![Solved EXERCISE 17. Determinant of Block Diagonal Matrix] ] | Chegg.com](https://media.cheggcdn.com/media/8fa/8fa02340-cf22-40b9-b5c3-a1da35b7af26/phpcZiugb)
%20is%20to%20learn%20low-dimensional%20representations%20of%20entities%20and%20relations%20for%20predicting%20missing%20facts.%20While%20rotation-based%20methods%20like%20RotatE%20and%20QuatE%20perform%20well%20in%20KGE%2C%20they%20face%20two%20challenges:%20limited%20model%20flexibility%20requiring%20proportional%20increases%20in%20relation%20size%20with%20entity%20dimension%2C%20and%20difficulties%20in%20generalizing%20the%20model%20for%20higher-dimensional%20rotations.%20To%20address%20these%20issues%2C%20we%20introduce%20OrthogonalE%2C%20a%20novel%20KGE%20model%20employing%20matrices%20for%20entities%20and%20block-diagonal%20orthogonal%20matrices%20with%20Riemannian%20optimization%20for%20relations.%20This%20approach%20enhances%20the%20generality%20and%20flexibility%20of%20KGE%20models.%20The%20experimental%20results%20indicate%20that%20our%20new%20KGE%20model%2C%20OrthogonalE%2C%20is%20both%20general%20and%20flexible%2C%20significantly%20outperforming%20state-of-the-art%20KGE%20models%20while%20substantially%20reducing%20the%20number%20of%20relation%20parameters.)
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