Learning Irreducible Representations of Noncommutative Lie Groups

Recent work has made exciting theoretical and practical progress towards neural networks that are equivariant to symmetries such as rotations. However, current techniques require explicit group representations, which generally limits us to those groups with analytically derived matrix formulas. In this work, we present a numerical technique for finding irreducible representations of noncommutative Lie groups. We demonstrate that the structure of the Lie algebras associated with these groups can be used to learn explicit representation matrices to high precision. This provides an automated program to build neural networks that are equivariant to a much wider class of transformations, including previously intractable cases such as the Poincar\'e group (rotations, translations, and boosts).