Unifying Graph Neural Networks Through a Common Layer Equation
2026-08-17 • Machine Learning
Machine Learning
AI summaryⓘ
The authors created a single common equation to describe many types of graph neural networks, breaking down their operations into seven key parts. This helps show what parts of the method move information and what information is moved, covering various architectures like attention or spectral filtering. They tested this framework on over 200 models to organize and compare them clearly. Their work also reveals how different design choices affect problems like oversmoothing and expressivity in graph networks. Lastly, they highlight the challenge of linking graph properties and tasks to the best network designs.
Graph Neural NetworksMessage PassingAttention MechanismSpectral FilteringPropagationOversmoothingOversquashingHeterophilyExpressivityGraph Architecture
Authors
Sai Karthik Navuluru, Siddhartha Shankar Das, Bo Ni, Hongjie Chen, Yu Wang, Baris Coskunuzer, Nesreen K. Ahmed, Franck Dernoncourt, Mahantesh Halappanavar, Tyler Derr, Ryan A. Rossi, Lakshman Tamil
Abstract
Graph neural networks are commonly described through family-specific equations whose notation obscures shared computations and structural differences. We introduce a common layer equation that represents covered architectures through seven components: an update domain, channel set, propagation bank, per-channel message maps, channel-fusion operator, ego/residual map, and update map. The central factorization separates where information moves, encoded by the propagation bank, from what moves, encoded by the message maps. Function-valued fillings extend the same equation across local message passing, attention, spectral filtering, global communication, relation-specific channels, higher-order domains, and geometric messages. We make this unification explicit and checkable through worked reductions of canonical layers and component assignments spanning seven nonexclusive architectural families. A fixed slot discipline assigns operations by computational role and defines the framework's coverage boundary. The decomposition also yields component-level theoretical insights: under endpoint-local messages and node-local updates, operator support bounds one-layer dependencies, and one-layer global mixing requires a full effective operator row under the stated hypotheses. The resulting framework organizes more than 200 architectures in a common design space, enables component-wise comparison and generation of structurally consistent architectures, and connects propagation choices to oversmoothing, oversquashing, heterophily, and expressivity. It further exposes the empirical inverse problem of mapping measurable graph and task properties to validated component choices.