arXiv2026
Efficient information spreading in stochastic multi agent systems is a core challenge when communication is noisy, bandwidth limited, and agents lack global coordination. Yet biological systems, including ant colonies and fish schools, routinely overcome these constraints. A small number of informed individuals can reliably guide large, uncoordinated populations using minimal, noisy signals. Motivated by these observations, we study how reliable information dissemination can be achieved in such bio inspired settings. A population of $n$ agents, each with a binary preference, includes a designated subset of source agents, and the goal is to converge to the majority preference among the sources. In the noisy $\mathcal{PULL}(h)$ model, each agent observes noisy messages from $h$ randomly sampled peers in every round. Prior work shows that convergence requires $Ω(n/h)$ rounds even under favorable conditions. We ask how far we can push simplicity, with no synchronization at the start time and minimal message size, without compromising convergence speed. We present a quasi self-stabilizing protocol using only 2-bit messages that converges from arbitrary initial states despite severe noise and initial asynchrony. It achieves optimal convergence time $O((n/h)\log n)$ with high probability, and in particular $O(\log n)$ time in the snapshot regime $h=Θ(n)$. A key subroutine is an even simpler 1-bit protocol assuming simultaneous start, based on a natural two phase listen then amplify mechanism. Together, our results show that simple, biologically inspired protocols can achieve optimal and robust information dissemination even in highly unreliable and uncoordinated systems.