Decentralized Phase Retrieval over Networks

We consider noiseless real Gaussian measurements and use the same mix–gradient–mix update at every iteration. We couple the network average to a population gradient trajectory and control the disagreement at each gradient evaluation. This gives a finite-accuracy recovery guarantee with explicit sample, iteration, and communication costs, including unequal batches and nodes with fewer than $d$ samples. The bound is conservative and polynomial in the dimension, initialization scale, and target accuracy. A separate local result gives exact convergence under additional regularity. Experiments show two-stage dynamics, recovery from individually underdetermined nodes, and a topology-dependent communication cost. To the best of our knowledge, this work provides the first systematic study jointly addressing statistical recovery, convergence, and communication complexity for decentralized phase retrieval over peer-to-peer networks from independent Gaussian node initializations.