HOPSE: Scalable Higher-Order Positional and Structural Encoder for Combinatorial Representations

Understand

While Graph Neural Networks (GNNs) have proven highly effective at modeling relational data, pairwise connections cannot fully capture multi-way relationships naturally present in complex real-world systems.

• In response to this, Topological Deep Learning (TDL) leverages more general combinatorial representations--such as simplicial or cellular complexes--to accommodate higher-order interactions.
• Existing TDL methods often extend GNNs through Higher-Order Message Passing (HOMP), but face critical scalability challenges due to the steep complexity overhead of propagating messages through combinatorial structures.
• To overcome this limitation, we propose HOPSE (Higher-Order Positional and Structural Encoder), a framework free of message passing layers that uses Hasse graph decompositions to derive efficient and expressive encodings over arbitrary higher-order domains.