C3NN - Cosmological Correlator Convolutional Neural Network - an interpretable machine learning tool for cosmological analyses

Aug 5, 2026

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Modern cosmological large-scale-structure studies increasingly rely on machine learning, where Convolutional Neural Networks (CNNs) excel in image classification and cosmological parameter inference. Yet CNN outputs are often criticized as “black boxes” because their predictions are hard to connect to underlying cosmological fields. C3NN addresses this by fusing CNN architectures with cosmological N-point correlation functions (NPCFs), enabling explicit, analytically tractable expressions. Auxiliary ranking of interpretable convolution outputs supports quantitative interpretation. Tests on binary tasks using Gaussian and Log-normal random fields and on weak-lensing convergence maps distinguish dark-energy scenarios. Results indicate a robust, explainable pathway to extract physical insights from observational data.

LanguageEnglish

CategoryResearch & Report

FormatPDF

Pages21

Reading Time53 min

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Abstract

Introduction

Machine learning in cosmology and CNNs

The interpretability problem

Existing interpretability approaches

C3NN approach and motivation

arXiv :2402 .09526v1 [ astro-ph .CO] 14 Feb 2024 Draft version February 16, 2024 Typeset using LATEX default style in AASTeX631 C3NN: Cosmological Correlator Convolutional Neural Network an interpretable machine learning tool for cosmological analyses Zhengyangguang Gong ,1, 2 Anik Halder ,1, 2 Annabelle Bohrdt,3, 4 Stella Seitz,1, 2 and David Gebauer1 1 Universit¨ats-Sternwarte, Fakult¨at f¨ur Physik, Ludwig-Maximilians-Universit¨at M¨unchen, Scheinerstraße 1, 81679 M¨unchen, Germany 2 Max Planck Institute for Extraterrestrial Physics, Giessenbachstraße 1, 85748 Garching, Germany 3 University of Regensburg, Universit¨atsstraße 31, Regensburg D-93053, Germany 4 Munich Center for Quantum Science and Technology, Schellingstraße 4, Munich D-80799, Germany ABSTRACT Modern cosmological research in large scale structure has witnessed an increasing number of applications of machine learning methods. Among them, Convolutional Neural Networks (CNNs) have received substantial attention due to their outstanding performance in image classification, cosmological parameter inference and various other tasks. However, many models which make use of CNNs are criticized as “black boxes” due to the difficulties in relating their outputs intuitively and quantitatively to the cosmological fields under investigation. To overcome this challenge, we present the Cosmological Correlator Convolutional Neural Network (C3NN)—a fusion of CNN architecture with the framework of cosmological N-point correlation functions (NPCFs) . We demonstrate that the output of this model can be expressed explicitly in terms of the analytically tractable NPCFs. Together with other auxiliary algorithms, we are able to open the “black box” by quantitatively ranking different orders of the interpretable convolution outputs based on their contribution to classification tasks. Asa proof of concept, we demonstrate this by applying our framework to a series of binary classification tasks using Gaussian and Log-normal random fields and relating its outputs to the analytical NPCFs describing the two fields. Furthermore, we exhibit the model’s ability to distinguish different dark energy scenarios (w0 = −0 .95 and −1 .05) using N-body simulated weak lensing convergence maps and discuss the physical implications coming from their interpretability. With these tests, we show that C3NN combines advanced aspects of machine learning architectures with the framework of cosmological NPCFs, thereby making it an exciting tool with the potential to extract physical insights in a robust and explainable way from observational data. Keywords: Astrostatistics techniques(1886)— Classification(1907)— Convolutional neural net works(1938)—Weak gravitational lensing(1797)—Cosmological parameters(339) 1. INTRODUCTION In recent years, numerous machine learning methods have found applications in cosmology and astrophysics ranging from classification and regression tasks to acceleration of computational methods (see Dvorkin et al. (2022) for a recent review) . Among the various machine learning techniques, Convolutional Neural Networks (CNNs) (LeCunet al. 2015) have been used extensively. Briefly, CNNs can compress a large dataset (e.g. images) into several feature representations through a series of alternative linear and nonlinear transformations. The large number of parameters in a CNN model is typically determined by training the model to numerous simulated data that aim at reproducing actual scientific phenomena. In the context of astronomy and cosmology, these compressed features can be used for classification, such as searching for strong gravitational lensing systems (Rojas et al. 2022) and classifying different galaxy morphologies (Dom´ınguez S´anchez et al. 2022), or for inference analyses such as constraining parameters in various cosmological models (Fluri et al. 2019; Fluri et al. 2022; Lu et al. 2023), to name a few. However, this impressive development of C

FAQs

What is the main goal of C3NN in cosmological analyses?

C3NN aims to make CNN-based features interpretable by expressing the model output explicitly in terms of cosmological N-point correlation functions (NPCFs).

Why are conventional CNNs considered “black boxes” in this context?

Conventional CNN output feature representations are difficult to relate intuitively and quantitatively to the cosmological fields used in the analysis.

How does C3NN demonstrate interpretability and scientific usefulness?

It applies the framework to binary classification tasks using Gaussian and Log-normal random fields, ranks interpretable convolution outputs by their contribution to classification, and distinguishes dark-energy scenarios using simulated weak-lensing convergence maps.

Aug 5, 2026

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