Track finding in particle data is a challenging pattern recognition problem in High Energy Physics. It takes as inputs a point cloud of space points and labels them so that space points created by the same particle have the same label. The list of space points with the same label is a track candidate. We argue that this pattern recognition problem can be formulated as a sorting problem, of which the inputs are a list of space points sorted by their distances away from the collision points and the outputs are the space points sorted by their labels. In this paper, we propose the TrackSorter algorithm: a Transformer-based algorithm for pattern recognition in particle data. TrackSorter uses a simple tokenization scheme to convert space points into discrete tokens. It then uses the tokenized space points as inputs and sorts the input tokens into track candidates. TrackSorter is a novel end-to-end track finding algorithm that leverages Transformer-based models to solve pattern recognition problems. It is evaluated on the TrackML dataset and has good track finding performance.

Simulating showers of particles in highly-granular detectors is a key frontier in the application of machine learning to particle physics. Achieving high accuracy and speed with generative machine learning models would enable them to augment traditional simulations and alleviate a major computing constraint. This work achieves a major breakthrough in this task by, for the first time, directly generating a point cloud of a few thousand space points with energy depositions in the detector in 3D space without relying on a fixed-grid structure. This is made possible by two key innovations: i) using recent improvements in generative modeling we apply a diffusion model to generate ii) an initial even higher-resolution point cloud of up to 40, 000 so-called Geant4 steps which is subsequently down-sampled to the desired number of up to 6, 000 space points. We showcase the performance of this approach using the specific example of simulating photon showers in the planned electromagnetic calorimeter of the International Large Detector (ILD) and achieve overall good modeling of physically relevant distributions.