Invariant-Based Diagnostics for Graph Benchmarks

Progress on graph foundation models is hindered by benchmark practices that conflate the contributions of node features and graph structure, making it hard to tell whether a model actually learns from connectivity, or whether it even needs to. We propose addressing this using graph invariants, i.e., permutation-invariant, task-agnostic structural descriptors that serve as a diagnostic framework for graph benchmarks. We show that (i) invariants are more expressive than standard GNNs, (ii) invariants characterize structural heterogeneity within and across benchmark datasets, (iii) invariants predict multi-task performance, and (iv) simple invariant-based models are competitive with, and sometimes exceed, transformer and message-passing baselines across 26 datasets. Our results suggest that expressivity is not the main driver of predictive performance, and that on tasks where structure matters, a non-trainable structural proxy often matches trained message-passing models. We thus posit that invariant baselines should become a standard for evaluating whether structure is required for a task and whether a model picks up on it, serving as a stepping stone towards graph foundation models.