A Theoretical and empirical evidence for ConE's design choice

Here we provide theoretical and empirical results to support that ConE's design choice makes sense, i.e., both rotation transformation and restricted transformation play a crucial role to the expressiveness of the model. A.1 Proof for transformations A.1.1 Proof for rotation transformation We will show that the rotation transformation in Eq. 10 can model all relation patterns that can be modeled by its Euclidean counterpart RotatE [7]. Three most common relation patterns are discussed in [7], including symmetry pattern, inverse pattern and composition pattern. Let T denote the set of all true triples. We formally define the three relation patterns as follows.