Mixture Density Networks for Neutrino Reconstruction at Hadron Colliders
Neutrino momentum reconstruction at hadron colliders is intrinsically ambiguous because the longitudinal momentum is not directly observed. We study this problem in semileptonic $t\bar{t}$ events using \monster{} (Mixture of Neutrino Solutions with Transformer Event Representation), a mixture density network that predicts a multivariate normal mixture for the conditional distribution of neutrino momentum from reconstructed event objects. The model uses a Transformer-based event encoder and yields a sampling-free point estimate of the neutrino momentum from the closed-form density. On the public benchmark introduced with \nuflows, \monster{} reduces the 68th percentile of the three-momentum residual by 5\% and the 95th percentile by 6\% relative to the empirical-mode \nuflows{} baseline, with per-variable root-mean-square errors smaller by 2 to 9\% at comparable bias, while running 2 to 8.5 times faster at inference, depending on the device and batch size. These results indicate that mixture density networks are a competitive alternative to normalizing flows for neutrino reconstruction.