Related papers: Riemannian Patch Assignment Gradient Flows

A proper labeling of a graph is an assignment of integers to some elements of a graph, which may be the vertices, the edges, or both of them, such that we obtain a proper vertex coloring via the labeling subject to some conditions. The…

A latent space model for a family of random graphs assigns real-valued vectors to nodes of the graph such that edge probabilities are determined by latent positions. Latent space models provide a natural statistical framework for graph…

In this paper we propose a new augmentation technique, called patch augmentation, that, in our experiments, improves model accuracy and makes networks more robust to adversarial attacks. In brief, this data-independent approach creates new…

A graph neural network transforms features in each vertex's neighborhood into a vector representation of the vertex. Afterward, each vertex's representation is used independently for predicting its label. This standard pipeline implicitly…

Balanced graph partitioning is a critical step for many large-scale distributed computations with relational data. As graph datasets have grown in size and density, a range of highly-scalable balanced partitioning algorithms have appeared…

Multi-label image classification is a prediction task that aims to identify more than one label from a given image. This paper considers the semantic consistency of the latent space between the visual patch and linguistic label domains and…

We propose an algorithm for deep learning on networks and graphs. It relies on the notion that many graph algorithms, such as PageRank, Weisfeiler-Lehman, or Message Passing can be expressed as iterative vertex updates. Unlike previous…

We propose the joint graph attention neural network (GAT), clustering with adaptive neighbors (CAN) and probabilistic graphical model for dynamic power flow analysis and fault characteristics. In fact, computational efficiency is the main…

Recurrent neural networks are powerful models for sequential data, able to represent complex dependencies in the sequence that simpler models such as hidden Markov models cannot handle. Yet they are notoriously hard to train. Here we…

Let $(M,g)$ be a closed Riemannian manifold, and let $F:M \to \mathbb{R}$ be a smooth function on $M$. We show the following holds generically for the function $F$: for each maximum $p$ of $F$, there exist two minima, denoted by $m_+(p)$…

This paper presents AutoMarks, an automated and transferable watermarking framework that leverages graph neural networks to reduce the watermark search overheads during the placement stage. AutoMarks's novel automated watermark search is…

This paper addresses the problems of spline interpolation on smooth Riemannian manifolds, with or without the inclusion of least-squares fitting. Our unified approach utilizes gradient flows for successively connected curves or networks,…

Graph-based semi-supervised learning usually involves two separate stages, constructing an affinity graph and then propagating labels for transductive inference on the graph. It is suboptimal to solve them independently, as the correlation…

We propose an infinity Laplacian method to address the problem of interpolation on an unstructured point cloud. In doing so, we find the labeling function with the smallest infinity norm of its gradient. By introducing the non-local…

Node classification using Graph Neural Networks (GNNs) has been widely applied in various real-world scenarios. However, in recent years, compelling evidence emerges that the performance of GNN-based node classification may deteriorate…

A central issue of the science of complex systems is the quantitative characterization of complexity. In the present work we address this issue by resorting to information geometry. Actually we propose a constructive way to associate to a -…

We provide an explicit solution of the problem of level-set percolation for multivariate Gaussians defined in terms of weighted graph Laplacians on complex networks. The solution requires an analysis of the heterogeneous micro-structure of…

Transport and mixing processes in fluid flows can be studied directly from Lagrangian trajectory data, such as obtained from particle tracking experiments. Recent work in this context highlights the application of graph-based approaches,…

The Mixup scheme suggests mixing a pair of samples to create an augmented training sample and has gained considerable attention recently for improving the generalizability of neural networks. A straightforward and widely used extension of…

We address a largely open problem of multilabel classification over graphs. Unlike traditional vector input, a graph has rich variable-size substructures which are related to the labels in some ways. We believe that uncovering these…