Related papers: Learning Laplacian Positional Encodings for Hetero…
Relative Positional Encoding (RPE), which encodes the relative distance between any pair of tokens, is one of the most successful modifications to the original Transformer. As far as we know, theoretical understanding of the RPE-based…
Existing approaches to analyzing the asymptotics of graph Laplacians typically assume a well-behaved kernel function with smoothness assumptions. We remove the smoothness assumption and generalize the analysis of graph Laplacians to include…
Many recent works have studied the performance of Graph Neural Networks (GNNs) in the context of graph homophily - a label-dependent measure of connectivity. Traditional GNNs generate node embeddings by aggregating information from a node's…
We propose a new point of view in the study of Fourier analysis on graphs, taking advantage of localization in the Fourier domain. For a signal $f$ on vertices of a weighted graph $\mathcal{G}$ with Laplacian matrix $\mathcal{L}$, standard…
Node classification on graphs is an important research problem with many applications. Real-world graph data sets may not be balanced and accurate as assumed by most existing works. A challenging setting is positive-unlabeled (PU) node…
Graph neural networks have attracted wide attentions to enable representation learning of graph data in recent works. In complement to graph convolution operators, graph pooling is crucial for extracting hierarchical representation of graph…
Learning embeddings of entities and relations is an efficient and versatile method to perform machine learning on relational data such as knowledge graphs. In this work, we propose holographic embeddings (HolE) to learn compositional vector…
We consider the problem of learning a sparse graph under the Laplacian constrained Gaussian graphical models. This problem can be formulated as a penalized maximum likelihood estimation of the Laplacian constrained precision matrix. Like in…
Graph Attention Network (GAT) is one of the most popular Graph Neural Network (GNN) architecture, which employs the attention mechanism to learn edge weights and has demonstrated promising performance in various applications. However, since…
Although graph-based learning has attracted a lot of attention, graph representation learning is still a challenging task whose resolution may impact key application fields such as chemistry or biology. To this end, we introduce GRALE, a…
This paper studies the problem of distribution shifts on non-homophilous graphs Mosting existing graph neural network methods rely on the homophilous assumption that nodes from the same class are more likely to be linked. However, such…
A multi-layer perceptron (MLP) is a type of neural networks which has a long history of research and has been studied actively recently in computer vision and graphics fields. One of the well-known problems of an MLP is the capability of…
Solving partial differential equations (PDEs) serves as a cornerstone for modeling complex dynamical systems. Recent progresses have demonstrated grand benefits of data-driven neural-based models for predicting spatiotemporal dynamics…
Real-world graphs exhibit increasing heterophily, where nodes no longer tend to be connected to nodes with the same label, challenging the homophily assumption of classical graph neural networks (GNNs) and impeding their performance.…
The study of complex systems benefits from graph models and their analysis. In particular, the eigendecomposition of the graph Laplacian lets emerge properties of global organization from local interactions; e.g., the Fiedler vector has the…
This paper studies the problem of conducting self-supervised learning for node representation learning on graphs. Most existing self-supervised learning methods assume the graph is homophilous, where linked nodes often belong to the same…
Graph neural networks process information on graphs represented at a given resolution scale. We analyze the effect of using different coarse-grained graph resolutions, obtained through the Laplacian renormalization group theory, on node…
Convolutional layers within graph neural networks operate by aggregating information about local neighbourhood structures; one common way to encode such substructures is through random walks. The distribution of these random walks evolves…
Graph Neural Networks (GNNs) learn from graph-structured data by passing local messages between neighboring nodes along edges on certain topological layouts. Typically, these topological layouts in modern GNNs are deterministically computed…
We introduce probabilistic embeddings using Laplacian priors (PELP). The proposed model enables incorporating graph side-information into static word embeddings. We theoretically show that the model unifies several previously proposed…