相关论文: Learning Latent Graph Geometry via Fixed-Point Sch…

We consider a generalized nonlinear Schr\"odinger equation (NLS) with a power nonlinearity |\psi|^2\mu\psi, of focusing type, describing propagation on the ramified structure given by N edges connected at a vertex (a star graph). To model…

Graph neural networks (GNNs) are important tools for transductive learning tasks, such as node classification in graphs, due to their expressive power in capturing complex interdependency between nodes. To enable graph neural network…

Social learning algorithms provide models for the formation of opinions over social networks resulting from local reasoning and peer-to-peer exchanges. Interactions occur over an underlying graph topology, which describes the flow of…

Classical planners can effectively solve very large deterministic MDPs represented in STRIPS or PDDL where states are sets of atoms over objects and relations, and lifted action schemas add or delete these atoms. This compact representation…

The scattering transform is a multilayered wavelet-based deep learning architecture that acts as a model of convolutional neural networks. Recently, several works have introduced generalizations of the scattering transform for non-Euclidean…

We introduce and implement a method to compute stationary states of nonlinear Schr\''odinger equations on metric graphs. Stationary states are obtained as local minimizers of the nonlinear Schr\''odinger energy at fixed mass. Our method is…

In this work we address graph based semi-supervised learning using the theory of the spatial segregation of competitive systems. First, we define a discrete counterpart over connected graphs by using direct analogue of the corresponding…

In this contribution, we demonstrate that Graph Neural Networks and Transformers can learn to reason about geometric constraints. We train them to predict spatial position of points in a discrete 2D grid from a set of constraints that…

Inferring the graph structure from observed data is a key task in graph machine learning to capture the intrinsic relationship between data entities. While significant advancements have been made in learning the structure of homogeneous…

We consider reflectionless wave propagation in networks modeled in terms of the nonlocal nonlinear Schr\"odinger (NNLS) equation on metric graphs, for which transparent boundary conditions are imposed at the vertices. By employing the…

Self-supervised learning of graph neural networks (GNNs) aims to learn an accurate representation of the graphs in an unsupervised manner, to obtain transferable representations of them for diverse downstream tasks. Predictive learning and…

This paper introduces Polynomial Graphical Lasso (PGL), a new approach to learning graph structures from nodal signals. Our key contribution lies in modeling the signals as Gaussian and stationary on the graph, enabling the development of a…

Traditional Graph Self-Supervised Learning (GSSL) struggles to capture complex structural properties well. This limitation stems from two main factors: (1) the inadequacy of conventional Graph Neural Networks (GNNs) in representing…

We introduce the weighted graph Laplacian and the notion of Schr\"odinger operator on a locally finite weighted graph . Concerning essential self-adjointness, we extend Wojciechowski's and Dodziuk's results for graphs with vertex constant…

In this paper, we propose an end-to-end graph learning framework, namely Deep Iterative and Adaptive Learning for Graph Neural Networks (DIAL-GNN), for jointly learning the graph structure and graph embeddings simultaneously. We first cast…

Our proposed framework attempts to break the trade-off between performance and explainability by introducing an explainable-by-design convolutional neural network (CNN) based on the lateral inhibition mechanism. The ExplaiNet model consists…

Multigrid modeling algorithms are a technique used to accelerate relaxation models running on a hierarchy of similar graphlike structures. We introduce and demonstrate a new method for training neural networks which uses multilevel methods.…

Graph Neural Networks leverage the connectivity structure of graphs as an inductive bias. Latent graph inference focuses on learning an adequate graph structure to diffuse information on and improve the downstream performance of the model.…

Graph matching can be formalized as a combinatorial optimization problem, where there are corresponding relationships between pairs of nodes that can be represented as edges. This problem becomes challenging when there are potential…

Graph neural networks use relational information as an inductive bias to enhance prediction performance. Not rarely, task-relevant relations are unknown and graph structure learning approaches have been proposed to learn them from data.…