Model performance and validation. The d 2 GNN model performance is evaluated by nested (K = 10, L = 10)-fold cross validation. In this scheme, unique structures are randomly split into K = 10 outer splits (90% train, 10% test), and all paths in a given structure are assigned accordingly. Thus no paths from the same structure may be split between the train and test sets. For each k th outer train split, the data is randomly divided into L = 10 inner splits (90% train, 10% test). A model is trained for each inner train split (using 10% of the data as validation sets for early stopping), then all inner models are used to predict the outer test set example, {∆H pi } L . We take the bootstrapped ensemble average as the final predicted value, ∆H pi = ⟨{∆H pi } L ⟩, and the standard deviation, σ pi = σ({∆H pi } L ), as a heuristic metric for the prediction uncertainty. Figure 3a-b show d 2 GNN vs. DFT test set parity for vacancy formation energies and path image energies, respectively. Figure shows d 2 GNN vs. DFT predicted E A , where some non-systematic error cancellation between the vacancy formation energies and the path image energies reduces the R 2 relative to the individual ∆H pi predictions. Here we show cross-validated test predictions only for stable materials with hull energies E H = 0 eV/atom, since model performance begins to degrade for test set predictions of unstable materials with E H ≳ 0.025 eV/atom, as discussed in the Supplementary Section 4.