Core-Halo Decomposition: Decentralizing Large-Scale Fixed-Point Problems

ArXi:2605.08681v1 Announce Type: cross We study solving large-scale fixed-point equation \(x^\star=\bar F(x^\star)\) with decomposition. Standard strict decomposition assigns each agent a disjoint block and evaluates updates using only owned coordinates. For most operators, however, a block update may depend on variables outside the block. Truncating these dependencies by strict decomposition changes the mean operator and creates structural bias that cannot be removed by samples, smaller stepsizes, or additional consensus.