Abstract:Open access to high-quality education is limited by the difficulty of providing student feedback. In this paper, we present Generative Grading with Neural Approximate Parsing (GG-NAP): a novel approach for providing feedback at scale that is capable of both accurately grading student work while also providing verifiability--a property where the model is able to substantiate its claims with a provable certificate. Our approach uses generative descriptions of student cognition, written as probabilistic programs, to synthesise millions of labelled example solutions to a problem; it then trains inference networks to approximately parse real student solutions according to these generative models. We achieve feedback prediction accuracy comparable to professional human experts in a variety of settings: short-answer questions, programs with graphical output, block-based programming, and short Java programs. In a real classroom, we ran an experiment where humans used GG-NAP to grade, yielding doubled grading accuracy while halving grading time.