Related papers: Information-Theoretic Limits of Node Localization …

Message passing graph neural networks are widely used for learning on graphs, yet their expressive power is limited by the one-dimensional Weisfeiler-Lehman test and can fail to distinguish structurally different nodes. We provide rigorous…

Learning node representations that incorporate information from graph structure benefits wide range of tasks on graph. The majority of existing graph neural networks (GNNs) have limited power in capturing position information for a given…

Learning embeddings from large-scale networks is an open challenge. Despite the overwhelming number of existing methods, is is unclear how to exploit network structure in a way that generalizes easily to unseen nodes, edges or graphs. In…

Graph Transformers, which incorporate self-attention and positional encoding, have recently emerged as a powerful architecture for various graph learning tasks. Despite their impressive performance, the complex non-convex interactions…

Several recent works use positional encodings to extend the receptive fields of graph neural network (GNN) layers equipped with attention mechanisms. These techniques, however, extend receptive fields to the complete graph, at substantial…

The graph identification problem consists of discovering the interactions among nodes in a network given their state/feature trajectories. This problem is challenging because the behavior of a node is coupled to all the other nodes by the…

We propose a novel positional encoding for learning graph on Transformer architecture. Existing approaches either linearize a graph to encode absolute position in the sequence of nodes, or encode relative position with another node using…

Molecular graph learning benefits from positional signals that capture both local neighborhoods and global topology. Two widely used families are spectral encodings derived from Laplacian or diffusion operators and anchor-based distance…

The guessing number of a directed graph (digraph), equivalent to the entropy of that digraph, was introduced as a direct criterion on the solvability of a network coding instance. This paper makes two contributions on the guessing number.…

Graph neural networks based on iterative one-hop message passing have been shown to struggle in harnessing the information from distant nodes effectively. Conversely, graph transformers allow each node to attend to all other nodes directly,…

Graph alignment, the problem of identifying corresponding nodes across multiple graphs, is fundamental to numerous applications. Most existing unsupervised methods embed node features into latent representations to enable cross-graph…

Graph matching can be formalized as a combinatorial optimization problem, where there are corresponding relationships between pairs of nodes that can be represented as edges. This problem becomes challenging when there are potential…

In this work, we theoretically demonstrate that current graph positional encodings (PEs) are not beneficial and could potentially hurt performance in tasks involving heterophilous graphs, where nodes that are close tend to have different…

The local inductive bias of message-passing graph neural networks (GNNs) hampers their ability to exploit key structural information (e.g., connectivity and cycles). Positional encoding (PE) and Persistent Homology (PH) have emerged as two…

We show that viewing graphs as sets of node features and incorporating structural and positional information into a transformer architecture is able to outperform representations learned with classical graph neural networks (GNNs). Our…

Graph Neural Networks (GNNs) have emerged as the de facto standard for modeling graph data, with attention mechanisms and transformers significantly enhancing their performance on graph-based tasks. Despite these advancements, the…

Positional encodings enable Transformers to incorporate sequential information, yet their theoretical understanding remains limited to two properties: distance attenuation and translation invariance. Because natural language lacks purely…

Temporal graph learning has applications in recommendation systems, traffic forecasting, and social network analysis. Although multiple architectures have been introduced, progress in positional encoding for temporal graphs remains limited.…

Accurate predictions rely on the expressiveness power of graph deep learning frameworks like graph neural networks and graph transformers, where a positional encoding mechanism has become much more indispensable in recent state-of-the-art…

Transformers are increasingly employed for graph data, demonstrating competitive performance in diverse tasks. To incorporate graph information into these models, it is essential to enhance node and edge features with positional encodings.…