Reviews: The spiked matrix model with generative priors

This paper investigates the matrix decomposition under the assumption that the spiked vector comes from a generated model. In particular, a single layer generating model with a linear/non-linear activation is considered. The authors study the phase transition on when the underlying spiked vector can be recovered, and shows that there is no algorithmic gap with generative-model priors, which is different from the sparse model. In addition, a new spectral method based on approximate messaging is proposed. The authors shows that this algorithm can reach the statistically optimal threshold. In general, this manuscript is well-written.