain a replay buffer of useful k-subsets: for classification, these can be masks with low validation loss; for MoE, they can be high-reward routes. 2. Pseudocode: F = select_top_useful_k_masks(buffer, M); u = len(F) / comb(n,k); target = comb(n,l) * Phi(p=k/n,q=l/n,u); repeatedly sample A uniformly from F, sample l-k elements from [n]\A, form B=A union extras, and insert B into a hash set until either the hash set size reaches min(target, budget) or the augmentation budget is exhausted; train on the resulting B masks. For a differentiable router, use the selected routes as teacher masks and add their logits to the corresponding augmented routes. 3. Compute from the paper: Phi, the lower-bound target, and the exact subset-containment construction. Estimate empirically: the actual unique-shadow size, duplicate rate, validation loss per mask, and the fraction of generated masks accepted by the model. For large n, never enumerate all subsets; estimate u from the replay buffer and use hashing or Bloom-filter deduplication. 4. First experiment: use CIFAR-10 or MNIST with an MLP or ViT whose input coordinates are randomly masked, n=32 or 64, k=4 or 8, and l=2k. Compare random l-subset masks, independent Bernoulli masks, and upper-shadow masks at equal augmentation count and FLOPs. Measure validation accuracy versus number of unique masks, duplicate rate, and robustness to unseen masks. The expected signal is higher unique-mask coverage and faster accuracy improvement at equal mask-generation budget; a negative result would be no gain over random supersets after controlling for marginal feature frequencies.