Title: Noether Embeddings: Fast Temporal Association Mining. Abstract: Simple and expressive in representing multi-relational events, temporal knowledge graphs (TKGs) have attracted increasing research interest. While temporal associations (TAs) reveal cause-effect relationships between event pairs across time, to the best of our knowledge, no previous work has paid attention to exploring such basic but meaningful regularities on TKGs. Despite the importance, temporal association mining (TAM) is prohibitively challenging due to its enormous search space. Inspired by Noether’s theorem in theoretical physics, we reduce the problem of TAM to search for conserved quantities with a search space invariant to the number of related events. We develop Noether Embeddings, an embedding model that jointly encodes the absolute time and relative interval of events and event pairs, respectively, by rotating complex vectors. It is proved theoretically and experimentally that our embedding model enforces convergence to a conserved quantity of decoding results implying time translation symmetries within associated event pairs. By using Noether Embeddings, a three-stage TAM framework is developed, respectively of the encoding, decoding, and selecting process. We successfully mined TAs both with semantic interpretability and statistical reliability. Experiments show that our method achieves a 23.7 times speedup over an optimized search algorithm for TAM on GDELT dataset.