  Since their introduction, graph attention networks achieved outstanding
results in graph representation learning tasks. However, these networks
consider only pairwise relationships among nodes and then they are not able to
fully exploit higher-order interactions present in many real world data-sets.
In this paper, we introduce Cell Attention Networks (CANs), a neural
architecture operating on data defined over the vertices of a graph,
representing the graph as the 1-skeleton of a cell complex introduced to
capture higher order interactions. In particular, we exploit the lower and
upper neighborhoods, as encoded in the cell complex, to design two independent
masked self-attention mechanisms, thus generalizing the conventional graph
attention strategy. The approach used in CANs is hierarchical and it
incorporates the following steps: i) a lifting algorithm that learns {\it edge
features} from {\it node features}; ii) a cell attention mechanism to find the
optimal combination of edge features over both lower and upper neighbors; iii)
a hierarchical {\it edge pooling} mechanism to extract a compact meaningful set
of features. The experimental results show that CAN is a low complexity
strategy that compares favorably with state of the art results on graph-based
learning tasks.
