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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. As a 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 ($w_0=-0.95$ 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., Comment: 19 pages, 8 figures, 5 tables; Comments are welcome!

We present the integrated 3-point correlation functions (3PCF) involving both the cosmic shear and the galaxy density fields. These are a set of higher-order statistics that describe the modulation of local 2-point correlation functions (2PCF) by large-scale features in the fields, and which are easy to measure from galaxy imaging surveys. Based on previous works on the shear-only integrated 3PCF, we develop the theoretical framework for modelling 5 new statistics involving the galaxy field and its cross-correlations with cosmic shear. Using realistic galaxy and cosmic shear mocks from simulations, we determine the regime of validity of our models based on leading-order standard perturbation theory with an MCMC analysis that recovers unbiased constraints of the amplitude of fluctuations parameter $A_s$ and the linear and quadratic galaxy bias parameters $b_1$ and $b_2$. Using Fisher matrix forecasts for a DES-Y3-like survey, relative to baseline analyses with conventional 3$\times$2PCFs, we find that the addition of the shear-only integrated 3PCF can improve cosmological parameter constraints by $20-40\%$. The subsequent addition of the new statistics introduced in this paper can lead to further improvements of $10-20\%$, even when utilizing only conservatively large scales where the tree-level models are valid. Our results motivate future work on the galaxy and shear integrated 3PCFs, which offer a practical way to extend standard analyses based on 3$\times$2PCFs to systematically probe the non-Gaussian information content of cosmic density fields., Comment: 19 pages, 8 figures + appendix. Comments are welcome!

The integrated shear 3-point correlation function $\zeta_{\pm}$ measures the correlation between the local shear 2-point function $\xi_{\pm}$ and the 1-point shear aperture mass in patches of the sky. Unlike other higher-order statistics, $\zeta_{\pm}$ can be efficiently measured from cosmic shear data, and it admits accurate theory predictions on a wide range of scales as a function of cosmological and baryonic feedback parameters. Here, we develop and test a likelihood analysis pipeline for cosmological constraints using $\zeta_{\pm}$. We incorporate treatment of systematic effects from photometric redshift uncertainties, shear calibration bias and galaxy intrinsic alignments. We also develop an accurate neural-network emulator for fast theory predictions in MCMC parameter inference analyses. We test our pipeline using realistic cosmic shear maps based on $N$-body simulations with a DES Y3-like footprint, mask and source tomographic bins, finding unbiased parameter constraints. Relative to $\xi_{\pm}$-only, adding $\zeta_{\pm}$ can lead to $\approx 10-25\%$ improvements on the constraints of parameters like $A_s$ (or $\sigma_8$) and $w_0$. We find no evidence in $\xi_{\pm} + \zeta_{\pm}$ constraints of a significant mitigation of the impact of systematics. We also investigate the impact of the size of the apertures where $\zeta_{\pm}$ is measured, and of the strategy to estimate the covariance matrix ($N$-body vs. lognormal). Our analysis solidifies the strong potential of the $\zeta_{\pm}$ statistic and puts forward a pipeline that can be readily used to improve cosmological constraints using real cosmic shear data., Comment: 21 pages, 11 figures, 3 tables. Comments welcome