AnyGRAM: Rotation-Invariant Global Operators for Fully-Inductive Node Classification

A fully-inductive node classifier is trained on some graphs and then applied, frozen and without gradient steps, to a new graph whose features, label space, and structure it did not see during training. Existing models combine a fixed bank of local propagation operators, a closed-form least-squares readout on the labeled support nodes, and a head, learned on the source graphs, that weighs the operators. Two parts of this design remain open: the operators see only local neighborhoods, and the choice of how to read the bank, which depends on the new graph, is learned in advance on other graphs. In this paper, we ask which parts of a fully-inductive classifier should be learned across graphs and which should be decided on the target graph from its support labels. We introduce $\text{AnyGRAM}$, which learns encoders whose inputs are invariant to rotations of the random feature projection and uses them to add global covariance operators to the local bank, applied in factored form without forming a node-by-node matrix. The ridge regularization of each branch and the branch used on each graph are selected by cross-validation on the support set of the target graph. Trained on a single source graph and applied frozen to 26 target graphs, $\text{AnyGRAM}$ reaches $71.98\%$ average accuracy, $6.16$ percentage points above the strongest zero-shot baseline and above end-to-end models trained on each target graph. Our empirical results show that the covariance branch family and the decisions made on the target graph contribute to this gain, and accuracy changes little with the choice or number of source graphs.