  In this paper we present a novel approach to interpretable AI inspired by
Quantum Field Theory (QFT) which we call the NCoder. The NCoder is a modified
autoencoder neural network whose latent layer is prescribed to be a subset of
$n$-point correlation functions. Regarding images as draws from a lattice field
theory, this architecture mimics the task of perturbatively constructing the
effective action of the theory order by order in an expansion using Feynman
diagrams. Alternatively, the NCoder may be regarded as simulating the procedure
of statistical inference whereby high dimensional data is first summarized in
terms of several lower dimensional summary statistics (here the $n$-point
correlation functions), and subsequent out-of-sample data is generated by
inferring the data generating distribution from these statistics. In this way
the NCoder suggests a fascinating correspondence between perturbative
renormalizability and the sufficiency of models. We demonstrate the efficacy of
the NCoder by applying it to the generation of MNIST images, and find that
generated images can be correctly classified using only information from the
first three $n$-point functions of the image distribution.
