Approximate Message Passing with Random Initialization for Phase Retrieval

What the math gives to ML

The paper gives a long-horizon Gaussian decomposition for approximate message passing (AMP) started from an uninformative Gaussian vector, showing that an initially vanishing signal overlap can grow to weak recovery. The transferable asset is an initialization-free unrolled inference architecture that preserves AMP residual correction and Onsager debiasing while allowing learned scalar denoisers. This is useful for phase retrieval and related single-index inverse problems where spectral initialization is expensive or brittle. The key experiment is whether random-start learned AMP can match informative initialization after enough iterations while remaining stable.