arXiv research

Graph Neural Nets (GNNs) have received increasing attentions, partially due to their superior performance in many node and graph classification tasks. However, there is a lack of understanding on what they are learning and how sophisticated the learned graph functions are. In this work, we propose a dissection of GNNs …

Graph convolutional networks adapt the architecture of convolutional neural networks to learn rich representations of data supported on arbitrary graphs by replacing the convolution operations of convolutional neural networks with graph-dependent linear operations. However, these graph-dependent linear operations are d…

In this paper, we study curvature dimension conditions on birth-death processes which correspond to linear graphs, i.e., weighted graphs supported on the infinite line or the half line. We give a combinatorial characterization of Bakry and Émery's $CD(K,n)$ condition for linear graphs and prove the triviality of edge w…

An embedding of a graph into $\mathbb{R}^3$ is said to be linear, if any edge of the graph is sent to be a line segment. And we say that an embedding $f$ of a graph $G$ into $\mathbb{R}^3$ is free, if $π_1(\mathbb{R}^3-f(G))$ is a free group. It was known that for any complete graph its linear embedding is always free.…

Linear-time graph optimization using reinforcement learning.

We study the Ollivier-Ricci curvature of graphs as a function of the chosen idleness. We show that this idleness function is concave and piecewise linear with at most $3$ linear parts, with at most $2$ linear parts in the case of a regular graph. We then apply our result to show that the idleness function of the Cartes…

New curvature concept preserves graph distances under operations.

In order to model entanglements of polymers in a confined region, we consider the linking numbers and writhes of cycles in random linear embeddings of complete graphs in a cube. Our main results are that for a random linear embedding of $K_n$ in a cube, the mean sum of squared linking numbers and the mean sum of square…

Notes a flaw in a proof about embedding graphs.

GOAT improves graph matching speed and accuracy using optimal transport.

Spheres in curve graphs are connected, proving Gromov boundary linearity.

The paper explores linearly free graphs and their embeddings into 3D space.

Graph Convolutional Networks (GCNs) are state-of-the-art graph based representation learning models by iteratively stacking multiple layers of convolution aggregation operations and non-linear activation operations. Recently, in Collaborative Filtering (CF) based Recommender Systems (RS), by treating the user-item inte…

Neural networks with DAGs show linearity as width increases.

Paper analyzes GCNN sensitivity to probabilistic graph perturbations.

We solve structure learning for cyclic linear causal models using observational data.

The study estimates the expressiveness of GCNs with bounds on the number of linear regions.

Paper proves flatness of anisotropic minimal graphs in half-spaces.

SASE improves attributed graph clustering for large graphs with linear time and space complexity.

We define a pseudo-inverse for line graphs using linear integer programming.

Linear time algorithm for random walk kernels on sparse graphs.

We analyze the necessary number of samples for sparse vector recovery in a noisy linear prediction setup. This model includes problems such as linear regression and classification. We focus on structured graph models. In particular, we prove that sufficient number of samples for the weighted graph model proposed by Heg…

Graph representation learning is of paramount importance for a variety of graph analytical tasks, ranging from node classification to community detection. Recently, graph convolutional networks (GCNs) have been successfully applied for graph representation learning. These GCNs generate node representation by aggregatin…

Graph neural networks improve solving linear optimization problems.

A new method for linear regression using feature graphs and hierarchical shrinkage.

Invariant and equivariant networks have been successfully used for learning images, sets, point clouds, and graphs. A basic challenge in developing such networks is finding the maximal collection of invariant and equivariant linear layers. Although this question is answered for the first three examples (for popular tra…

Graph manifolds' Thurston norms are sums of linear functionals, and every such norm can be realized.

Graph convolution improves linear separability and generalizes to out-of-distribution data.

Sketch-GNN reduces GNN training time and memory usage to sublinear scales.

Refines Ozsváth-Szabó d-invariants for knot concurrence.

Essential curves in certain graph manifolds imply non-linear groups.

Unified framework for multi-user bandits using Laplacian kernels.

Kernel and linear regression have been recently explored in the prediction of graph signals as the output, given arbitrary input signals that are agnostic to the graph. In many real-world problems, the graph expands over time as new nodes get introduced. Keeping this premise in mind, we propose a method to recursively …

We develop a multi-kernel based regression method for graph signal processing where the target signal is assumed to be smooth over a graph. In multi-kernel regression, an effective kernel function is expressed as a linear combination of many basis kernel functions. We estimate the linear weights to learn the effective …

New method linearizes nonlinear coupled oscillators on graphs.

We establish a new framework for statistical estimation of directed acyclic graphs (DAGs) when data are generated from a linear, possibly non-Gaussian structural equation model. Our framework consists of two parts: (1) inferring the moralized graph from the support of the inverse covariance matrix; and (2) selecting th…

Minimal graph theorem proven for convex domains.

We give upper bounds, linear in rank, to the topological dimensions of the Gromov boundaries of the intersection graph, the free factor graph and the cyclic splitting graph of a finitely generated free group.

It is a key to construct a similarity graph in graph-oriented subspace learning and clustering. In a similarity graph, each vertex denotes a data point and the edge weight represents the similarity between two points. There are two popular schemes to construct a similarity graph, i.e., pairwise distance based scheme an…

BAM model learns graph structure from data with robustness across linear and non-linear dependencies.

AutoLL uses neural networks to automatically reorder graph nodes for linear layouts.

A new graph neural network framework captures long-range interactions efficiently.

New curvature measure defined for graphs, with bounds on diameter and spectral gap.

Graph convolutions can enhance high frequencies, leading to over-sharpening.

Improved graph embedding through refined linear transformation and community recovery.

Graph embedding learns low-dimensional representations for nodes in a graph and effectively preserves the graph structure. Recently, a significant amount of progress has been made toward this emerging research area. However, there are several fundamental problems that remain open. First, existing methods fail to preser…

Estimates multiple linear systems on a graph with smoothness constraints.

Study $p$-parabolicity on graphs using various energy functionals.