af2bb2b2280d36f8842e440b4e275152-Supplemental-Conference.pdf

A.1 Proof of Theorem 1 In this proof, we adopt a simplified version of our message-passing function that ignores the skipconnection: The HGNN trained in the experimental results shown in Figure 2 also does not use skip-connections and hence represents a theoretically-exact KTN component. In the real experiments, we use (1) skip-connections, exploiting their usual benefits (12), and (2) the trainable version of KTN. Without loss of generality, we prove the result for the case where R = {(s,t): s,t T }, meaning the type of an edge is identified with the (ordered) types of the neighbor nodes. In other words, there is only one edge modality possible, such as a social networks with multiple node types (e.g. "friendship" and "message"), the result is extended trivially (through with more algebraically-dense forms of ats and qts). The output of Aggregate is a concatenation of edge-type-specific aggregations (see Equation 3).