The Cosmic Graph: Optimal Information Extraction from Large-Scale Structure using Catalogues

TL;DR

This paper introduces a novel graph-based neural network approach using IMNNs to extract cosmological information from large-scale structure catalogues, significantly improving parameter constraints over traditional methods.

Contribution

It develops an implicit likelihood method with graph neural networks and IMNNs for optimal information extraction from cosmological catalogues, outperforming traditional statistics.

Findings

High sensitivity of graph structures to cosmology in noise-free limit

Automatic combination of mass and clustering information by networks

Effective information extraction from noisy survey data

Abstract

We present an implicit likelihood approach to quantifying cosmological information over discrete catalogue data, assembled as graphs. To do so, we explore cosmological parameter constraints using mock dark matter halo catalogues. We employ Information Maximising Neural Networks (IMNNs) to quantify Fisher information extraction as a function of graph representation. We a) demonstrate the high sensitivity of modular graph structure to the underlying cosmology in the noise-free limit, b) show that graph neural network summaries automatically combine mass and clustering information through comparisons to traditional statistics, c) demonstrate that networks can still extract information when catalogues are subject to noisy survey cuts, and d) illustrate how nonlinear IMNN summaries can be used as asymptotically optimal compressed statistics for Bayesian simulation-based inference. We reduce the area of joint $\Omega_m, \sigma_8$ parameter constraints with small ($\sim$100 object) halo catalogues by a factor of 42 over the two-point correlation function, and demonstrate that the networks automatically combine mass and clustering information. This work utilises a new IMNN implementation over graph data in Jax, which can take advantage of either numerical or auto-differentiability. We also show that graph IMNNs successfully compress simulations away from the fiducial model at which the network is fitted, indicating a promising alternative to n-point statistics in catalogue simulation-based analyses.