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We consider the problem of probabilistic forecasting over categories withgraph structure, where the dynamics at a vertex depends on its localconnectivity structure. We present GOPHER, a method that combines the inductivebias of graph neural networks with neural ODEs to capture the intrinsic localcontinuous-time dynamics of our probabilistic forecasts. We study the benefitsof these two inductive biases by comparing against baseline models that helpdisentangle the benefits of each. We find that capturing the graph structure iscrucial for accurate in-domain probabilistic predictions and more sampleefficient models. Surprisingly, our experiments demonstrate that the continuoustime evolution inductive bias brings little to no benefit despite reflectingthe true probability dynamics.

GOPHER: Categorical probabilistic forecasting with graph structure via local continuous-time dynamics