ASAP: Adaptive Structure Aware Pooling for Learning Hierarchical Graph Representations (1911.07979v3)

Abstract: Graph Neural Networks (GNN) have been shown to work effectively for modeling graph structured data to solve tasks such as node classification, link prediction and graph classification. There has been some recent progress in defining the notion of pooling in graphs whereby the model tries to generate a graph level representation by downsampling and summarizing the information present in the nodes. Existing pooling methods either fail to effectively capture the graph substructure or do not easily scale to large graphs. In this work, we propose ASAP (Adaptive Structure Aware Pooling), a sparse and differentiable pooling method that addresses the limitations of previous graph pooling architectures. ASAP utilizes a novel self-attention network along with a modified GNN formulation to capture the importance of each node in a given graph. It also learns a sparse soft cluster assignment for nodes at each layer to effectively pool the subgraphs to form the pooled graph. Through extensive experiments on multiple datasets and theoretical analysis, we motivate our choice of the components used in ASAP. Our experimental results show that combining existing GNN architectures with ASAP leads to state-of-the-art results on multiple graph classification benchmarks. ASAP has an average improvement of 4%, compared to current sparse hierarchical state-of-the-art method.

Overview of ASAP: Adaptive Structure Aware Pooling for Learning Hierarchical Graph Representations

The paper "ASAP: Adaptive Structure Aware Pooling for Learning Hierarchical Graph Representations" introduces a novel graph pooling method designed to address the limitations observed in existing Graph Neural Network (GNN) pooling architectures. The proposed method, named Adaptive Structure Aware Pooling (ASAP), aims to generate effective graph-level representations by hierarchically capturing local structural information in graphs, a task crucial for applications like graph classification.

Context and Motivation

Graph Neural Networks have become a prominent tool for tasks involving graph-structured data due to their ability to model the intricate dependencies and relationships between nodes through edge connections. However, traditional GNN architectures lack the mechanisms to model these dependencies hierarchically. This hierarchical modeling is essential to capture and leverage the rich substructure information inherently present in arbitrary graph shapes, especially when extending beyond flat node-level interpretations to graph-level tasks.

Existing graph pooling mechanisms have either been unable to capture local substructures due to their inherently flat nature or have faced scalability issues when applied to large graphs. DiffPool, for instance, uses dense soft assignment matrices, making it unscalable, while methods like TopK and SAGPool do not sufficiently capture graph structure due to their sparse node selection strategy without node aggregation.

Methodological Contributions

ASAP is introduced as a sparse and differentiable pooling method that successfully combines the structural advantages of hierarchical node aggregation with the efficiency of sparse pooling approaches. Key components of ASAP include:

• Master2Token (M2T) Attentional Framework: This self-attention mechanism improves upon previous Token2Token and Source2Token frameworks by using a master query to hierarchically aggregate node information within a fixed neighborhood. M2T dynamically determines node membership within clusters, thereby accurately forming clusters that reflect local graph neighborhoods.
• Local Extrema Convolution (LEConv): LEConv is proposed as a novel convolution method able to learn functions of local extremas, which helps in scoring clusters based on their global and local importances. This component enables ASAP to focus on nodes that are representative of distinct graph structures while maintaining efficiency in terms of sparse matrix operations.

Through rigorous theoretical analysis and experiments, the authors demonstrate that ASAP improves edge connectivity within pooled graphs, effectively addressing the sparseness and scalability challenges that have hindered previous methods.

Empirical Evaluation

Experimental results show that integrating ASAP with existing GNN architectures yields state-of-the-art performance across multiple graph classification benchmarks, demonstrating an average improvement of 4% over the leading sparse hierarchical methods. These empirical results validate the efficacy of ASAP in leveraging local structural information to enhance graph-level representations.

Implications and Future Directions

ASAP's approach to pooling emphasizes the need for methodologies that consider both sparse and dense information in graph networks, presenting a practical model that scales efficiently while maintaining the hierarchical integrity of graph data. The strong numerical outcomes of ASAP suggest significant potential for applications that require capturing complex graph substructures, such as biochemical molecule classification and social network analysis.

Future research directions may explore the integration of ASAP with other types of AI models to further enhance the flexibility and adaptability of graph pooling. Additionally, investigating the interplay between ASAP's hierarchical methods and emerging unsupervised learning paradigms could offer insights into novel applications and enhanced learning strategies for complex graph structures. The adaptability and efficiency of ASAP warrant continued exploration and enhancement of pooling methods for ever-evolving graph-based tasks in AI research.