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@@ -970,21 +970,22 @@ non-IID data.
 \label{section:conclusion}
 
 We proposed D-Cliques, a sparse topology that recovers the convergence
-speed of a fully-connected topology in the presence of local class bias.
-D-Cliques is based on assembling cliques of nodes such that their joint local
-distribution is representative of the global distribution so as to locally
-recover IIDness. Cliques are joined in a sparse inter-clique topology so that
+speed of a fully-connected network in the presence of local class bias.
+D-Cliques is based on assembling subsets of nodes into cliques such
+that the clique-level class distribution is representative of the global
+distribution, thereby locally recovering IIDness. Cliques are joined in a
+sparse inter-clique topology so that
 they quickly converge to the same model. We proposed Clique
 Averaging to remove the non-IID bias in gradient computation by
 averaging gradients only with other nodes within the clique. Clique Averaging
 can in turn be used to implement unbiased momentum to recover the convergence
 speed usually only possible with IID mini-batches. Through our experiments, we
 showed that the clique structure of D-Cliques is critical in obtaining these
-results and that a small-world inter-clique topology with $O(n
-+ log (n))$ edges seems to achieve the best compromise between
+results and that a small-world inter-clique topology with only $O(n
++ log (n))$ edges achieves the best compromise between
 convergence speed and scalability with the number of nodes.
 
-D-Cliques thus appears to be promising to reduce bandwidth
+D-Cliques thus appears to be very promising to reduce bandwidth
 usage on FL servers and to implement fully decentralized alternatives in a
 wider range of applications where global coordination is impossible or costly.
 For instance, the presence and relative frequency of classes in each node
@@ -994,10 +995,9 @@ PeerSampling~\cite{jelasity2007gossip}. This will be investigated in future work
 We also believe that our ideas can be useful to deal
 with more general types of data non-IIDness beyond the important case of
 local class bias that we studied in this paper. An important example is
-covariate shift or feature distribution skew \cite{kairouz2019advances}, where
-local density estimates could be used as basis to construct cliques that
-approximately
-recover the global distribution.
+covariate shift or feature distribution skew \cite{kairouz2019advances}, for
+which local density estimates could be used as basis to construct cliques that
+approximately recover the global distribution.
 
 %\section{Future Work}
 %\begin{itemize}