Hierarchical summaries for primordial non-Gaussianities

The advent of Stage IV galaxy redshift surveys such as DESI and marks the beginning of an era of precision cosmology, with one key objective being the detection of primordial non-Gaussianities (PNG), which are potential signatures of inflationary physics. In particular, constraining the amplitude of local-type PNG, parametrised by fnl, with σ_ Euclid ∼ 1, would provide a critical test of single-versus-multi-field inflation scenarios. While current large-scale structure and cosmic microwave background analyses have achieved σ_ ∼ 5--9, further improvements demand novel data compression strategies. We propose a hybrid estimator that hierarchically combines standard two-point and three-point statistics with a field-level neural summary, motivated by recent theoretical works that have indicated that such a combination is nearly optimal in effectively disentangling primordial from late-time non-Gaussianity. We employed , a convolutional neural network that extracts small-scale information from sub-volumes (i.e. patches) of the halo number density field, while large-scale information is retained via the power spectrum and bispectrum. Using simulations, we evaluated the Fisher information of this combined estimator across various redshifts, halo mass cuts, and scale cuts. Our results demonstrate that the inclusion of patch-based field-level compression always enhances constraints on fnl, reaching gains of 30--45% at low k_̊m max (∼ 0.1 , h , PatchNet Quijote-PNG Mpc ^ -1 ) and of 15--25% when the standard summary statistics include k modes comparable to those probed by the patches (k_ ̊m max ∼ 0.4 , h , Mpc ^ -1 ). This shows that, even in this configuration, information from beyond the bispectrum can be captured. This approach offers a computationally efficient and scalable pathway to tightening the PNG constraints with forthcoming survey data.