Interpretability of deep-learning methods applied to large-scale structure surveys

¹ Université Paris-Saclay, CNRS, Institut d’Astrophysique Spatiale, 91405 Orsay, France
² Université Paris-Saclay, Université Paris Cité, CEA, CNRS, AIM, 91191 Gif-sur-Yvette, France
³ Institute for Particle Physics and Astrophysics, ETH Zurich, 8093 Zurich, Switzerland
⁴ University Observatory Munich, Scheinerstraße 1, D-81679 Munich, Germany
⁵ University of Applied Sciences Northwestern Switzerland, FHNW, Bahnhofstrasse 6, 5210 Windisch, Switzerland

^★ Corresponding author: This email address is being protected from spambots. You need JavaScript enabled to view it.

Received: 30 January 2025
Accepted: 19 February 2026

Abstract

Deep learning and convolutional neural networks in particular are powerful and promising tools for cosmological analysis of large-scale structure surveys. They already provide similar performance levels to classical analysis methods using fixed summary statistics and show potential to break key degeneracies through better probe combinations. They will also likely improve rapidly in the coming years as progress is made in terms of physical modelling through both software and hardware improvement. One key issue remains: unlike classical analysis, a convolutional neural network’s inference process is hidden from the user as the network optimises millions of parameters with no interpretable physical meaning. This prevents a clear understanding of the potential limitations and biases of the analysis, making it hard to rely on as a main analysis method. In this work, we explored the behaviour of such a convolutional neural network through a novel method. Instead of trying to analyse a network a posteriori, i.e. after training has been completed, we studied the impact on the constraining power of training the network and predicting parameters with degraded data, where we removed part of the information. This allowed us to gain an understanding of which parts and features of tomographic, weak gravitational lensing maps are most important in the network’s inference process. For Stage-III-like noise levels, we find that the network’s inference process relies on a mix of both Gaussian and non-Gaussian information, and it seems to put an emphasis on structures whose scales are at the limit between linear and non-linear regimes. When studying a noiseless survey, we find that the relative importance of small scales increases, indicating that they hold relevant cosmological information that is inaccessible when including realistic levels of shape noise.