Understanding Pooling in Graph Neural Networks

Abstract

Inspired by the conventional pooling layers in convolutional neural networks, many recent works in the field of graph machine learning have introduced pooling operators to reduce the size of graphs. The great variety in the literature stems from the many possible strategies for coarsening a graph, which may depend on different assumptions on the graph structure or the specific downstream task. In this paper we propose a formal characterization of graph pooling based on three main operations, called selection, reduction, and connection, with the goal of unifying the literature under a common framework. Following this formalization, we introduce a taxonomy of pooling operators and categorize more than thirty pooling methods proposed in recent literature. We propose criteria to evaluate the performance of a pooling operator and use them to investigate and contrast the behavior of different classes of the taxonomy on a variety of tasks.Preprint. Under review.

Pooling Strategies for Simplicial Convolutional Networks

“…Following the pooling paradigm introduced in [19] for GNNs, we propose to model the layer in (6) as the composition of three operations: a local aggregation step, a selection step, and a reduction step. The local aggregation step is responsible for providing summary signals Z ∈ R E×F of the input signals Z ∈ R E×F leveraging the connectivity induced by the complex X .…”

“…The goal of this work is to introduce pooling strategies for SCNs. Taking inspiration from the select-reduceconnect (SRC) paradigm [19], we introduce a general simplicial pooling layer that comprises three steps: i) a local aggregation step responsible for providing a meaningful summary of the input signals; ii) a selection step responsible for selecting a proper subset of simplices; finally, iii) a reduction step that downsamples the input complex and the aggregated signals of step i) based on the simplices selected in step ii). By tailoring steps ii) and iii), we introduce four different simplicial pooling layers that generalize the well-known graph pooling strategies.…”

DOTIN: Dropping Task-Irrelevant Nodes for GNNs

“…Proof To prove the theorem, we first prove the average pooling can reduce the distance, and in the second step, we prove the weighted by attentiveness pooling will construct a new node with larger attentiveness. By the definition, we have: (10) where the first term equals to l 2 (x g W 1 , avg(x i )W 2 ) and the second term equals to avg(l 2 (x i W 2 , avg(x j )W 2 )), which are thus both non-negative. For shallow GNNs, the node features are usually different, leading the second term R.H.S larger than 0.…”