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Exact asymptotics for phase retrieval and compressed sensing with random generative priors

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Academic year: 2021

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Figure 1: Mean squared error obtained by running the AMP algorithm (dots) from [7], for d = 2.10 3 averaged on 10 samples, compared to the MSE obtained from the state evolution eqs
Figure 2: Phase diagrams for the compressed sensing problem with (left) linear generative prior and (right) ReLU generative prior, in the plane (ρ, α)
Figure 4: Phase diagrams for the compressed sensing (left) and phase retrieval (right) problems for different depths of the prior, with ReLU activation and fixed layer-wise compression β l = 3
Figure 6: Algorithmic gap ∆ alg = α alg − α IT for small ρ and linear activation, as a function of (left) the compression β ≡ β l for fixed depth L = 4 and of (right) depth for a fixed compression β = 2.

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