Go to ICLR 2024 Conference homepageDeep probabilistic 3D angular regression for directional dark matter detectors
Modern detectors of elementary particles are approaching a fundamental sensitivity limit where individual quanta of charge can be localized and counted in 3D. This enables novel detectors capable of unambiguously demonstrating the particle nature of dark matter by inferring the 3D directions of elementary particles from complex point cloud data. The most complex scenario involves inferring the initial directions of low-energy electrons from their tortuous trajectories. To address this problem we develop and demonstrate the first probabilistic deep learning model that predicts 3D directions using a heteroscedastic von Mises-Fisher distribution that allows us to model data uncertainty. Our approach generalizes the cosine distance loss which is a special case of our loss function in which the uncertainty is assumed to be uniform across samples. We utilize a sparse 3D convolutional neural network architecture and develop approximations to the negative log-likelihood loss which stabilize training. On a simulated Monte Carlo test set, our end-to-end deep learning approach achieves a mean cosine distance of $0.104$ $(26^\circ)$ compared to $0.556$ $(64^\circ) $ achieved by a non-machine learning algorithm. We demonstrate that the model is well-calibrated and allows selecting low-uncertainty samples to improve accuracy. This advancement in probabilistic 3D directional learning could significantly contribute to directional dark matter detection.