Randomly initialized Bayes-optimal AMP provably achieves the weak-recovery threshold δ=1/2 and arbitrarily accurate recovery for δ>1.13 in proportional-regime noiseless phase retrieval.
arXiv preprint arXiv:2602.09959 , year=
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Approximate Message Passing with Random Initialization for Phase Retrieval
Randomly initialized Bayes-optimal AMP provably achieves the weak-recovery threshold δ=1/2 and arbitrarily accurate recovery for δ>1.13 in proportional-regime noiseless phase retrieval.