Related papers: Optimization-Induced Graph Implicit Nonlinear Diff…

Recent advancements in graph unlearning models have enhanced model utility by preserving the node representation essentially invariant, while using gradient ascent on the forget set to achieve unlearning. However, this approach causes a…

Representing visual signals by coordinate-based deep fully-connected networks has been shown advantageous in fitting complex details and solving inverse problems than discrete grid-based representation. However, acquiring such a continuous…

Linearized Graph Neural Networks (GNNs) have attracted great attention in recent years for graph representation learning. Compared with nonlinear Graph Neural Network (GNN) models, linearized GNNs are much more time-efficient and can…

Graph neural networks (GNNs) are one of the most popular research topics for deep learning. GNN methods typically have been designed on top of the graph signal processing theory. In particular, diffusion equations have been widely used for…

Data selection methods, such as active learning and core-set selection, are useful tools for improving the data efficiency of deep learning models on large-scale datasets. However, recent deep learning models have moved forward from…

A comprehensive understanding of heat transport is essential for optimizing various mechanical and engineering applications, including 3D printing. Recent advances in machine learning, combined with physics-based models, have enabled a…

With the growing interest in foundation models for brain signals, graph-based pretraining has emerged as a promising paradigm for learning transferable representations from connectome data. However, existing contrastive and masked…

Graph neural networks (GNNs) work remarkably well in semi-supervised node regression, yet a rigorous theory explaining when and why they succeed remains lacking. To address this gap, we study an aggregate-and-readout model that encompasses…

Graph Neural Networks (GNNs) with numerical node features and graph structure as inputs have demonstrated superior performance on various supervised learning tasks with graph data. However the numerical node features utilized by GNNs are…

The dominant paradigm for learning on graph-structured data is message passing. Despite being a strong inductive bias, the local message passing mechanism suffers from pathological issues such as over-smoothing, over-squashing, and limited…

Out-of-distribution (OOD) generalization has gained increasing attentions for learning on graphs, as graph neural networks (GNNs) often exhibit performance degradation with distribution shifts. The challenge is that distribution shifts on…

Node features of graph neural networks (GNNs) tend to become more similar with the increase of the network depth. This effect is known as over-smoothing, which we axiomatically define as the exponential convergence of suitable similarity…

We consider the problem of learning a graph from a finite set of noisy graph signal observations, the goal of which is to find a smooth representation of the graph signal. Such a problem is motivated by the desire to infer relational…

Graph neural networks (GNNs) manifest pathologies including over-smoothing and limited discriminating power as a result of suboptimally expressive aggregating mechanisms. We herein present a unifying framework for stochastic aggregation…

Graph representation learning has recently been applied to a broad spectrum of problems ranging from computer graphics and chemistry to high energy physics and social media. The popularity of graph neural networks has sparked interest, both…

Implicit graph neural networks have gained popularity in recent years as they capture long-range dependencies while improving predictive performance in static graphs. Despite the tussle between performance degradation due to the…

Graph representation learning is gaining popularity in a wide range of applications, such as social networks analysis, computational biology, and recommender systems. However, different with positive results from many academic studies,…

Text-attributed graphs require models to effectively combine strong textual understanding with structurally informed reasoning. Existing approaches either rely on GNNs--limited by over-smoothing and hop-dependent diffusion--or employ…

We analyze graph smoothing with \emph{mean aggregation}, where each node successively receives the average of the features of its neighbors. Indeed, it has quickly been observed that Graph Neural Networks (GNNs), which generally follow some…

This work presents a new algorithm for training recurrent neural networks (although ideas are applicable to feedforward networks as well). The algorithm is derived from a theory in nonconvex optimization related to the diffusion equation.…