Heterogeneous Sheaf Neural Networks

Heterogeneous graphs, whose nodes and edges can belong to different types and feature spaces, arise in many real-world domains, including biology, recommendation, social networks, and computer systems. Existing heterogeneous graph neural networks typically handle this heterogeneity at the architectural level through relation-specific modules, meta-path machinery or type-aware attention, which often leads to increasingly specialised, parameter-heavy designs. In this work, we propose \textsc{HetSheaf}, a framework for learning heterogeneous graphs through \emph{cellular sheaves}. Instead of encoding heterogeneity solely in the architecture, \textsc{HetSheaf} represents it directly in the underlying data structure by assigning type-aware local feature spaces and learning restriction maps conditioned on node features, node types, and edge types. To support graph-level prediction, we further introduce \textsc{SheafPool}, a universal stalk-space readout that aggregates node representations while being invariant to local changes of basis, thereby making graph classification with sheaf networks well-defined and achieving an F1 Score up to 42 percentage points higher than mean pooling. Across a diverse suite of benchmarks (node classification, link prediction and graph classification), \textsc{HetSheaf} consistently achieves up to 2 percentage points higher performance (up to 94.93\% Macro F1 Score on node classification and up to 99.64\% on link prediction) on the Heterogeneous Graph Benchmark (HGB) framework against homogeneous (GCN, GAT, GIN, GraphSAGE), heterogeneous (R-GCN, HAN, HGT) and type-agnostic sheaf baselines, while reducing the number of parameters by up to 10$\times$.