Jian Tang Mila & HEC Montreal Zhiqing Sun, Zhihong Deng, Jian-Yun Nie, and Jian Tang. “RotatE: Knowledge Graph Embedding by Relational Rotation in Complex Space.” In submission to ICLR’19.

3 ROTATE: RELATIONAL ROTATION IN COMPLEX VECTOR SPACE In this section, we introduce our proposed RotatE model. We first introduce three important relation patterns that are widely studied

A rotation of the sphere S2 is a map r = rp,α described by spinning the sphere (actually, spinning the ambient space R3) about the line through the origin and the point p ∈ S2, counterclockwise through …

We introduce SIREN-RoPE, a concrete instantiation of this idea, which popu-lates the rotation dimension with heterogeneous signals—continuous timestamps, cyclical temporal patterns, and …

Recall that every linear transformation R. = 67 ... given by rotating by radians (in the counter-clockwise direction about ~0). That is, for each vector ~v in R2, R(~v) is the result of rotating ~v by radians (in …

By using vectors and defining appropriate operations between them, physical laws can often be written in a simple form. Since we will making extensive use of vectors in Dynamics, we will summarize …

This tutorial discusses the dynamics of an object rotating about a fixed axis and introduces the concepts of torque and moment of inertia.