  This paper studies sequences of graphs satisfying the finite-time consensus
property (i.e., iterating through such a finite sequence is equivalent to
performing global or exact averaging) and their use in Gradient Tracking. We
provide an explicit weight matrix representation of the studied sequences and
prove their finite-time consensus property. Moreover, we incorporate the
studied finite-time consensus topologies into Gradient Tracking and present a
new algorithmic scheme called Gradient Tracking for Finite-Time Consensus
Topologies (GT-FT). We analyze the new scheme for nonconvex problems with
stochastic gradient estimates. Our analysis shows that the convergence rate of
GT-FT does not depend on the heterogeneity of the agents' functions or the
connectivity of any individual graph in the topology sequence. Furthermore,
owing to the sparsity of the graphs, GT-FT requires lower communication costs
than Gradient Tracking using the static counterpart of the topology sequence.
