With tangent space optimization, we can use standard Euclidean optimization techniques, and respect the geometry of the manifold. All experiments were run on Intel Cascade Lake CPUs, with microprocessors Intel Xeon Gold 6230 (20 Cores, 40 Threads, 2.1 GHz, 28MB Cache, 125W TDP). The red dot corresponds to the relation addition R . Datasets: Stats about the datasets used in Knowledge graph experiments can be found in Table 4. Results: In addition to the results provided in 6.1, in Table 5 we provide a comparison with other We include ComplEx [77], Tucker [9], and Quaternion [92]. In Figure 6 we add equivalent plots to the ones explained in 6.4 for other relations from Same grid search is applied to baselines.

With tangent space optimization, we can use standard Euclidean optimization techniques, and respect the geometry of the manifold. All experiments were run on Intel Cascade Lake CPUs, with microprocessors Intel Xeon Gold 6230 (20 Cores, 40 Threads, 2.1 GHz, 28MB Cache, 125W TDP). The red dot corresponds to the relation addition R . Datasets: Stats about the datasets used in Knowledge graph experiments can be found in Table 4. Results: In addition to the results provided in 6.1, in Table 5 we provide a comparison with other We include ComplEx [77], Tucker [9], and Quaternion [92]. In Figure 6 we add equivalent plots to the ones explained in 6.4 for other relations from Same grid search is applied to baselines.