Maximal multiscale differential block

1. Integration point: insert the block after a CNN stage or after a 2D transformer patch-embedding layer, before the next learned projection. Use K = 3 or 4 dyadic scales and preserve the input resolution by upsampling every pooled residual to H by W. 2. Pseudocode: R = 0; for each scale k, compute A[k] = avg_pool(X, kernel=2k, stride=1), E[k] = broadcast(avg_pool(X, kernel=2k, stride=2**k), H, W), and D[k] = A[k] - E[k]; parameterize nu[k] = nu_max * tanh(raw_nu[k]); then set R = R + nu[k] * D[k] and Y = X + gate * R. The stride-1 average can use same padding, while E uses non-overlapping pooling and nearest-neighbor broadcasting. 3. Cache all D[k] tensors. For every interval a to b, form the cumulative sum S[b+1] - S[a], where S[j] = sum_{k<j} nu[k] * D[k], and compute the maximum Frobenius norm or spectral norm. Add lambda times this maximum to the task loss. The paper provides the interval-transform structure and maximal-control motivation; nu_max, lambda, gate initialization, and the precise tensor norm are empirical choices. 4. For a noncommutative variant, partition channels into groups of d channels, reshape each group into a d by d matrix, and apply W_left[k] @ D[k] @ W_right[k], normalizing both matrices by two-step power iteration so their spectral norms are at most one. 5. First cheap experiment: train a small ConvNeXt-T or ViT-T on CIFAR-100, comparing a standard three-level feature pyramid, an unregularized multiscale residual sum, and this bounded differential block at equal parameter count and pooling FLOPs. Evaluate ordinary accuracy plus accuracy after random test-time resizing and interpolation. Success is improved scale-shift accuracy, fewer activation spikes, lower maximum interval-response norm, or faster validation-loss descent at equal compute. Ablate the maximal-response penalty and coefficient bound independently.