NCoder -- A Quantum Field Theory approach to encoding data

Abstract: 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.