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Given i.i.d. observations uniformly distributed on a closed submanifold of the Euclidean space, we study higher-order generalizations of graph Laplacians, so-called Hodge Laplacians on graphs, as approximations of the Laplace-Beltrami…

Graphical models capture relations between entities in a wide range of applications including social networks, biology, and natural language processing, among others. Graph neural networks (GNN) are neural models that operate over graphs,…

We investigate the optimization of neural networks on symmetric data, and compare the strategy of constraining the architecture to be equivariant to that of using data augmentation. Our analysis reveals that that the relative geometry of…

Sequential recommender systems (SRS) are designed to predict users' future behaviors based on their historical interaction data. Recent research has increasingly utilized contrastive learning (CL) to leverage unsupervised signals to…

Contrastive learning has been widely applied to graph representation learning, where the view generators play a vital role in generating effective contrastive samples. Most of the existing contrastive learning methods employ pre-defined…

We study the spectral convergence of a symmetrized Graph Laplacian matrix induced by a Gaussian kernel evaluated on pairs of embedded data, sampled from a manifold with boundary, a sub-manifold of $\mathbb{R}^m$. Specifically, we deduce the…

The recent contrastive learning methods, due to their effectiveness in representation learning, have been widely applied to modeling graph data. Random perturbation is widely used to build contrastive views for graph data, which however,…

Graph Contrastive Learning (GCL) has emerged as a powerful tool for extracting consistent representations from graphs, independent of labeled information. However, existing methods predominantly focus on undirected graphs, disregarding the…

Underlying data structures, such as symmetries or invariances to transformations, are often exploited to improve the solution of learning tasks. However, embedding these properties in models or learning algorithms can be challenging and…

In the interdisciplinary field of network science, a complex-valued network, with edges assigned complex weights, provides a more nuanced representation of relationships by capturing both the magnitude and phase of interactions.…

Deriving meaningful representations from complex, high-dimensional data in unsupervised settings is crucial across diverse machine learning applications. This paper introduces a framework for multi-scale graph network embedding based on…

In this note, we study Laplacians on graphs for which connectivity within certain subgraphs tends to infinity. Our main focus are graphs sharing a common node set on which edge weights within certain clusters grow to infinity. As…

Advanced graph neural networks have shown great potentials in graph classification tasks recently. Different from node classification where node embeddings aggregated from local neighbors can be directly used to learn node labels, graph…

Learning generalizable self-supervised graph representations for downstream tasks is challenging. To this end, Contrastive Learning (CL) has emerged as a leading approach. The embeddings of CL are arranged on a hypersphere where similarity…

Node representation learning has demonstrated its efficacy for various applications on graphs, which leads to increasing attention towards the area. However, fairness is a largely under-explored territory within the field, which may lead to…

Among different existing graph self-supervised learning strategies, graph contrastive learning (GCL) has been one of the most prevalent approaches to this problem. Despite the remarkable performance those GCL methods have achieved, existing…

Recent contrastive methods show significant improvement in self-supervised learning in several domains. In particular, contrastive methods are most effective where data augmentation can be easily constructed e.g. in computer vision.…

Contrastive learning is a popular form of self-supervised learning that encourages augmentations (views) of the same input to have more similar representations compared to augmentations of different inputs. Recent attempts to theoretically…

Improving the accuracy and robustness of deep neural nets (DNNs) and adapting them to small training data are primary tasks in deep learning research. In this paper, we replace the output activation function of DNNs, typically the…

Recently, Graph Neural Networks (GNNs) achieve remarkable success in Recommendation. To reduce the influence of data sparsity, Graph Contrastive Learning (GCL) is adopted in GNN-based CF methods for enhancing performance. Most GCL methods…