Rotor-Router Neighborhood Sampler

Integrate this at the neighborhood-sampling layer before message passing, not inside the GNN weights. Store one integer rotor pointer q_v in {0,...,d_v-1} for every graph vertex and a fixed neighbor array N_v; initialize q_v randomly once, or deterministically from a hash of the vertex ID. For each minibatch seed s, run K short trajectories of length L: set x=s, add x to the sampled-node set, read neighbor u=N_x[q_x], update q_x=(q_x+1) mod d_x, and set x=u. The line updating q_x is the paper's rho_{t+1}(X_t)=pi_{X_t}(rho_t(X_t)) rule. Deduplicate visited nodes, gather their induced edges or one-hop message-passing neighborhoods, and feed the resulting subgraph to the baseline GraphSAGE, GAT, or GCN. For directed graphs, use outgoing neighbors; for undirected graphs, store both orientations. Compare against length-L uniform random walks with the same number of sampled edges and against standard neighbor sampling. Measure per-node and per-edge visitation-count variance, duplicate rate, GPU data-loading time, gradient cosine similarity to a full-batch gradient, training loss at equal sampled edges, and validation accuracy. The mathematical discrepancy bound is computed exactly from visit counts; coverage, gradient bias, and accuracy must be measured empirically. Start with Cora or Reddit on a two-layer GraphSAGE, using 1,000--10,000 seeds and K=2--8, L=8--32. Success means lower duplicate rate and gradient variance, with equal or better validation accuracy and no more than 5% sampler overhead. Also test a reset ablation: reset rotors after each minibatch versus persistent rotors, since persistence is the proposed source of coverage improvement.