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Hierarchical Graph Representation Learning via Differentiable Pooling

Stanford University TU Dortmund University University of Southern California

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Rex Ying, Jiaxuan You, Christopher Morris, William L. Hamilton, Xiang Ren, Jure Leskovec

Motivation: ML for Graphs

▪ Graph classification tasks:

▪ Molecule prediction

▪ Classify molecule properties (toxicity, drug-likeness etc.)

▪ Social networks

▪ Predict social group properties

▪ Biological applications

▪ Model disease pathways in PPI networks

▪ Physical systems

▪ Evolving dynamical systems

2 Hierarchical Graph Representation Learning via Differentiable Pooling

Graph Pooling

3 Hierarchical Graph Representation Learning via Differentiable Pooling

Graph Neural Networks (GNNs) have revolutionized machine learning with graphs But GNNs learn individual node representations and then simply globally aggregate them:

▪ Mean/max/sum of all node embeddings (e.g. structure2vec) ▪ Pool by sorting (e.g. DGCNN, PatchySan)

Problem:

• blem: How to aggregate information in a

hierarchical way to capture the entire graph

Pooling for GNNs

4 Hierarchical Graph Representation Learning via Differentiable Pooling

Pr Prob

• blem

lem: Learn a hierarchical pooling strategy that respects graph structure Our sol

• luti

tion

• n:

: DIFFPOOL

▪ Learns hierarchical pooling analogous to CNNs ▪ Sets of nodes are pooled hierarchically ▪ Soft assignment of nodes to next-level nodes

DIFFPOOL Architecture

Our approach

• ach: Use two sets of GNNs

▪ GNN1 to learn how to pool the network

▪ Learn cluster assignment matrix

▪ GNN2 to learn the node embeddings

Jure Leskovec, Stanford 5

A different GNN is learned at every level of abstraction

DIFFPOOL Architecture

6 Hierarchical Graph Representation Learning via Differentiable Pooling

Assuming ing general ral GNN model:

Concret etel ely:

Two-tower er arc rchit hitect ecture Embedding Assignment Aggreg egate e embed edding ding vi via ass assignme nment nt to to genera rate next-le level el representa esentati tions

• ns and adj

djacen cency cy

Experimental Results

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An average of 6.27% improvement in accuracy for graph classification tasks

• n biological and social networks

Hierarchical Graph Representation Learning via Differentiable Pooling

Experimental Results

DIFFPOOL learns reasonable pooling architectures

Jure Leskovec, Stanford 8

Thank you!

Poster: AB #14

Code: https://github.com/RexYing/diffpool

Jure Leskovec, Stanford 9