Graph neural networks (GNNs) work remarkably well in semi-supervised node regression, yet a rigorous theory explaining when and why they succeed remains lacking. To address this gap, we study an aggregate-and-readout model that encompasses several common message passing architectures: node features are first propagated over the graph then mapped to responses via a nonlinear function. For least-squares estimation over GNNs with linear graph convolutions and a deep ReLU readout, we prove a sharp non-asymptotic risk bound that separates approximation, stochastic, and optimization errors. The bound makes explicit how performance scales with the fraction of labeled nodes and graph-induced dependence. Approximation guarantees are further derived for graph-smoothing followed by smooth nonlinear readouts, yielding convergence rates that recover classical nonparametric behavior under full supervision while characterizing performance when labels are scarce. Numerical experiments validate our theory, providing a systematic framework for understanding GNN performance and limitations.

's are real-valued weights depending on the accuracy of h

Neural Information Processing Systems http://nips.cc/

In what follows, we will focus on this regime and assume that d > n.

Work done during an internship at Google Research 37th Conference on Neural Information Processing Systems (NeurIPS 2023).

Neural architecture search(NAS) has gained immense popularity owing to its ability toautomate neural architecture design.

Neural Information Processing Systems http://nips.cc/