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Data augmentation is critical to the empirical success of modern self-supervised representation learning, such as contrastive learning and masked language modeling. However, a theoretical understanding of the exact role of augmentation…

Generalizable, transferrable, and robust representation learning on graph-structured data remains a challenge for current graph neural networks (GNNs). Unlike what has been developed for convolutional neural networks (CNNs) for image data,…

Graph representation learning is fundamental for analyzing graph-structured data. Exploring invariant graph representations remains a challenge for most existing graph representation learning methods. In this paper, we propose a cross-view…

For data sampled from an arbitrary density on a manifold embedded in Euclidean space, the Continuous k-Nearest Neighbors (CkNN) graph construction is introduced. It is shown that CkNN is geometrically consistent in the sense that under…

Spectral methods that are based on eigenvectors and eigenvalues of discrete graph Laplacians, such as Diffusion Maps and Laplacian Eigenmaps are often used for manifold learning and non-linear dimensionality reduction. It was previously…

Contrastive learning has become a key component of self-supervised learning approaches for graph-structured data. Despite their success, existing graph contrastive learning methods are incapable of uncertainty quantification for node…

Graph contrastive learning (GCL) is an effective paradigm for node representation learning in graphs. The key components hidden behind GCL are data augmentation and positive-negative pair selection. Typical data augmentations in GCL, such…

Contrastive graph node clustering via learnable data augmentation is a hot research spot in the field of unsupervised graph learning. The existing methods learn the sampling distribution of a pre-defined augmentation to generate data-driven…

Contrastive learning (CL), which can extract the information shared between different contrastive views, has become a popular paradigm for vision representation learning. Inspired by the success in computer vision, recent work introduces CL…

Graph contrastive learning (GCL) improves graph representation learning, leading to SOTA on various downstream tasks. The graph augmentation step is a vital but scarcely studied step of GCL. In this paper, we show that the node embedding…

Recent analyses of self-supervised learning (SSL) find the following data-centric properties to be critical for learning good representations: invariance to task-irrelevant semantics, separability of classes in some latent space, and…

Benefiting from the effectiveness of graph neural networks (GNNs) and contrastive learning, GNN-based contrastive learning has become mainstream for knowledge-aware recommendation. However, most existing contrastive learning-based methods…

Graph Neural Networks have become the preferred tool to process graph data, with their efficacy being boosted through graph data augmentation techniques. Despite the evolution of augmentation methods, issues like graph property distortions…

The recent surge in contrast-based graph self-supervised learning has prominently featured an intensified exploration of spectral cues. Spectral augmentation, which involves modifying a graph's spectral properties such as eigenvalues or…

Graph contrastive learning has become a powerful technique for several graph mining tasks. It learns discriminative representation from different perspectives of augmented graphs. Ubiquitous in our daily life, singed-directed graphs are the…

High-dimensional data arises in numerous applications, and the rapidly developing field of geometric deep learning seeks to develop neural network architectures to analyze such data in non-Euclidean domains, such as graphs and manifolds.…

Recent self-supervised contrastive methods have been able to produce impressive transferable visual representations by learning to be invariant to different data augmentations. However, these methods implicitly assume a particular set of…

I prove that the spectrum of the Laplace-Beltrami operator with the Neumann boundary condition on a compact Riemannian manifold with boundary admits a fast approximation by the spectra of suitable graph Laplacians on proximity graphs on the…

What role do augmentations play in contrastive learning? Recent work suggests that good augmentations are label-preserving with respect to a specific downstream task. We complicate this picture by showing that label-destroying augmentations…

Bi-stochastic normalization provides an alternative normalization of graph Laplacians in graph-based data analysis and can be computed efficiently by Sinkhorn-Knopp (SK) iterations. This paper proves the convergence of bi-stochastically…