Extracting Cosmological Information from Lightcone Data: A Comparison of CNNs and Summary-Statistic-Based Approaches

TL;DR

This paper compares CNN-based and summary statistic-based methods for extracting cosmological information from lightcone data, finding that both approaches can be effective with different strengths, informing future galaxy survey analyses.

Contribution

It introduces a CNN+2D approach for lightcone analysis and systematically compares it with traditional summary statistics and fully connected networks, highlighting their relative performance.

Findings

FC networks with $a_{\ell m}$ and WST outperform 2PCF-based methods.

CNN+2D achieves the smallest uncertainties for a fiducial cosmology.

Both learned features and summary statistics are effective for cosmological inference.

Abstract

Lightcone observations are the natural data format of galaxy surveys, but their evolving geometry breaks the translational symmetry assumed by standard convolutional neural networks (CNNs). In particular, applying CNNs to 3D gridded lightcone data implicitly treats the line-of-sight direction as translationally invariant, despite encoding cosmic time evolution. We propose a simple alternative (CNN+2D) that divides the lightcone into redshift slices, projects each onto a HEALPix sphere, and analyzes them with a 2D CNN. Using \texttt{AbacusSummit} halo lightcone mocks ($0.3<z<0.8$, $40^\circ\times40^\circ$), we compare this approach with fully connected networks (FC) applied to different summary statistics, including spherical harmonic coefficients ($a_{\ell m}$), wavelet scattering transform (WST) coefficients, and the angular two-point correlation function (2PCF), along with standard 2PCF likelihood and Fisher forecasts. We find that multiple statistics beyond CNNs can achieve competitive performance: FC networks combined with $a_{\ell m}$ and especially WST significantly outperform 2PCF-based methods, with FC+WST yielding the best overall parameter constraints across cosmologies. Meanwhile, for a fiducial cosmology with multiple realizations, the CNN+2D approach achieves the smallest statistical uncertainties. These results demonstrate that both learned features and carefully constructed summary statistics can effectively extract cosmological information from lightcone data, providing flexible and robust analysis strategies for upcoming surveys such as DESI, Euclid, and CSST.