An Efficient Lorentz Equivariant Graph Neural Network for Jet Tagging - Gong, Shiqi; Meng, Qi; Zhang, Jue; Qu, Huilin; Li, Congqiao; Qian, Sitian; Du, Weitao; Ma, Zhi-Ming; Liu, Tie-Yan (2022)
Machine learning methods especially deep learning have become popular on jet representation in particle physics. Most of these methods focus on the handcrafted feature design or tuning the structure of existing black-box deep neural networks, while they ignore the Lorentz group equivariance, a fundamental space-time symmetry in the law for jet production. Inspired by the spirit that new physics insights may emerge more easily with the inclusion of underlying symmetry, we propose a new design of symmetry-preserving deep learning model named LorentzNet for jet tagging in this paper. Specifically, LorentzNet updates the geometric tensors via the Minkowski dot product attention, which aggregates the tensors with the embedding of the pairwise Minkowski dot product as the weights. The construction of LorentzNet is guided by the universal approximation theory on Lorentz equivariant mapping which ensures the equivariance and the universality of the LorentzNet. Experiments on two representative jet tagging datasets show that LorentzNet can achieve the best tagging performance compared with the baselines (e.g., ParticleNet) on both clean and Lorentz rotated test data. Even with 0.5% fraction of training samples, LorentzNet still achieves competitive performance, which shows the benefit of the inductive bias brought by the Lorentz group symmetry.