arXiv research

New principle controls graph-informed adversarial discrepancies.

The study connects Kleinian group divergence to random walk recurrence.

Can neural networks learn to compare graphs without feature engineering? In this paper, we show that it is possible to learn representations for graph similarity with neither domain knowledge nor supervision (i.e.\ feature engineering or labeled graphs). We propose Deep Divergence Graph Kernels, an unsupervised method …

Graph Laplacian spectrum serves as a robust feature representation.

Square percolation determines threshold for group divergence in random graphs.

Graph Laplacians converge under symmetric divergence conditions.

We provide geometric conditions on a pair of hyperplanes of a CAT(0) cube complex that imply divergence bounds for the cube complex. As an application, we classify all right-angled Coxeter groups with quadratic divergence and show right-angled Coxeter groups cannot exhibit a divergence function between quadratic and cu…

Sparse RSP routing improves graph exploration and classification.

We speed up marginal inference by ignoring factors that do not significantly contribute to overall accuracy. In order to pick a suitable subset of factors to ignore, we propose three schemes: minimizing the number of model factors under a bound on the KL divergence between pruned and full models; minimizing the KL dive…

Fine-tunes GNNs by preserving generative patterns to improve transferability.

Classifies divergence and thickness in right-angled Coxeter groups.

This work improves policy-based training by proposing an evaluation balance objective for GFlowNets.

A graph theory approach defines curl and decomposes vector fields.

Study measures complexity of surfaces using a new graph to prove group properties.

Graphon autoencoder generates graphs with arbitrary sizes using Chebyshev filters.

A new graph generator uses heat diffusion on graph Laplacians to create new graph structures.

New $\alpha$-BP algorithm improves belief propagation for graphs with loops.

Unified interpretation of softmax cross-entropy and negative sampling for knowledge graph embedding.

Threshold found for hyperbolicity in random Coxeter groups.

New GAN design uses conditional independence graphs to improve model-based GANs.

We establish bounds on the KL divergence between two multivariate Gaussian distributions in terms of the Hamming distance between the edge sets of the corresponding graphical models. We show that the KL divergence is bounded below by a constant when the graphs differ by at least one edge; this is essentially the tighte…

New separation concepts for Anosov representations help bound Thurston asymmetric metric.

In this paper we study asymptotically hyperbolic manifolds given as graphs of asymptotically constant functions over hyperbolic space $\bH^n$. The graphs are considered as subsets of $\bH^{n+1}$ and carry the induced metric. For such manifolds the scalar curvature appears in the divergence of a 1-form involving the int…

We give a group theoretic characterization of geodesics with superlinear divergence in the Cayley graph of a right-angled Artin group A(G) with connected defining graph G. We use this to determine when two points in an asymptotic cone of A(G) are separated by a cut-point. As an application, we show that if G does not d…

A graph-based method for two-sample testing across connected nodes.

Divergence functions of a metric space estimate the length of a path connecting two points $A$, $B$ at distance $\le n$ avoiding a large enough ball around a third point $C$. We characterize groups with non-linear divergence functions as groups having cut-points in their asymptotic cones. By Olshanskii-Osin-Sapir, that…

We propose a direct estimation method for Rényi and f-divergence measures based on a new graph theoretical interpretation. Suppose that we are given two sample sets $X$ and $Y$, respectively with $N$ and $M$ samples, where $η:=M/N$ is a constant value. Considering the $k$-nearest neighbor ($k$-NN) graph of $Y$ in the j…

We propose a number of techniques for obtaining a global ranking from data that may be incomplete and imbalanced -- characteristics almost universal to modern datasets coming from e-commerce and internet applications. We are primarily interested in score or rating-based cardinal data. From raw ranking data, we construc…

We establish area bounds for two-dimensional immersions in R^3 and R^n. Namely, for μ-stable immersions in R^3 (R^n), for graphs in $\mathbb R^3$ which solve quasilinear equations in divergence form, and for graphs which are critical for Fermat-type variational problems in R^n.

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…

Belief propagation (BP) can do exact inference in loop-free graphs, but its performance could be poor in graphs with loops, and the understanding of its solution is limited. This work gives an interpretable belief propagation rule that is actually minimization of a localized $α$-divergence. We term this algorithm as $α…

The paper studies recovering hidden nearest neighbor graphs in large networks.

RényiCL uses Rényi divergence for robust contrastive learning with stronger data augmentations.

Modeling generative process of growing graphs has wide applications in social networks and recommendation systems, where cold start problem leads to new nodes isolated from existing graph. Despite the emerging literature in learning graph representation and graph generation, most of them can not handle isolated new nod…

This paper studies how to capture dependency graph structures from real data which may not be Gaussian. Starting from marginal loss functions not necessarily derived from probability distributions, we utilize an additive over-parametrization with shrinkage to incorporate variable dependencies into the criterion. An ite…

New method synchronizes graphs with probability measures on rotations.

We consider complete asymptotically flat Riemannian manifolds that are the graphs of smooth functions over $\mathbb R^n$. By recognizing the scalar curvature of such manifolds as a divergence, we express the ADM mass as an integral of the product of the scalar curvature and a nonnegative potential function, thus provin…

In this paper we extend a recent result of Collin-Rosenberg ({\it a solution to the minimal surface equation in the Euclidean disc has radial limits almost everywhere}) to a large class of differential operators in Divergence form. Moreover, we construct an example (in the spirit of \cite{CR2}) of a minimal graph in $\…

Information theoretic measures (e.g. the Kullback Liebler divergence and Shannon mutual information) have been used for exploring possibly nonlinear multivariate dependencies in high dimension. If these dependencies are assumed to follow a Markov factor graph model, this exploration process is called structure discover…

We study two global structural properties of a graph $Γ$, denoted AS and CFS, which arise in a natural way from geometric group theory. We study these properties in the Erdös--Rényi random graph model G(n,p), proving a sharp threshold for a random graph to have the AS property asymptotically almost surely, and giving f…

This paper studies the problem of cross-network node classification to overcome the insufficiency of labeled data in a single network. It aims to leverage the label information in a partially labeled source network to assist node classification in a completely unlabeled or partially labeled target network. Existing met…

We construct a parabolic entire minimal graph $S$ over a finite topology complete Riemannian surface $Σ$ of curvature $-1$ and infinite area (thus of non-parabolic conformal type). The vertical projection of this graph yields a harmonic diffeomorphism from $S$ onto $Σ$. The proof uses the theory of divergence lines to …

Contrastive divergence (CD) is a promising method of inference in high dimensional distributions with intractable normalizing constants, however, the theoretical foundations justifying its use are somewhat shaky. This document proposes a framework for understanding CD inference, how/when it works, and provides multiple…

The von Neumann graph entropy (VNGE) facilitates measurement of information divergence and distance between graphs in a graph sequence. It has been successfully applied to various learning tasks driven by network-based data. While effective, VNGE is computationally demanding as it requires the full eigenspectrum of the…

New method models aptamer libraries as Boltzmann-weighted graph ensembles for better affinity predictions.

Proposes a new neural head for asymmetric representation learning.

A Bayesian factor graph reduced to normal form consists in the interconnection of diverter units (or equal constraint units) and Single-Input/Single-Output (SISO) blocks. In this framework localized adaptation rules are explicitly derived from a constrained maximum likelihood (ML) formulation and from a minimum KL-dive…

SGRNN models evolving graph data for better property prediction.