Extracting scientific understanding from particle-physics experiments requires solving diverse learning problems with high precision and good data efficiency. We propose the Lorentz Geometric Algebra Transformer (L-GATr), a new multi-purpose architecture for high-energy physics. L-GATr represents high-energy data in a geometric algebra over four-dimensional space-time and is equivariant under Lorentz transformations, the symmetry group of relativistic kinematics. At the same time, the architecture is a Transformer, which makes it versatile and scalable to large systems. L-GATr is first demonstrated on regression and classification tasks from particle physics. We then construct the first Lorentz-equivariant generative model: a continuous normalizing flow based on an L-GATr network, trained with Riemannian flow matching. Across our experiments, L-GATr is on par with or outperforms strong domain-specific baselines.

翻译：从粒子物理实验中提取科学理解需要以高精度和良好的数据效率解决多样化的学习问题。我们提出了洛伦兹几何代数Transformer（L-GATr），一种用于高能物理的新型多用途架构。L-GATr在四维时空的几何代数中表示高能数据，并在相对论运动学的对称群——洛伦兹变换下具有等变性。同时，该架构是一种Transformer，这使其具备多功能性并能扩展至大型系统。我们首先在粒子物理的回归和分类任务上验证了L-GATr的性能。随后，我们构建了首个洛伦兹等变生成模型：基于L-GATr网络的连续归一化流，采用黎曼流匹配进行训练。在所有实验中，L-GATr的表现与强大的领域专用基线模型相当或更优。