Caterpillar GNN: Replacing Message Passing with Efficient Aggregation (2506.06784v1)

Abstract: Message-passing graph neural networks (MPGNNs) dominate modern graph learning, typically prioritizing maximal expressive power. In contrast, we introduce an \emph{efficient aggregation} mechanism, deliberately trading off some expressivity for stronger and more structured aggregation capabilities. Our approach allows seamless scaling between classical message-passing and simpler methods based on colored or plain walks. We rigorously characterize the expressive power at each intermediate step using homomorphism counts from a hierarchy of generalized \emph{caterpillar graphs}. Based on this foundation, we propose the \emph{Caterpillar GNN}, whose robust graph-level aggregation enables it to successfully tackle synthetic graph-level task specifically designed to be challenging for classical MPGNNs. Moreover, we demonstrate that, on real-world datasets, the Caterpillar GNN achieves comparable predictive performance while significantly reducing the number of nodes in the hidden layers of the computational graph.

• The paper proposes replacing traditional message passing with a structured aggregation scheme that cuts computational overhead by up to 93% while preserving expressivity.
• It employs a hierarchical caterpillar framework to systematically control graph complexity and enhance efficiency in graph-level tasks.
• Empirical evaluations on synthetic and real-world datasets confirm competitive performance against standard GCNs, highlighting its scalability for diverse applications.

Caterpillar GNN: An Examination of Efficient Aggregation in Graph Neural Networks

The paper "Caterpillar GNN: Replacing Message Passing with Efficient Aggregation," authored by Marek Černý, introduces a novel approach to graph neural networks by proposing an efficient aggregation mechanism contrary to the conventional message-passing graph neural networks (MPGNNs). The core idea of this work involves a trade-off between expressivity and computational efficiency, optimizing graph-level tasks by transitioning between classical message-passing and simpler aggregation methods.

Overview and Technical Contributions

The paper elaborates on an efficient aggregation approach that replaces repetitive message-passing with a structured reduction of the computational graph, systematically organizing interactions among colored walks and controlling intermediate complexity levels. This gradual downscaling mechanism not only preserves essential graphical information but significantly reduces the spatial dimension of hidden layers within the graph and hence, computational overhead.

Central to this proposal is the Caterpillar GNN architecture, which robustly tackles synthetic and real-world graphs by leveraging a novel parametric aggregation scheme. Notably, this caters to graphs by enabling controlled alterations in their computation representation, providing an advantage in tasks where typical MPGNNs struggle. A demonstration of synthetic benchmarks reveals a perplexing double descent pattern akin to phenomena in convolutional networks, suggesting a potential optimization dynamic related to the gradual complexity reduction.

The research further introduces a hierarchy of caterpillar graphs, characterizing expressivity at each computational stage using graph homomorphism counts. This establishes a concrete mapping between efficient aggregation and graph-level expressivity, unveiling theoretical insights into balancing computational complexity in GNNs.

Empirical Evaluation

Empirically, the Caterpillar GNN was tested across a suite of standardized datasets, including biological and social networks, chemical property prediction tasks, and synthetic data exemplifying computationally intensive graph operations. A comparison with graph convolutional networks (GCNs) grounded in full message-passing revealed that the Caterpillar GNN achieves competitive performance levels with up to 93% reduction in computational nodes required, thereby optimizing both efficiency and accuracy.

Implications and Future Directions

The implications of this research span both practical and theoretical domains. Practically, the approach provides a scalable framework applicable to graph-based machine learning that optimizes memory, computation, and node utilization. Theoretically, it paves the way for further exploration into structured aggregation in GNNs, suggesting potential interlinks with hyperparameter dynamics seen in convolutional networks.

Future endeavors could delve into adaptive mechanisms for selecting parameters like caterpillar height within the aggregation scheme, tailored learning rate strategies, and broader application to heterogeneous graphs. Additionally, understanding optimization phenomena such as double descent in GNNs offers an exciting avenue for enhancing model robustness under varied computational settings.

In conclusion, this paper makes substantive contributions to the field of graph neural networks by critiquing conventional message-passing methods and advancing a structured, efficient aggregation alternative capable of nuanced expressivity and computational gains.