Related papers: Improving Expressive Power of Spectral Graph Neura…
We precisely characterize the expressivity of computable Recurrent Graph Neural Networks (recurrent GNNs). We prove that recurrent GNNs with finite-precision parameters, sum aggregation, and ReLU activation, can compute any graph algorithm…
Geometric variations like rotation, scaling, and viewpoint changes pose a significant challenge to visual understanding. One common solution is to directly model certain intrinsic structures, e.g., using landmarks. However, it then becomes…
Graph neural networks (GNNs) hold the promise of learning efficient representations of graph-structured data, and one of its most important applications is semi-supervised node classification. However, in this application, GNN frameworks…
Spectral Graph Neural Networks (GNNs) are gaining attention for their ability to surpass the limitations of message-passing GNNs. They rely on supervision from downstream tasks to learn spectral filters that capture the graph signal's…
Message-Passing Graph Neural Networks (GNNs) are known to have limited expressive power, due to their message passing structure. One mechanism for circumventing this limitation is to add unique node identifiers (IDs), which break the…
Collaborative Filtering (CF) is a pivotal research area in recommender systems that capitalizes on collaborative similarities between users and items to provide personalized recommendations. With the remarkable achievements of node…
The use of graph convolution in the development of recommender system algorithms has recently achieved state-of-the-art results in the collaborative filtering task (CF). While it has been demonstrated that the graph convolution operation is…
It has been recently shown that general policies for many classical planning domains can be expressed and learned in terms of a pool of features defined from the domain predicates using a description logic grammar. At the same time, most…
Despite recent advances in representation learning in hypercomplex (HC) space, this subject is still vastly unexplored in the context of graphs. Motivated by the complex and quaternion algebras, which have been found in several contexts to…
Graph Neural Networks (GNNs) exhibit excellent performance when graphs have strong homophily property, i.e. connected nodes have the same labels. However, they perform poorly on heterophilic graphs. Several approaches address the issue of…
The core operation of current Graph Neural Networks (GNNs) is the aggregation enabled by the graph Laplacian or message passing, which filters the neighborhood information of nodes. Though effective for various tasks, in this paper, we show…
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,…
The spectrum of the normalized graph Laplacian yields a very comprehensive set of invariants of a graph. In order to understand the information contained in those invariants better, we systematically investigate the behavior of this…
Heterogeneous Graph Neural Networks (HGNNs) have gained significant popularity in various heterogeneous graph learning tasks. However, most existing HGNNs rely on spatial domain-based methods to aggregate information, i.e., manually…
Learning a graph with a specific structure is essential for interpretability and identification of the relationships among data. It is well known that structured graph learning from observed samples is an NP-hard combinatorial problem. In…
Polynomial filters, a kind of Graph Neural Networks, typically use a predetermined polynomial basis and learn the coefficients from the training data. It has been observed that the effectiveness of the model is highly dependent on the…
We study deep neural networks with polynomial activations, particularly their expressive power. For a fixed architecture and activation degree, a polynomial neural network defines an algebraic map from weights to polynomials. The image of…
Deep neural networks can be trained in reciprocal space, by acting on the eigenvalues and eigenvectors of suitable transfer operators in direct space. Adjusting the eigenvalues, while freezing the eigenvectors, yields a substantial…
Self-supervised learning has shown its promising capability in graph representation learning in recent work. Most existing pre-training strategies usually choose the popular Graph neural networks (GNNs), which can be seen as a special form…
Designing spectral convolutional networks is a formidable task in graph learning. In traditional spectral graph neural networks (GNNs), polynomial-based methods are commonly used to design filters via the Laplacian matrix. In practical…