Hybrid summary statistics: neural weak lensing inference beyond the power spectrum

TL;DR

This paper introduces a hybrid method combining physics-based and neural summary statistics to improve parameter inference from weak lensing maps, significantly enhancing information extraction over traditional power spectrum analysis.

Contribution

It presents a novel hybrid approach that optimizes neural summaries to complement physics-based summaries, boosting inference accuracy and efficiency in cosmological parameter estimation.

Findings

Information update formalism extracts 3-8 times more information than the power spectrum.

Neural summaries are highly complementary to 2-point statistics.

Smaller, physics-informed networks achieve comparable results to larger models with fewer simulations.

Abstract

In inference problems, we often have domain knowledge which allows us to define summary statistics that capture most of the information content in a dataset. In this paper, we present a hybrid approach, where such physics-based summaries are augmented by a set of compressed neural summary statistics that are optimised to extract the extra information that is not captured by the predefined summaries. The resulting statistics are very powerful inputs to simulation-based or implicit inference of model parameters. We apply this generalisation of Information Maximising Neural Networks (IMNNs) to parameter constraints from tomographic weak gravitational lensing convergence maps to find summary statistics that are explicitly optimised to complement angular power spectrum estimates. We study several dark matter simulation resolutions in low- and high-noise regimes. We show that i) the information-update formalism extracts at least $3\times$ and up to $8\times$ as much information as the angular power spectrum in all noise regimes, ii) the network summaries are highly complementary to existing 2-point summaries, and iii) our formalism allows for networks with smaller, physically-informed architectures to match much larger regression networks with far fewer simulations needed to obtain asymptotically optimal inference.