Masked Universal Host Layer

Integrate this at the sparse aggregation operation of a graph neural network or at a block-sparse attention layer. First choose a fixed host graph with \(N\) slots and directional edge types \(H^{(a)}\); for molecules, use a degree-bounded host such as a padded radius-neighbor graph, while for routing use a fixed expert-token bipartite supergraph. Store one CSR/CSC index layout for all \(H^{(a)}\), and store a per-example binary mask \(M^{(a)}\) with the same edge ordering. Pseudocode: input node features \(X\), masks \(M^{(a)}\); set \(Y=X\Theta_0\); for each direction \(a\), compute messages \(V_a=X\Theta_a\), zero masked edges, and perform the precompiled sparse gather/scatter \(Y\mathrel{+}=\operatorname{scatter}(M^{(a)}\odot H^{(a)},V_a)\); return \(\sigma(Y)\). During training, either use fixed dataset masks or sample masks from a library of target graphs; retain the same \(\Theta_a\) across all masks. The paper supplies the binary-program abstraction and fixed-operator reuse; engineering choices such as host degree, padding, and mask generation must be measured empirically. Compare against separate per-pattern sparse kernels, dense padding, and a standard dynamically constructed COO graph layer on QM9 or OGB-Molhiv using a small 4-layer GNN. Measure end-to-end examples per second, kernel-launch count, peak memory, and validation accuracy at matched parameter count. Success requires at least 1.3x higher throughput or 25% lower peak memory at no more than 1% absolute accuracy loss, with the largest expected gain when one batch contains many different graph sparsity patterns.