  We consider a wireless network comprising $n$ nodes located within a circular
area of radius $R$, which are participating in a decentralized learning
algorithm to optimize a global objective function using their local datasets.
To enable gradient exchanges across the network, we assume each node
communicates only with a set of neighboring nodes, which are within a distance
$R n^{-\beta}$ of itself, where $\beta\in(0,\frac{1}{2})$. We use tools from
network information theory and random geometric graph theory to show that the
communication delay for a single round of exchanging gradients on all the links
throughout the network scales as
$\mathcal{O}\left(\frac{n^{2-3\beta}}{\beta\log n}\right)$, increasing (at
different rates) with both the number of nodes and the gradient exchange
threshold distance.
