Graph Parsing Networks

TL;DR

This work tackles the rigidity of fixed pooling in hierarchical graph pooling by introducing Graph Parsing Network (GPN), which learns a personalized pooling tree for each graph through a graph parsing algorithm inspired by bottom-up grammar induction. GPN combines graph information encoding, a non-differentiable graph parsing step with DOM/EXP/GEN operators, and a DeepSets-based multiset computation to produce adaptive pooling while preserving node information and maintaining memory efficiency. Empirical results show state-of-the-art performance on several graph-classification benchmarks, competitive results for node classification, and a graph reconstruction task that visualizes preserved structure; efficiency analyses confirm improved memory and time scaling. Overall, GPN provides a principled, end-to-end framework for learning per-graph pooling structures, with practical implications for scalable, structure-aware graph representation learning.

Abstract

Graph pooling compresses graph information into a compact representation. State-of-the-art graph pooling methods follow a hierarchical approach, which reduces the graph size step-by-step. These methods must balance memory efficiency with preserving node information, depending on whether they use node dropping or node clustering. Additionally, fixed pooling ratios or numbers of pooling layers are predefined for all graphs, which prevents personalized pooling structures from being captured for each individual graph. In this work, inspired by bottom-up grammar induction, we propose an efficient graph parsing algorithm to infer the pooling structure, which then drives graph pooling. The resulting Graph Parsing Network (GPN) adaptively learns personalized pooling structure for each individual graph. GPN benefits from the discrete assignments generated by the graph parsing algorithm, allowing good memory efficiency while preserving node information intact. Experimental results on standard benchmarks demonstrate that GPN outperforms state-of-the-art graph pooling methods in graph classification tasks while being able to achieve competitive performance in node classification tasks. We also conduct a graph reconstruction task to show GPN's ability to preserve node information and measure both memory and time efficiency through relevant tests.

Figures (12)

• Figure 1: Comparison of graph pooling methods. The colors of the nodes indicate their pooling levels. The solid/dotted lines with arrows represent hard/soft node assignment matrixes.
• Figure 2: Proposed graph parsing networks, driven by the graph parsing algorithm $\mathcal{A}$. The box with three stages indicates the graph pooling layer, which recurrently builds the entire model. The red box shows the details and an example of how $\mathcal{A}$ works.
• Figure 3: Graph-level and node-level GPN architecture. Each un-pooling layer receives an assignment matrix and node feature through a skip-connection from its corresponding pooling layer.
• Figure 4: Graph reconstruction task on ring and grid synthetic graphs, which tests whether a graph pooling model can preserve node information intact.
• Figure 5: Memory efficiency test, "x" indicate the out-of-memory error.

Theorems & Definitions (10)

• Definition 1
• Definition 2
• Definition 3
• Proposition 4
• Proposition 5
• Proposition 6
• proof
• proof
• proof
• proof