Review for NeurIPS paper: Information theoretic limits of learning a sparse rule

Summary and Contributions: The paper considers the generalized linear model, in the high-dimensional sparse setting. In this setting the authors prove the existence of an'all-or-nothing phenomenon' (see GZ, RXZ) wherein there exists a function m_*(n) (sublinear in the ambient dimension n) such that - if the # samples m (1 eps) m_*, the error in estimating the signal vanishes; and - if m (1-eps) m_*, the error converges to the'trivial' error of estimating from the prior. Classical statistical or learning theory typically demonstrates a'graceful' decay of error as the number of samples grows large. The current work is in a line of work demonstrating a'sharp cutoff' phenomenon instead. This was initiated by GZ, RXZ in linear regression setting.