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

arXiv: https://arxiv.org/abs/2207.05202 · HTML: https://mlsanity.com/paper/2207.05202/

## Key facts

- Cited by 14 papers in the map (data through 14 Oct 2026).
- Builds on 10 of its 30 references that are in the map.
- First posted on arXiv 11 Jul 2022.

## Builds on (most cited first, 10 of 10)

- [Gaussian Error Linear Units (GELUs)](https://mlsanity.com/paper/1606.08415/) (2016)
- [Relational inductive biases, deep learning, and graph networks](https://mlsanity.com/paper/1806.01261/) (2018)
- [Geometric Deep Learning: Grids, Groups, Graphs, Geodesics, and Gauges](https://mlsanity.com/paper/2104.13478/) (2021)
- [Discovering Symbolic Models from Deep Learning with Inductive Biases](https://mlsanity.com/paper/2006.11287/) (2020)
- [E(n) Equivariant Normalizing Flows](https://mlsanity.com/paper/2105.09016/) (2021)
- [Rediscovering orbital mechanics with machine learning](https://mlsanity.com/paper/2202.02306/) (2022)
- [Solving high-dimensional parameter inference: marginal posterior densities & Moment Networks](https://mlsanity.com/paper/2011.05991/) (2020)
- [Learning cosmology and clustering with cosmic graphs](https://mlsanity.com/paper/2204.13713/) (2022)
- [Estimating Cosmological Parameters from the Dark Matter Distribution](https://mlsanity.com/paper/1711.02033/) (2017)
- [deep21: a Deep Learning Method for 21cm Foreground Removal](https://mlsanity.com/paper/2010.15843/) (2020)

## Built on by (most cited first, 14 of 14)

- [Robust Field-level Likelihood-free Inference with Galaxies](https://mlsanity.com/paper/2302.14101/) (2023)
- [Domain Adaptive Graph Neural Networks for Constraining Cosmological Parameters Across Multiple Data Sets](https://mlsanity.com/paper/2311.01588/) (2023)
- [Robust field-level inference with dark matter halos](https://mlsanity.com/paper/2209.06843/) (2022)
- [A Cosmic-Scale Benchmark for Symmetry-Preserving Data Processing](https://mlsanity.com/paper/2410.20516/) (2024)
- [Cosmology from Galaxy Redshift Surveys with PointNet](https://mlsanity.com/paper/2211.12346/) (2022)
- [Field-level simulation-based inference with galaxy catalogs: the impact of systematic effects](https://mlsanity.com/paper/2310.15234/) (2023)
- [CosmoBench: A Multiscale, Multiview, Multitask Cosmology Benchmark for Geometric Deep Learning](https://mlsanity.com/paper/2507.03707/) (2025)
- [Uncovering dark matter density profiles in dwarf galaxies with graph neural networks](https://mlsanity.com/paper/2208.12825/) (2022)
- [Fishnets: Information-Optimal, Scalable Aggregation for Sets and Graphs](https://mlsanity.com/paper/2310.03812/) (2023)
- [Topological Neural Networks: Mitigating the Bottlenecks of Graph Neural Networks via Higher-Order Interactions](https://mlsanity.com/paper/2402.06908/) (2024)
- [Hybrid summary statistics: neural weak lensing inference beyond the power spectrum](https://mlsanity.com/paper/2407.18909/) (2024)
- [Cosmology with Persistent Homology: Parameter Inference via Machine Learning](https://mlsanity.com/paper/2412.15405/) (2024)
- [Score Matching on Large Geometric Graphs for Cosmology Generation](https://mlsanity.com/paper/2508.16990/) (2025)
- [Galaxy Phase-Space and Field-Level Cosmology: The Strength of Semi-Analytic Models](https://mlsanity.com/paper/2512.10222/) (2025)

## Abstract (arXiv)

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 Omegam, σ8 parameter constraints with small (~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.