PotencyGNN: Amortized Epistemic Potency with Dual-Feasible Certificates

Auxiliary observations can reduce causal uncertainty under latent confounding even when effects remain only partially identified. We formalize this gain through realized observational epistemic potency: the reduction in sharp identified-set width obtained when moving from the treatment–outcome marginal distribution to the full observational distribution while keeping the causal graph, query, and model class fixed. Exact computation requires four response-function linear programs and becomes rapidly expensive as parent counts grow. We introduce PotencyGNN, a query-conditioned relational graph neural network with separate parent, child, and bidirected message-passing channels, together with a dual-certificate network that provides certified lower bounds on potency. On screened core-disjoint three-to-five- and exact-six-variable benchmarks, PotencyGNN attains held-out $R^2=0.829$ and $0.779$, remaining competitive with the evaluated graph transformer and outperforming the other baselines. Under matched CPU inputs, PotencyGNN inference is $8.22\times$ faster than cached exact evaluation for individual queries and achieves $26.17\times$ higher batched throughput. Across $79,200$ certificate evaluations, all satisfy the numerical validity criteria, with $43.4\%$ yielding certified potency above the reporting threshold.