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Graph Neural Networks (GNNs) have become the standard method for learning from networks across fields ranging from biology to social systems, yet a principled understanding of what enables them to extract meaningful representations, or why…

This paper reviews concepts, modeling approaches, and recent findings along a spectrum of different levels of abstraction of neural network models including generalization across (1) Samples, (2) Distributions, (3) Domains, (4) Tasks, (5)…

In complex systems, information propagation can be defined as diffused or delocalized, weakly localized, and strongly localized. This study investigates the application of graph neural network models to learn the behavior of a linear…

Machine learning on graphs, especially using graph neural networks (GNNs), has seen a surge in interest due to the wide availability of graph data across a broad spectrum of disciplines, from life to social and engineering sciences. Despite…

Effective Field Theories (EFTs) provide a framework for capturing the effects of yet unseen heavy degrees of freedom in a model-independent manner. However, constructing a complete and minimal set of operators, especially at higher mass…

In this work, we provide a theoretical understanding of the framelet-based graph neural networks through the perspective of energy gradient flow. By viewing the framelet-based models as discretized gradient flows of some energy, we show it…

Generative Flow Networks (GFlowNets, GFNs) are a generative framework for learning unnormalized probability mass functions over discrete spaces. Since their inception, GFlowNets have proven to be useful for learning generative models in…

Gene finding is the task of identifying the locations of coding sequences within the vast amount of genetic code contained in the genome. With an ever increasing quantity of raw genome sequences, gene finding is an important avenue towards…

Despite the celebrated popularity of Graph Neural Networks (GNNs) across numerous applications, the ability of GNNs to generalize remains less explored. In this work, we propose to study the generalization of GNNs through a novel…

Understanding the learning dynamics of neural networks is a central topic in the deep learning community. In this paper, we take an empirical perspective to study the learning dynamics of neural networks in real-world settings.…

Generalization in generative modeling is defined as the ability to learn an underlying distribution from a finite dataset and produce novel samples, with evaluation largely driven by held-out performance and perceived sample quality. In…

We propose an end-to-end framework based on a Graph Neural Network (GNN) to balance the power flows in energy grids. The balancing is framed as a supervised vertex regression task, where the GNN is trained to predict the current and power…

Graph Neural Networks (GNNs) are proposed without considering the agnostic distribution shifts between training and testing graphs, inducing the degeneration of the generalization ability of GNNs on Out-Of-Distribution (OOD) settings. The…

Generalized linear models (GLMs) arise in high-dimensional machine learning, statistics, communications and signal processing. In this paper we analyze GLMs when the data matrix is random, as relevant in problems such as compressed sensing,…

Proposing an effective and flexible matrix to represent a graph is a fundamental challenge that has been explored from multiple perspectives, e.g., filtering in Graph Fourier Transforms. In this work, we develop a novel and general…

Characterizing precisely the asymptotic generalization error of neural networks using parameters that can be estimated efficiently is a crucial problem in machine learning, which relies heavily on heuristics and practitioners' intuition to…

Graph neural networks (GNNs), as the de-facto model class for representation learning on graphs, are built upon the multi-layer perceptrons (MLP) architecture with additional message passing layers to allow features to flow across nodes.…

While Graph Neural Networks (GNNs) have achieved remarkable success, their design largely relies on empirical intuition rather than theoretical understanding. In this paper, we present a comprehensive analysis of GNN behavior through three…

Foundation models are pretrained on large-scale corpora to learn generalizable patterns across domains and tasks -- such as contours, textures, and edges in images, or tokens and sentences in text. In contrast, discovering such generalities…

Recent advancements in graph learning have revolutionized the way to understand and analyze data with complex structures. Notably, Graph Neural Networks (GNNs), i.e. neural network architectures designed for learning graph representations,…