Uncertainty-Guided Adaptive Expert Selection for Graph Neural Networks

Graph Mixture-of-Experts (MoE) models use a router to assign node-specific probabilities to expert networks and combine selected expert outputs for node classification. The router typically varies which experts are selected while fixing their number across nodes. Our observations show that the benefit of additional experts varies with predictive uncertainty, motivating node-specific control of expert participation. We propose D${}^2$MoE, which uses entropy from cached predictions to specify how much of the router's probability distribution over experts should be retained. At each layer, experts are selected in descending probability order until this coverage target is reached. Predictive uncertainty thus determines the requested coverage, while the router's preferences determine which experts participate and how many are needed. Our analysis identifies a weighted participation cost in load balancing. In a controlled multiclass comparison with fixed routing probabilities, expert responses, and costs, the preferred expert count and retained probability are nondecreasing with reference entropy when the reference prediction is correct. Across 13 homophilous and heterophilous benchmarks, D${}^2$MoE variants collectively achieve the highest performance among the evaluated methods, with relative gains of up to 7.92% on heterophilous graphs. End-to-end comparisons on two large graphs further show reductions reaching 73.07% in peak GPU memory and 46.53% in training time to early stopping.