# Function Space Pooling For Graph Convolutional Networks

## TL;DR

This paper introduces a novel graph pooling method that maps vertex representations to a function space, improving graph classification performance over existing pooling techniques.

## Contribution

The paper proposes a new pooling approach for graph neural networks that operates in a function space, offering better performance than traditional vector or sequence-based pooling methods.

## Key findings

- Outperforms most baseline pooling methods in graph classification
- Achieves best performance in some cases
- Demonstrates the effectiveness of function space pooling

## Abstract

Convolutional layers in graph neural networks are a fundamental type of layer which output a representation or embedding of each graph vertex. The representation typically encodes information about the vertex in question and its neighbourhood. If one wishes to perform a graph centric task, such as graph classification, this set of vertex representations must be integrated or pooled to form a graph representation. In this article we propose a novel pooling method which maps a set of vertex representations to a function space representation. This method is distinct from existing pooling methods which perform a mapping to either a vector or sequence space. Experimental graph classification results demonstrate that the proposed method generally outperforms most baseline pooling methods and in some cases achieves best performance.