Sam Gunn, a computer scientist at UC Berkeley, presents this Institute for Advanced Study seminar on the data deletion problem: after some precomputation, how quickly can you predict what a trained model would have output if a chosen subset of its training data had been removed? Gunn describes a deletion scheme for deep learning that achieves arbitrarily small error and failure probability, with precomputation and prediction costs only polylogarithmic factors slower than ordinary training and inference, and storage proportional to that of a handful of models. He grounds the result in a stability assumption about training that, unlike prior approaches, remains compatible with powerful modern models, and explains the core technique, a method for locally sketching an arithmetic circuit using higher order derivatives in random complex directions. The talk is aimed at a discrete mathematics and computer science seminar audience and draws on his recent paper on the subject.