  We study the asymptotic learning rates under linear and log-linear
combination rules of belief vectors in a distributed hypothesis testing
problem. We show that under both combination strategies, agents are able to
learn the truth exponentially fast, with a faster rate under log-linear fusion.
We examine the gap between the rates in terms of network connectivity and
information diversity. We also provide closed-form expressions for special
cases involving federated architectures and exchangeable networks.
