Related papers: Simplifying the Theory on Over-Smoothing

The performance of graph neural nets (GNNs) is known to gradually decrease with increasing number of layers. This decay is partly attributed to oversmoothing, where repeated graph convolutions eventually make node embeddings…

Graph Neural Networks (GNNs) learn node representations through iterative network-based message-passing. While powerful, deep GNNs suffer from oversmoothing, where node features converge to a homogeneous, non-informative state. We re-frame…

Graph Neural Networks (GNNs) are models that leverage the graph structure to transmit information between nodes, typically through the message-passing operation. While widely successful, this approach is well known to suffer from the…

Studies continually find that message-passing graph convolutional networks suffer from the over-smoothing issue. Basically, the issue of over-smoothing refers to the phenomenon that the learned embeddings for all nodes can become very…

Over-smoothing and over-squashing have been extensively studied in the literature on Graph Neural Networks (GNNs) over the past years. We challenge this prevailing focus in GNN research, arguing that these phenomena are less critical for…

Data with geometric structure is ubiquitous in machine learning often arising from fundamental symmetries in a domain, such as permutation-invariance in graphs and translation-invariance in images. Group-convolutional architectures, which…

Oversmoothing in Graph Neural Networks (GNNs) refers to the phenomenon where increasing network depth leads to homogeneous node representations. While previous work has established that Graph Convolutional Networks (GCNs) exponentially lose…

Graph neural networks (GNNs) have emerged as powerful tools for processing relational data in applications. However, GNNs suffer from the problem of oversmoothing, the property that the features of all nodes exponentially converge to the…

Graph Convolutional Neural Network (GCN), a widely adopted method for analyzing relational data, enhances node discriminability through the aggregation of neighboring information. Usually, stacking multiple layers can improve the…

In this paper, we explore the approximation theory of functions defined on graphs. Our study builds upon the approximation results derived from the $K$-functional. We establish a theoretical framework to assess the lower bounds of…

The complicated syntax structure of natural language is hard to be explicitly modeled by sequence-based models. Graph is a natural structure to describe the complicated relation between tokens. The recent advance in Graph Neural Networks…

We analyze graph smoothing with \emph{mean aggregation}, where each node successively receives the average of the features of its neighbors. Indeed, it has quickly been observed that Graph Neural Networks (GNNs), which generally follow some…

Graph convolutional networks have been successfully applied in various graph-based tasks. In a typical graph convolutional layer, node features are updated by aggregating neighborhood information. Repeatedly applying graph convolutions can…

Graph neural networks (GNNs), which learn the representation of a node by aggregating its neighbors, have become an effective computational tool in downstream applications. Over-smoothing is one of the key issues which limit the performance…

Graph Neural Networks (GNNs) typically operate by message-passing, where the state of a node is updated based on the information received from its neighbours. Most message-passing models act as graph convolutions, where features are mixed…

In this paper, we study the factors that contribute to the effect of oversmoothing in deep Graph Neural Networks (GNNs). Specifically, our analysis is based on a new metric (Mean Average Squared Distance - $MASED$) to quantify the extent of…

Graph neural networks have shown significant success in the field of graph representation learning. Graph convolutions perform neighborhood aggregation and represent one of the most important graph operations. Nevertheless, one layer of…

Graph Convolutional Networks (GCNs) are powerful for processing graph-structured data and have achieved state-of-the-art performance in several tasks such as node classification, link prediction, and graph classification. However, it is…

Graph convolutional networks (GCNs) are a powerful deep learning approach for graph-structured data. Recently, GCNs and subsequent variants have shown superior performance in various application areas on real-world datasets. Despite their…

It has been discovered that Graph Convolutional Networks (GCNs) encounter a remarkable drop in performance when multiple layers are piled up. The main factor that accounts for why deep GCNs fail lies in over-smoothing, which isolates the…