Deep learning methods have been increasingly adopted to study jets in particle physics. Since symmetry-preserving behavior has been shown to be an important factor for improving the performance of deep learning in many applications, Lorentz group equivariance — a fundamental spacetime symmetry for elementary particles — has recently been incorporated into a deep learning model for jet tagging. However, the design is computationally costly due to the analytic construction of high-order tensors. In this article, we introduce LorentzNet, a new symmetry-preserving deep learning model for jet tagging. The message passing of LorentzNet relies on an efficient Minkowski dot product attention. Experiments on two representative jet tagging benchmarks show that LorentzNet achieves the best tagging performance and improves significantly over existing state-of-the-art algorithms. The preservation of Lorentz symmetry also greatly improves the efficiency and generalization power of the model, allowing LorentzNet to reach highly competitive performance when trained on only a few thousand jets.

Markov state models (MSMs) play a key role in studying protein conformational dynamics. A sliding count window with a fixed lag time is widely used to sample sub-trajectories for transition counting and MSM construction. However, subtrajectories sampled with a fixed lag time may not perform well under different selections of lag time, which requires strong prior practice and leads to less robust estimation. To alleviate it, we propose a novel stochastic method from a Poisson process to generate perturbative lag time for sub-trajectory sampling and utilize it to construct a Markov chain. Comprehensive evaluations on the double-well system, WW domain, BPTI, and RBD−ACE2 complex of SARS-CoV-2 reveal that our algorithm significantly increases the robustness and power of a constructed MSM without disturbing the Markovian properties. Furthermore, the superiority of our algorithm is amplified for slow dynamic modes in complex biological processes.

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