  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.
