Cell Attention Networks

TL;DR

Cell Attention Networks (CANs) extend graph attention by capturing higher-order interactions through a cell complex structure, improving learning tasks with a hierarchical, low-complexity approach.

Contribution

Introduces Cell Attention Networks that leverage cell complexes to model higher-order interactions, generalizing graph attention mechanisms with a hierarchical architecture.

Findings

CAN outperforms state-of-the-art methods on graph learning tasks.

The approach effectively captures higher-order relationships in data.

It maintains low computational complexity.

Abstract

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.