A Path based Reasoning with A* Algorithm

Here we prove the correctness of path-based reasoning with A* algorithm. Second, we demonstrate that Eqn. 7 can be solved by Eqn. 8 if paths with the same length and the A.3, we merge paths by their length and stop nodes, A.3 Reasoning with A* Algorithm Finally, we prove that the A* iteration (Eqn. In order to prove Thm. A.4, we first prove a lemma for the analytic form of A.5 and Eqn. 5, it is Specifically, padding-free operations construct IDs for each sample in the batch, such that we can distinguish different samples when we apply operations to the whole batch. Alg. 2 provides the pseudo code for padding-free topk in PyTorch. Dataset statistics for transductive and inductive knowledge graph reasoning is summarized in Tab.