Noncommutative adjacency-degree moments

Integrate this at the graph-level input stage of a message-passing GNN or graph transformer. For each graph with adjacency A, degree diagonal D, n nodes, and maximum word length L, construct vectors recursively: initialize v_empty=ones(n); for every current vector v_w, create v_wx=A @ v_w and v_wy=D @ v_w. Store both the nodewise vectors v_w and scalar sums ones^T @ v_w. Concatenate selected normalized node channels to the original node features and concatenate normalized scalar moments to the graph readout. Use s_w=(1+mean degree)^{number of x symbols plus number of y symbols}, or estimate each scale from the training set; apply a signed log transform to large moments. Begin with all 2^k words through L=4, then use random words or a learned top-k subset for L=6-8. The exact mathematical quantities are the recursive matrix-vector products and moments; truncation and normalization are empirical choices. First test a 3-6 layer GIN baseline on synthetic trees with depth and branching labels, using a held-out set of non-isomorphic trees and equal hidden width. Also test available ten-vertex switching examples. Success means higher graph classification accuracy or lower regression error when baseline node embeddings collide, with permutation-invariant moments and acceptable feature-computation overhead.