  Generative neural networks (GNNs) have gained renown for efficaciously
capturing intrinsic low-dimensional structure in natural images. Here, we
investigate the subgaussian demixing problem for two Lipschitz signals, with
GNN demixing as a special case. In demixing, one seeks identification of two
signals given their sum and prior structural information. Here, we assume each
signal lies in the range of a Lipschitz function, which includes many popular
GNNs as a special case. We prove a sample complexity bound for nearly optimal
recovery error that extends a recent result of Bora, et al. (2017) from the
compressed sensing setting with gaussian matrices to demixing with subgaussian
ones. Under a linear signal model in which the signals lie in convex sets,
McCoy & Tropp (2014) have characterized the sample complexity for
identification under subgaussian mixing. In the present setting, the signal
structure need not be convex. For example, our result applies to a domain that
is a non-convex union of convex cones. We support the efficacy of this demixing
model with numerical simulations using trained GNNs, suggesting an algorithm
that would be an interesting object of further theoretical study.
