Reproduce “Deep Learning Symmetries and Their Lie Groups, Algebras, and Subalgebras from First Principles” on OpenResearch
Turn your favorite coding agents into research agents that review literature, develop hypotheses, and run experiments.
Universal app for Apple silicon and Intel. Requires macOS 11 or later.
About this paper
Roy T. Forestano, Konstantin T. Matchev, Katia Matcheva, Alexander Roman, Eyup Unlu, Sarunas Verner
Researchers from the University of Florida developed a deep learning algorithm that autonomously discovers and classifies continuous symmetries in datasets by learning infinitesimal transformations, extracting their generators, and determining their Lie algebraic structure, demonstrated across SO(n) groups and the Lorentz group. The method correctly identifies the structure constants for groups like SO(3) and SO(1,3) and can discover subalgebras even with discontinuous oracle functions.
Key insights
- Symmetry discovery can be formulated as an optimization problem solvable through deep learning, by learning infinitesimal transformations and their generators.
- The structure constants, learned by the algorithm, provide a unique 'fingerprint' for classifying the discovered Lie algebras, differentiating between groups like SO(3) and SO(1,3).
- The algorithm can systematically discover not only full Lie algebras but also their nested subalgebras by varying the number of generators, revealing hierarchical symmetry structures.
Summary by alphaXiv.
Tip: change arxiv.org to autoarxiv.org in any arXiv abstract link to open the paper here.