Graph Logic Flows: Global Constrained Transport for Dynamic Graph Prediction

Temporal graph models typically hide each state transition inside memory, attention, or neighbourhood operations, making the transition difficult to inspect as a single computational object. Graph Logic Flows (GLF) takes a different view: each snapshot transition is defined by one global constrained transport problem on a learned graph geometry. GLF transports a node belief distribution over learned positive edge weights; temporal total variation acts directly on the state update, while Bellman consistency shapes the learned graph potential during training. Solving the transport problem produces the next belief state and edge transport variable together with numerical and structural diagnostics of the same transition. We derive a finite-step bound for the state-coupled residual penalty and specialise standard Wasserstein stability results to the learned geometry. On the JODIE Wikipedia, Reddit, and LastFM benchmarks under a 100-negative full-node protocol, GLF has mean MRR close to TGN on Wikipedia and LastFM and higher than TGN on Reddit. Residual ablations show that the structural terms materially affect prediction, while fixed-probe rankings recover the temporal smoothness induced by TV. On Wikipedia, GLF trains substantially faster than TGAT and DyGFormer, and the matched single-file implementation processes the tested snapshots faster than all three baseline reproductions. Together, these results suggest a different design principle for temporal graph learning: make the state transition an explicit, solved object so that prediction and evidence about how the state changed arise from the same update.