Related papers: Generalization Performance of Hypergraph Neural Ne…
Graph neural networks are widely used tools for graph prediction tasks. Motivated by their empirical performance, prior works have developed generalization bounds for graph neural networks, which scale with graph structures in terms of the…
Graph neural networks (GNNs) are the most widely adopted model in graph-structured data oriented learning and representation. Despite their extraordinary success in real-world applications, understanding their working mechanism by theory is…
In this paper, we derive generalization bounds for the two primary classes of graph neural networks (GNNs), namely graph convolutional networks (GCNs) and message passing GNNs (MPGNNs), via a PAC-Bayesian approach. Our result reveals that…
Graph neural networks have demonstrated excellent applicability to a wide range of domains, including social networks, biological systems, recommendation systems, and wireless communications. Yet a principled theoretical understanding of…
This extended abstract describes a framework for analyzing the expressiveness, learning, and (structural) generalization of hypergraph neural networks (HyperGNNs). Specifically, we focus on how HyperGNNs can learn from finite datasets and…
There has been considerable effort to better understand the generalization capabilities of deep neural networks both as a means to unlock a theoretical understanding of their success as well as providing directions for further improvements.…
Convolutional neural networks (CNNs) have achieved breakthrough performances in a wide range of applications including image classification, semantic segmentation, and object detection. Previous research on characterizing the generalization…
Despite enormous successful applications of graph neural networks (GNNs), theoretical understanding of their generalization ability, especially for node-level tasks where data are not independent and identically-distributed (IID), has been…
Deep Neural Networks can generalize despite being significantly overparametrized. Recent research has tried to examine this phenomenon from various view points and to provide bounds on the generalization error or measures predictive of the…
Understanding the generalization behavior of deep neural networks remains a fundamental challenge in modern statistical learning theory. Among existing approaches, PAC-Bayesian norm-based bounds have demonstrated particular promise due to…
Graph Neural Networks (GNNs) are powerful tools for learning on structured data, yet the relationship between their expressivity and predictive performance remains unclear. We introduce a family of premetrics that capture different degrees…
Both PAC-Bayesian and Sample Compress learning frameworks are instrumental for deriving tight (non-vacuous) generalization bounds for neural networks. We leverage these results in a meta-learning scheme, relying on a hypernetwork that…
Understanding the generalization of deep neural networks is one of the most important tasks in deep learning. Although much progress has been made, theoretical error bounds still often behave disparately from empirical observations. In this…
The growing interest in hypergraph neural networks (HGNNs) is driven by their capacity to capture the complex relationships and patterns within hypergraph structured data across various domains, including computer vision, complex networks,…
Hyperbolic neural networks (HNNs) have demonstrated notable efficacy in representing real-world data with hierarchical structures via exploiting the geometric properties of hyperbolic spaces characterized by negative curvatures. Curvature…
Generalization of deep neural networks remains one of the main open problems in machine learning. Previous theoretical works focused on deriving tight bounds of model complexity, while empirical works revealed that neural networks exhibit…
Graph Neural Networks (GNNs) extend convolutional neural networks to operate on graphs. Despite their impressive performances in various graph learning tasks, the theoretical understanding of their generalization capability is still…
We study the generalization capabilities of Message Passing Neural Networks (MPNNs), a prevalent class of Graph Neural Networks (GNN). We derive generalization bounds specifically for MPNNs with normalized sum aggregation and mean…
Recent research has used margin theory to analyze the generalization performance for deep neural networks (DNNs). The existed results are almost based on the spectrally-normalized minimum margin. However, optimizing the minimum margin…
Many real world data analysis problems exhibit invariant structure, and models that take advantage of this structure have shown impressive empirical performance, particularly in deep learning. While the literature contains a variety of…