Antichain Multiscale Attention Windows

Integrate this into the window generator before sparse attention is executed, rather than into the QK dot-product. Represent an image or video frame as an H by W token grid. Candidate windows are dyadic rectangles R=(x_0,y_0,w,h), where width and height are powers of two. At each layer, generate candidates from a lightweight router using pooled token features. Select windows greedily in descending router score: accept a candidate only if it is not contained in any already accepted window, does not contain an already accepted window, and its predicted token-overlap budget is respected. For an MVP, maintain an integer occupancy map h[H,W] and a list of accepted rectangles. For each candidate, perform dyadic-coordinate containment checks, reject it when max(h[R]) is at least K, otherwise accept it and increment h over R. Execute local attention independently inside accepted windows, optionally caching K/V tensors for tokens reused by multiple windows. During soft training, use g_b=sigmoid((s_b-theta)/T) and h[v]=sum_b g_b indicator(v in R_b), then add the log-moment penalty from the formula with coefficient lambda. The paper supplies the structural guarantee and exponential-tail motivation; K, tau, lambda, theta, and T must be tuned empirically. First test a small Swin-T-like classifier on CIFAR-100 or ImageNet-100 at 224 by 224 resolution. Compare shifted windows, unrestricted multiscale windows, and antichain windows at matched accepted-window FLOPs. Record peak occupancy, activation/KV memory, wall-clock latency, validation accuracy, and the 99th-percentile token reuse. A successful result is lower memory or latency at matched accuracy, ideally 1.5x fewer attention-window FLOPs, with maximum occupancy remaining stable as resolution grows.