相关论文: Graph Fourier Transform with Negative Edges for De…

The Perfect Graph Theorems are important results in graph theory describing the relationship between clique number $\omega(G) $ and chromatic number $\chi(G) $ of a graph $G$. A graph $G$ is called \emph{perfect} if $\chi(H)=\omega(H)$ for…

Graph neural networks (GNNs) have been widely used in representation learning on graphs and achieved state-of-the-art performance in tasks such as node classification and link prediction. However, most existing GNNs are designed to learn…

As opposed to natural languages, source code understanding is influenced by grammatical relationships between tokens regardless of their identifier name. Graph representations of source code such as Abstract Syntax Tree (AST) can capture…

In the past decade, several multi-resolution representation theories for graph signals have been proposed. Bipartite filter-banks stand out as the most natural extension of time domain filter-banks, in part because perfect reconstruction,…

We show theoretically and empirically that the linear Transformer, when applied to graph data, can implement algorithms that solve canonical problems such as electric flow and eigenvector decomposition. The Transformer has access to…

We propose an inexact method for the graph Fourier transform of a graph signal, as defined by the signal decomposition over the Jordan subspaces of the graph adjacency matrix. This method projects the signal over the generalized eigenspaces…

Signed Graph Neural Networks (SGNNs) are effective in learning expressive representations for signed graphs but typically require substantial task-specific labels, limiting their applicability in label-scarce industrial scenarios. In…

Transformers have revolutionized performance in Natural Language Processing and Vision, paving the way for their integration with Graph Neural Networks (GNNs). One key challenge in enhancing graph transformers is strengthening the…

Shift-invariant spaces (SISs) on the real line provide a natural framework for representing, analyzing and processing signals with inherent shift-invariant structure. In this paper, we extend this framework to the finite undirected graph…

The de novo generation of molecules with desirable properties is a critical challenge, where diffusion models are computationally intensive and autoregressive models struggle with error propagation. In this work, we introduce the Graph…

The $\mathcal{Q}$-graph of a graph $G$, denoted by $\mathcal{Q}(G)$, is the graph derived from $G$ by plugging a new vertex to each edge of $G$ and adding a new edge between two new vertices which lie on adjacent edges of $G$. In this…

Decoding visual neural representations from Electroencephalography (EEG) signals remains a formidable challenge due to their high-dimensional, noisy, and non-Euclidean nature. In this work, we propose a Spatial-Functional Awareness…

Graph heterophily poses a formidable challenge to the performance of Message-passing Graph Neural Networks (MP-GNNs). The familiar low-pass filters like Graph Convolutional Networks (GCNs) face performance degradation, which can be…

This work introduces the multidimensional Graph Fourier Transformation Neural Network (GFTNN) for long-term trajectory predictions on highways. Similar to Graph Neural Networks (GNNs), the GFTNN is a novel network architecture that operates…

Point signatures based on the Laplacian operators on graphs, point clouds, and manifolds have become popular tools in machine learning for graphs, clustering, and shape analysis. In this work, we propose a novel point signature, the power…

Existing sequence to sequence models for structured language tasks rely heavily on the dot product self attention mechanism, which incurs quadratic complexity in both computation and memory for input length N. We introduce the Graph Wavelet…

The short-time Fourier transform (STFT) is widely used to analyze the spectra of temporal signals that vary through time. Signals defined over graphs, due to their intrinsic complexity, exhibit large variations in their patterns. In this…

An integrated photonic circuit architecture to perform a modified-convolution operation based on the Discrete Fractional Fourier Transform (DFrFT) is introduced. This is accomplished by utilizing two nonuniformly-coupled waveguide lattices…

Graph Contrastive Learning (GCL) excels at managing noise and fluctuations in input data, making it popular in various fields (e.g., social networks, and knowledge graphs). Our study finds that the difference in high-frequency information…

Graph neural networks (GNNs) have emerged as a powerful tool for modeling graph-structured data. However, existing GNNs often struggle with heterophilic graphs, where connected nodes tend to have dissimilar features or labels. While…