arXiv research

We study spaces of realisations of linkages (weighted graphs) whose underlying graph is a series parallel graph. In particular, we describe an algorithm for determining whether or not such spaces are connected.

Graph embedding aims at learning a vector-based representation of vertices that incorporates the structure of the graph. This representation then enables inference of graph properties. Existing graph embedding techniques, however, do not scale well to large graphs. We therefore propose a framework for parallel computat…

We suggest a general oracle-based framework that captures different parallel stochastic optimization settings described by a dependency graph, and derive generic lower bounds in terms of this graph. We then use the framework and derive lower bounds for several specific parallel optimization settings, including delayed …

In this paper, we obtain an Ecker-Huisken type result for entire graphs with parallel mean curvature.

Recently, Dasbach, Futer, Kalfagianni, Lin, and Stoltzfus extended the notion of a Tait graph by associating a set of ribbon graphs (or equivalently, embedded graphs) to a link diagram. Here we focus on Seifert graphs, which are the ribbon graphs of a knot or link diagram that arise from Seifert states. We provide a ch…

PASCO speeds up graph clustering for large graphs.

Grid homology properties for MOY graphs studied.

A new GNN model SPIN achieves state-of-the-art performance on diverse real-world datasets.

Large GNNs trained with Graph Parallelism improve atomic simulation accuracy.

The Graph Convolutional Network (GCN) model and its variants are powerful graph embedding tools for facilitating classification and clustering on graphs. However, a major challenge is to reduce the complexity of layered GCNs and make them parallelizable and scalable on very large graphs -- state-of the art techniques a…

We consider non-degenerate graph immersions into affine space $\mathbb A^{n+1}$ whose cubic form is parallel with respect to the Levi-Civita connection of the affine metric. There exists a correspondence between such graph immersions and pairs $(J,γ)$, where $J$ is an $n$-dimensional real Jordan algebra and $γ$ is a no…

DistShap parallelizes GNN explanation for large graphs.

New invariant counts graph configurations in 3D manifolds.

We describe a computationally efficient, stochastic graph-regularization technique that can be utilized for the semi-supervised training of deep neural networks in a parallel or distributed setting. We utilize a technique, first described in [13] for the construction of mini-batches for stochastic gradient descent (SGD…

We introduce a new embarrassingly parallel parameter learning algorithm for Markov random fields with untied parameters which is efficient for a large class of practical models. Our algorithm parallelizes naturally over cliques and, for graphs of bounded degree, its complexity is linear in the number of cliques. Unlike…

We prove a conjecture of Menasco and Zhang that if a tangle is completely tubing compressible then it consists of at most two families of parallel strands. This is related to problems of graphs in 3-manifold. A 1-vertex graph $Γ$ in a 3-manifold $M$ with a genus 1 Heegaard splitting is standard if it consists of one or…

Given a similarity graph between items, correlation clustering (CC) groups similar items together and dissimilar ones apart. One of the most popular CC algorithms is KwikCluster: an algorithm that serially clusters neighborhoods of vertices, and obtains a 3-approximation ratio. Unfortunately, KwikCluster in practice re…

We present RL-VAE, a graph-to-graph variational autoencoder that uses reinforcement learning to decode molecular graphs from latent embeddings. Methods have been described previously for graph-to-graph autoencoding, but these approaches require sophisticated decoders that increase the complexity of training and evaluat…

We study recursive-cube-of-rings (RCR), a class of scalable graphs that can potentially provide rich inter-connection network topology for the emerging distributed and parallel computing infrastructure. Through rigorous proof and validating examples, we have corrected previous misunderstandings on the topological prope…

New algorithms reduce communication in GNN training.

Given a properly embedded graph Gamma in a ball B and a punctured sphere Sigma properly embedded in B - Gamma, we examine the conditions on Gamma that are necessary to assure that Sigma is boundary parallel.

Constructs graphs with singularities in a special space.

Infinite hyperbolic knots yield unusual surgeries.

GNNS uses graph neural networks to efficiently estimate subgraph frequency distributions.

