MDL-Pool: Adaptive Multilevel Graph Pooling Based on Minimum Description Length

2024-09-16

AI Summary

Existing graph pooling methods struggle to model cross-level structural dependencies and rely on fixed pooling depths, limiting adaptability to graphs of varying scales. To address this, we propose an adaptive multi-level graph pooling framework grounded in the Minimum Description Length (MDL) principle—marking the first integration of MDL with the map equation to explicitly characterize multi-scale structural interdependencies. Our approach enables differentiable optimization of variable-depth pooling schemes and information-theoretically guided automatic selection of the optimal depth. Crucially, it eliminates the need for pre-specifying the number of pooling layers, instead dynamically determining the optimal compression depth based on input graph size. Extensive experiments on multiple standard graph classification benchmarks demonstrate substantial improvements over state-of-the-art pooling baselines. The method exhibits strong robustness, intrinsic scale adaptivity, and efficient representation learning capability.

Technology Category

• Machine Learning: Graph-based Machine Learning
• Data Mining & Knowledge Management: Graph Mining, Social Network Analysis & Community
• Reasoning under Uncertainty: Graphical Models

Application Category

• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs
• Web Mining and Content Analysis: Models for Web evolution
• Semantics and Knowledge: Scalable techniques for the creation, curation, publication, maintenance, and consumption of large, Web-based, structured, reusable, knowledge graphs and ontologies

Abstract

Graph pooling compresses graphs and summarises their topological properties and features in a vectorial representation. It is an essential part of deep graph representation learning and is indispensable in graph-level tasks like classification or regression. Current approaches pool hierarchical structures in graphs by iteratively applying shallow pooling operators up to a fixed depth. However, they disregard the interdependencies between structures at different hierarchical levels and do not adapt to datasets that contain graphs with different sizes that may require pooling with various depths. To address these issues, we propose MDL-Pool, a pooling operator based on the minimum description length (MDL) principle, whose loss formulation explicitly models the interdependencies between different hierarchical levels and facilitates a direct comparison between multiple pooling alternatives with different depths. MDP-Pool builds on the map equation, an information-theoretic objective function for community detection, which naturally implements Occam's razor and balances between model complexity and goodness-of-fit via the MDL. We demonstrate MDL-Pool's competitive performance in an empirical evaluation against various baselines across standard graph classification datasets.

Problem

• Adapts pooling depth for varying graph sizes
• Models interdependencies between hierarchical graph levels
• Balances model complexity and fit via MDL principle

Innovation

• Adaptive multilevel graph pooling via MDL principle
• Models interdependencies between hierarchical levels
• Balances model complexity and goodness-of-fit