Partially Trained Graph Convolutional Networks Resist Oversmoothing

TL;DR

This paper explores how partially trained Graph Convolutional Networks (GCNs) can generate meaningful embeddings and resist oversmoothing, especially useful in scenarios with limited feature information.

Contribution

It introduces a theoretical framework for understanding untrained GCN layers, links partial training to oversmoothing reduction, and demonstrates benefits in low-feature scenarios.

Findings

Partially trained GCNs produce meaningful embeddings.

Untrained layers' effects can be predicted theoretically.

Deep networks with partial training resist oversmoothing.

Abstract

In this work we investigate an observation made by Kipf \& Welling, who suggested that untrained GCNs can generate meaningful node embeddings. In particular, we investigate the effect of training only a single layer of a GCN, while keeping the rest of the layers frozen. We propose a basis on which the effect of the untrained layers and their contribution to the generation of embeddings can be predicted. Moreover, we show that network width influences the dissimilarity of node embeddings produced after the initial node features pass through the untrained part of the model. Additionally, we establish a connection between partially trained GCNs and oversmoothing, showing that they are capable of reducing it. We verify our theoretical results experimentally and show the benefits of using deep networks that resist oversmoothing, in a ``cold start'' scenario, where there is a lack of feature information for unlabeled nodes.