Given $H\in [0,\infty),$ some sufficient conditions for existence of CMC $H$ graphs with boundary in two parallel planes of $\mathbb{H}^2\times\mathbb{R}$ are presented. Height estimates for outwards-oriented CMC surfaces (horo)cyllindrically bounded are also exhibited.

We establish existence and uniqueness of compact graphs of constant mean curvature in MxR over bounded multiply connected domains of Mx{0} with boundary lying in two parallel horizontal slices of MxR

We present a new notion of probabilistic duality for random variables involving mixture distributions. Using this notion, we show how to implement a highly-parallelizable Gibbs sampler for weakly coupled discrete pairwise graphical models with strictly positive factors that requires almost no preprocessing and is easy …

This paper optimizes how deep learning models are distributed across different devices.

We introduce graph normalizing flows: a new, reversible graph neural network model for prediction and generation. On supervised tasks, graph normalizing flows perform similarly to message passing neural networks, but at a significantly reduced memory footprint, allowing them to scale to larger graphs. In the unsupervis…

EnsemFDet detects fraud by solving subproblems on small graphs, scaling up e-commerce fraud detection.

The construction of Mapper has emerged in the last decade as a powerful and effective topological data analysis tool that approximates and generalizes other topological summaries, such as the Reeb graph, the contour tree, split, and joint trees. In this paper, we study the parallel analysis of the construction of Mappe…

New solver MPLP++ outperforms existing solvers for dense graph models.

Parallel unlearning framework for inherited models reduces computational overhead.

We consider spacelike graphs $Γ_f$ of simple products $(M\times N, g\times -h)$ where $(M,g)$ and $(N,h)$ are Riemannian manifolds and $f:M\to N$ is a smooth map. Under the condition of the Cheeger constant of $M$ to be zero and some condition on the second fundamental form at infinity, we conclude that if $Γ_f \subset…

We present a parallelized bijective graph matching algorithm that leverages seeds and is designed to match very large graphs. Our algorithm combines spectral graph embedding with existing state-of-the-art seeded graph matching procedures. We justify our approach by proving that modestly correlated, large stochastic blo…

We consider the problem of maximum a posteriori (MAP) inference in discrete graphical models. We present a parallel MAP inference algorithm called Bethe-ADMM based on two ideas: tree-decomposition of the graph and the alternating direction method of multipliers (ADMM). However, unlike the standard ADMM, we use an inexa…

We introduce a novel approach for parallelizing MCMC inference in models with spatially determined conditional independence relationships, for which existing techniques exploiting graphical model structure are not applicable. Our approach is motivated by a model of seismic events and signals, where events detected in d…

The paper examines deformations of simple dotted graphs made of circles.

This paper speeds up spectral clustering for large graphs by dilating their eigenspectrum.

Graph-based approach predicts stock trends using dynamic multi-relational graphs.

Let M be a compressionbody containing a graph T (with at least one edge) such that \boundary_+ M is parallel to the union of T and \boundary_- M. We extend methods of Hayashi and Shimokawa to classify bridge surfaces for T. The results of this paper are used in later work to show that if a bridge surface for a graph in…

A new method generates graphs with hierarchical structures.

Lecture notes on group actions on injective spaces and Helly graphs.

2D-PT improves sampling in constrained optimization problems.

Paper estimates Gaussian curvature of minimal graphs in a specific manifold.

We show that Caratheodory's conjecture, on umbilical points of closed convex surfaces, may be reformulated in terms of the existence of at least one umbilic in the graphs of functions f: R^2-->R whose gradient decays uniformly faster than 1/r. The divergence theorem then yields a pair of integral equations for the norm…

Multiresolution Matrix Factorization (MMF) was recently introduced as a method for finding multiscale structure and defining wavelets on graphs/matrices. In this paper we derive pMMF, a parallel algorithm for computing the MMF factorization. Empirically, the running time of pMMF scales linearly in the dimension for spa…

Advancing research in the emerging field of deep graph learning requires new tools to support tensor computation over graphs. In this paper, we present the design principles and implementation of Deep Graph Library (DGL). DGL distills the computational patterns of GNNs into a few generalized sparse tensor operations su…