Related papers: Efficient Curvature-aware Graph Network

Graph Neural Networks (GNNs) have emerged as a dominant paradigm for learning on graph-structured data, thanks to their ability to jointly exploit node features and relational information encoded in the graph topology. This joint modeling,…

Message passing graph neural networks (GNNs) are a popular learning architectures for graph-structured data. However, one problem GNNs experience is oversquashing, where a GNN has difficulty sending information between distant nodes.…

We propose a new graph kernel for graph classification and comparison using Ollivier Ricci curvature. The Ricci curvature of an edge in a graph describes the connectivity in the local neighborhood. An edge in a densely connected…

Graph Neural Networks are highly effective at learning from relational data, leveraging node and edge features while maintaining the symmetries inherent to graph structures. However, many real-world systems, such as social or biological…

This thesis is an exposition of Ollivier-Ricci Curvature of metric spaces as introduced by Yann Ollivier, which is based upon the 1-Wasserstein Distance and optimal transport theory. We present some of the major results and proofs that…

We perform the first adversarial robustness study into Graph Neural Networks (GNNs) that are provably more powerful than traditional Message Passing Neural Networks (MPNNs). In particular, we use adversarial robustness as a tool to uncover…

The characterization of complex networks with tools originating in geometry, for instance through the statistics of so-called Ricci curvatures, is a well established tool of network science. There exist various types of such Ricci…

Randomly Wired Neural Networks (RWNNs) serve as a valuable testbed for investigating the impact of network topology in deep learning by capturing how different connectivity patterns impact both learning efficiency and model performance. At…

Head pose estimation is a crucial challenge for many real-world applications, such as attention and human behavior analysis. This paper aims to estimate head pose from a single image by applying notions of network curvature. In the real…

The monitoring of large dynamic networks is a major chal- lenge for a wide range of application. The complexity stems from properties of the underlying graphs, in which slight local changes can lead to sizable variations of global prop-…

In this paper, we consider the problem of approximately aligning/matching two graphs. Given two graphs $G_{1}=(V_{1},E_{1})$ and $G_{2}=(V_{2},E_{2})$, the objective is to map nodes $u, v \in G_1$ to nodes $u',v'\in G_2$ such that when $u,…

The highly non-linear nature of deep neural networks causes them to be susceptible to adversarial examples and have unstable gradients which hinders interpretability. However, existing methods to solve these issues, such as adversarial…

The adversarial robustness of Graph Neural Networks (GNNs) has been questioned due to the false sense of security uncovered by strong adaptive attacks despite the existence of numerous defenses. In this work, we delve into the robustness…

Generative adversarial network (GAN) is widely used for generalized and robust learning on graph data. However, for non-Euclidean graph data, the existing GAN-based graph representation methods generate negative samples by random walk or…

We introduce ORC-ManL, a new algorithm to prune spurious edges from nearest neighbor graphs using a criterion based on Ollivier-Ricci curvature and estimated metric distortion. Our motivation comes from manifold learning: we show that when…

Graph Neural Networks (GNNs) have emerged as a powerful technique for learning on relational data. Owing to the relatively limited number of message passing steps they perform -- and hence a smaller receptive field -- there has been…

Recent advances in emergent geometry and discretized approaches to quantum gravity have relied upon the notion of a discrete measure of graph curvature. We focus on the two main measures that have been studied, the so-called Ollivier-Ricci…

The human brain forms functional networks on all spatial scales. Modern fMRI scanners allow to resolve functional brain data in high resolutions, allowing to study large-scale networks that relate to cognitive processes. The analysis of…

Community detection in complex networks is a fundamental problem, open to new approaches in various scientific settings. We introduce a novel community detection method, based on Ricci flow on graphs. Our technique iteratively updates edge…

Message passing is the dominant paradigm in Graph Neural Networks (GNNs). The efficiency of message passing, however, can be limited by the topology of the graph. This happens when information is lost during propagation due to being…