A Tale of Two Fields: Neural Network-Enhanced non-Gaussianity Search with Halos

It was recently shown that neural networks can be combined with the analytic method of scale-dependent bias to obtain a measurement of local primordial non-Gaussianity, which is optimal in the squeezed limit that dominates the signal-to-noise. The method is robust to non-linear physics, but also inherits the statistical precision offered by neural networks applied to very non-linear scales. In prior work, we assumed that the neural network has access to the full matter distribution. In this work, we apply our method to halos. We first describe a novel two-field formalism that is optimal even when the matter distribution is not observed. We show that any N halo fields can be compressed to two fields without losing information, and obtain optimal loss functions to learn these fields. We then apply the method to high-resolution AbacusSummit and AbacusPNG simulations. In the present work, the two neural networks observe the local population statistics, in particular the halo mass and concentration distribution in a patch of the sky. While the traditional mass-binned halo analysis is optimal in practice without further halo properties on AbacusPNG, our novel formalism easily allows to include additional halo properties such as the halo concentration, which can improve $f_{NL}$ constraints by a factor of a few. We also explore whether shot noise can be lowered with machine learning compared to a traditional reconstruction, finding no improvement for our simulation parameters.