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MaxCutPool: differentiable feature-aware Maxcut for pooling in graph neural networks

Carlo Abate, Filippo Maria Bianchi

TL;DR

The paper tackles the challenge of graph pooling in neural networks for heterophilic and attributed graphs by formulating a differentiable MAXCUT-based partitioning method called MaxCutPool. It integrates a ScoreNet to produce high-frequency node scores, selects a subset of supernodes via top-$K$ scoring, and uses a nearest-neighbor assignment to form a sparse, trainable pooled graph; an auxiliary loss $\mathcal{L}_{\text{cut}}$ guides the partition toward cutting more edges. The approach bridges scoring-based and dense pooling by employing consistent CON/RED operations and offers an expressive variant (-E) that propagates features through all nodes via an assignment matrix. Empirically, MaxCutPool achieves competitive or superior performance on graph and node classification tasks, especially in heterophilic settings, and demonstrates favorable time/memory complexity compared to soft-clustering pooling methods. The work also provides a synthetic heterophilic graph dataset to benchmark pooling methods and discusses potential benefits of pretraining auxiliary losses for more general graph pooling strategies.

Abstract

We propose a novel approach to compute the MAXCUT in attributed graphs, i.e., graphs with features associated with nodes and edges. Our approach works well on any kind of graph topology and can find solutions that jointly optimize the MAXCUT along with other objectives. Based on the obtained MAXCUT partition, we implement a hierarchical graph pooling layer for Graph Neural Networks, which is sparse, trainable end-to-end, and particularly suitable for downstream tasks on heterophilic graphs.

MaxCutPool: differentiable feature-aware Maxcut for pooling in graph neural networks

TL;DR

The paper tackles the challenge of graph pooling in neural networks for heterophilic and attributed graphs by formulating a differentiable MAXCUT-based partitioning method called MaxCutPool. It integrates a ScoreNet to produce high-frequency node scores, selects a subset of supernodes via top- scoring, and uses a nearest-neighbor assignment to form a sparse, trainable pooled graph; an auxiliary loss guides the partition toward cutting more edges. The approach bridges scoring-based and dense pooling by employing consistent CON/RED operations and offers an expressive variant (-E) that propagates features through all nodes via an assignment matrix. Empirically, MaxCutPool achieves competitive or superior performance on graph and node classification tasks, especially in heterophilic settings, and demonstrates favorable time/memory complexity compared to soft-clustering pooling methods. The work also provides a synthetic heterophilic graph dataset to benchmark pooling methods and discusses potential benefits of pretraining auxiliary losses for more general graph pooling strategies.

Abstract

We propose a novel approach to compute the MAXCUT in attributed graphs, i.e., graphs with features associated with nodes and edges. Our approach works well on any kind of graph topology and can find solutions that jointly optimize the MAXCUT along with other objectives. Based on the obtained MAXCUT partition, we implement a hierarchical graph pooling layer for Graph Neural Networks, which is sparse, trainable end-to-end, and particularly suitable for downstream tasks on heterophilic graphs.
Paper Structure (44 sections, 16 equations, 11 figures, 15 tables, 2 algorithms)

This paper contains 44 sections, 16 equations, 11 figures, 15 tables, 2 algorithms.

Table of Contents

  1. Introduction
  2. Contributions
  3. MAXCUT for attributed graphs.
  4. Graph pooling and coarsening.
  5. Improved scoring-based pooling framework.
  6. Heterophilic graph classification dataset.
  7. Background
  8. The MAXCUT problem and the continuous relaxations
  9. Message passing in GNNs
  10. Graph pooling
  11. Method
  12. Auxiliary loss
  13. Homophilic and heterophilic operations
  14. Relation with other pooling methods
  15. Experimental evaluation
  16. ...and 29 more sections

Figures (11)

  • Figure 1: Top row: Partitions induced by the sign of the elements in ${\bm{u}}_{\max}$. The nodes are colored based on the partition and the red edges are those not cut (the less, the better). Middle row: histograms of ${\bm{u}}_{\max}$ inducing the partitions above. While in bipartite graphs the separation is sharp, the more a graph is irregular and dense the more the values are clustered around zero, making it difficult to find the optimal MAXCUT. Bottom row: histograms of the score vectors generated by our model, which always produce a clear and sharp partition.
  • Figure 2: (a) The nodes with the $K=9$ highest scores are selected. (b-c) Their ID is propagated to the unselected nodes until all are covered or until a maximum number of iterations ($2$ here) is reached. (d) The $4$ remaining nodes are assigned randomly. (e) The pooled graph is obtained by aggregating the nodes with the same ID and coalescing the edges connecting nodes from different groups.
  • Figure 3: Scheme of the layer.
  • Figure 4: Scheme of the ScoreNet.
  • Figure 5: Scheme of the model used for computing the MAXCUT.
  • ...and 6 more figures