  This paper investigates federated learning (FL) in a multi-hop communication
setup, such as in constellations with inter-satellite links. In this setup,
part of the FL clients are responsible for forwarding other client's results to
the parameter server. Instead of using conventional routing, the communication
efficiency can be improved significantly by using in-network model aggregation
at each intermediate hop, known as incremental aggregation (IA). Prior works
[1] have indicated diminishing gains for IA under gradient sparsification. Here
we study this issue and propose several novel correlated sparsification methods
for IA. Numerical results show that, for some of these algorithms, the full
potential of IA is still available under sparsification without impairing
convergence. We demonstrate a 15x improvement in communication efficiency over
conventional routing and a 11x improvement over state-of-the-art (SoA) sparse
IA.
