Semi‑Supervised Learning on Graphs with GNNs

We study semi‑supervised node prediction on graphs where responses arise from a graph‑aware feature operator followed by a smooth regression map. Within a class combining skip‑connected GCN propagation with a fully connected ReLU network, we (i) derive an oracle inequality for population risk under random label masks that separates approximation and estimation error and exposes dependence on the labeled fraction, covering numbers, and a receptive‑field constant; (ii) show skip connections exactly represent multi‑hop polynomial filters, mitigating over‑smoothing; (iii) give covering‑number bounds; and (iv) quantify robustness of our algorithm. These results link classical graph regularization and modern GNN design.