Related papers: The G\^ateaux-Hopfield Neural Network method

Graph neural network (GNN) has gained increasing popularity in recent years owing to its capability and flexibility in modeling complex graph structure data. Among all graph learning methods, hypergraph learning is a technique for exploring…

In this article, a new deep learning architecture, named JDNN, has been proposed to approximate a numerical solution to Partial Differential Equations (PDEs). The JDNN is capable of solving high-dimensional equations. Here, Jacobi Deep…

A new class of non-monotone finite difference (FD) approximation methods for approximating solutions to non-degenerate stationary Hamilton-Jacobi problems with Dirichlet boundary conditions is proposed and analyzed. The new FD methods add a…

Physics-informed neural networks solve partial differential equations by training neural networks. Since this method approximates infinite-dimensional PDE solutions with finite collocation points, minimizing discretization errors by…

Graph Neural Networks (GNNs) have demonstrated impressive performance in learning representations from graph-structured data. However, their message-passing mechanism inherently relies on the assumption of label consistency among connected…

This paper investigates the convergence properties of the hypergradient descent method (HDM), a 25-year-old heuristic originally proposed for adaptive stepsize selection in stochastic first-order methods. We provide the first rigorous…

Graph neural networks (GNNs) have demonstrated excellent performance in semi-supervised node classification tasks. Despite this, two primary challenges persist: heterogeneity and heterophily. Each of these two challenges can significantly…

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…

The Hopfield model is a paradigmatic model of neural networks that has been analyzed for many decades in the statistical physics, neuroscience, and machine learning communities. Inspired by the manifold hypothesis in machine learning, we…

Domain decomposition methods (DDMs) are popular solvers for discretized systems of partial differential equations (PDEs), with one-level and multilevel variants. These solvers rely on several algorithmic and mathematical parameters,…

Topological solitons, which are stable, localized solutions of nonlinear differential equations, are crucial in various fields of physics and mathematics, including particle physics and cosmology. However, solving these solitons presents…

Our algorithm GNN: Graph Neural Network and Large Language Model for Data Discovery inherit the benefits of \cite{hoang2024plod} (PLOD: Predictive Learning Optimal Data Discovery), \cite{Hoang2024BODBO} (BOD: Blindly Optimal Data Discovery)…

Representation learning in dynamic graphs is a challenging problem because the topology of graph and node features vary at different time. This requires the model to be able to effectively capture both graph topology information and…

Time, cost, and energy efficiency are critical considerations in Deep-Learning (DL), particularly when processing long texts. Transformers, which represent the current state of the art, exhibit quadratic computational complexity relative to…

In this paper, the authors propose the utilization of Fibonacci Neural Networks (FNN) for solving arbitrary order differential equations. The FNN architecture comprises input, middle, and output layers, with various degrees of Fibonacci…

We propose a learning-augmented framework for accelerating max-flow computation and image segmentation by integrating Graph Neural Networks (GNNs) with the Ford-Fulkerson algorithm. Rather than predicting initial flows, our method learns…

Graph neural networks (GNNs) for link prediction can loosely be divided into two broad categories. First, \emph{node-wise} architectures pre-compute individual embeddings for each node that are later combined by a simple decoder to make…

Graph representation learning methods are highly effective in handling complex non-Euclidean data by capturing intricate relationships and features within graph structures. However, traditional methods face challenges when dealing with…

Heterogeneous Graph Neural Networks (HGNNs) have achieved promising results in various heterogeneous graph learning tasks, owing to their superiority in capturing the intricate relationships and diverse relational semantics inherent in…

Link prediction is a fundamental task in graph learning, inherently shaped by the topology of the graph. While traditional heuristics are grounded in graph topology, they encounter challenges in generalizing across diverse graphs. Recent…