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

Abstract

Cosmological inference relies on compressed forms of the raw data for analysis, with traditional methods exploiting physics knowledge to define summary statistics, such as power spectra, that are known to capture much of the information. An alternative approach is to ask a neural network to find a set of informative summary statistics from data, which can then be analysed either by likelihood- or simulation-based inference. This has the advantage that for non-Gaussian fields, they may capture more information than two-point statistics. However, a disadvantage is that the network almost certainly relearns that two-point statistics are informative. In this paper, we introduce a new hybrid method, which combines the best of both: we use our domain knowledge to define informative physics-based summary statistics, and explicitly ask the network to augment the set with extra statistics that capture information that is not already in the existing summaries. This yields a new, general loss formalism that reduces both the number of simulations and network size needed to extract useful non-Gaussian information from cosmological fields, and guarantees that the resulting summary statistics are at least as informative as the power spectrum. In combination, they can then act as powerful inputs to implicit inference of model parameters. We use a generalisation of Information Maximising Neural Networks (IMNNs) to obtain the extra summaries, and obtain parameter constraints from simulated tomographic weak gravitational lensing convergence maps. 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× and up to 8× 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 extremely lightweight architectures to match much larger regression networks with far fewer simulations needed to obtain asymptotically optimal inference.