Fig. 1: Pipeline for an example neutrino interaction.

a Detection of the vertex activity (VA) region in the input event. The zoomed-in view unveils the particle mosaic at the interaction vertex. b Utilisation of the VA image, combined with the reconstructed kinematic parameters of the escaping muon, as input for the transformer encoder. The transformer encoder processes the input, resulting in c the reconstruction of the interaction vertex position and d an embedded representation of the VA event for the decoder. e The transformer decoder initially processes the encoder’s information, resulting in a prediction for the kinematics of the most energetic particle in the input VA. Simultaneously, it generates a boolean variable to signify the existence of additional particles that require reconstruction. In cases where additional particles are identified, the transformer decoder proceeds to iteratively provide their kinematic predictions in descending order of the kinetic energies of the particles. This process continues by incorporating encoder data and the kinematics of the previously predicted particle until the boolean variable signals termination, indicating that the transformer has determined no further particles are present in the VA event. f A generative adversarial network (GAN) generator produces images of particles based on the kinematics predicted by the transformer. Using the initial reconstructed kinematics, the GAN is also employed to generate an image of the escaping muon. g The generated images are aggregated by summing their voxel photoelectrons, and h compared with the input VA event to verify the decomposition process. The workflow may return to step 6 to further optimise kinematic parameters.