Related papers: Spectral-graph Based Classifications: Linear Regre…
Approximation-based spectral graph neural networks, which construct graph filters with function approximation, have shown substantial performance in graph learning tasks. Despite their great success, existing works primarily employ…
Graph neural networks (GNNs) have achieved impressive performance in graph domain adaptation. However, extensive source graphs could be unavailable in real-world scenarios due to privacy and storage concerns. To this end, we investigate an…
Existing large-dimensional theory for spectral algorithms resolves either the optimally tuned point or the interpolation limit, but leaves the under-regularized regime unexplored. We study the learning curve and benign overfitting of…
Spectral Graph Neural Networks (GNNs) with various graph filters have received extensive affirmation due to their promising performance in graph learning problems. However, it is known that GNNs do not always perform well. Although graph…
Unified understanding of neuro networks (NNs) gets the users into great trouble because they have been puzzled by what kind of rules should be obeyed to optimize the internal structure of NNs. Considering the potential capability of random…
Graph neural networks (GNNs) are commonly used in semi-supervised settings. Previous research has primarily focused on finding appropriate graph filters (e.g. aggregation methods) to perform well on both homophilic and heterophilic graphs.…
Graph representation learning has become a standard approach for analyzing networked data, with latent embeddings widely used for link prediction, community detection, and related tasks. Yet a basic design choice, the latent dimension, is…
Spectral graph convolutional networks are generalizations of standard convolutional networks for graph-structured data using the Laplacian operator. A common misconception is the instability of spectral filters, i.e. the impossibility to…
Label propagation is a powerful and flexible semi-supervised learning technique on graphs. Neural networks, on the other hand, have proven track records in many supervised learning tasks. In this work, we propose a training framework with a…
This paper investigates the convergence properties of spectral algorithms -- a class of regularization methods originating from inverse problems -- under covariate shift. In this setting, the marginal distributions of inputs differ between…
Spectral Graph Neural Networks (SGNNs) have achieved remarkable performance in tasks such as node classification due to their ability to learn flexible filters. Typically, these filters are learned under the supervision of downstream tasks,…
In our era of enormous neural networks, empirical progress has been driven by the philosophy that more is better. Recent deep learning practice has found repeatedly that larger model size, more data, and more computation (resulting in lower…
Shape matching is a fundamental task in computer graphics and vision, with deep functional maps becoming a prominent paradigm. However, existing methods primarily focus on learning informative feature representations by constraining…
Graph neural networks (GNNs) have shown remarkable performance on homophilic graph data while being far less impressive when handling non-homophilic graph data due to the inherent low-pass filtering property of GNNs. In general, since…
Graph neural networks have developed by leaps and bounds in recent years due to the restriction of traditional convolutional filters on non-Euclidean structured data. Spectral graph theory mainly studies fundamental graph properties using…
Graph Convolutional Neural Networks (GCNNs) are generalizations of CNNs to graph-structured data, in which convolution is guided by the graph topology. In many cases where graphs are unavailable, existing methods manually construct graphs…
Spectral clustering (SC) and graph-based semi-supervised learning (SSL) algorithms are sensitive to how graphs are constructed from data. In particular if the data has proximal and unbalanced clusters these algorithms can lead to poor…
Despite classical statistical theory predicting severe overfitting, modern massively overparameterized neural networks still generalize well. This unexpected property is attributed to the network's so-called implicit bias, which describes…
Predictions over graphs play a crucial role in various domains, including social networks and medicine. Graph Neural Networks (GNNs) have emerged as the dominant approach for learning on graph data. Although a graph-structure is provided as…
Graph construction is a crucial step in spectral clustering (SC) and graph-based semi-supervised learning (SSL). Spectral methods applied on standard graphs such as full-RBF, $\epsilon$-graphs and $k$-NN graphs can lead to poor performance…