arXiv research

SHADOWCAST generates graphs with user-specified attributes.

Fewer obstructions for small graphs in knotless embedding.

We consider immersions admitting uniform graph representations over the affine tangent space over a ball of fixed radius r>0. We show that for sufficiently small C^0-norm of the graph functions, each graph function is smooth with small C^1-norm.

Improved graph generation model for small organic molecules.

The paper investigates why GNNs struggle to generalize from small to large graphs.

The study proves sampling-based GNNs can approximate training on full graphs with small subgraphs.

New bounds for bandits with graph feedback, improving previous results.

We explain and generalise a construction due to Gromov to realise geometric small cancellation groups over graphs of groups as fundamental groups of non-positively curved 2-dimensional complexes of groups. We then give conditions so that the hyperbolicity and some finiteness properties of the small cancellation quotien…

Enhances graph classification models on small datasets.

We focus on developing a novel scalable graph-based semi-supervised learning (SSL) method for a small number of labeled data and a large amount of unlabeled data. Due to the lack of labeled data and the availability of large-scale unlabeled data, existing SSL methods usually encounter either suboptimal performance beca…

Bayesian SSR on graphs improves regression with noisy labels.

Graph manifolds with small homology have non-trivial SU(2) representations.

A new test for IRG models using KSD for small networks.

Graphs can be fooled by small edge changes, but this work protects them.

Graph neural networks denote a group of neural network models introduced for the representation learning tasks on graph data specifically. Graph neural networks have been demonstrated to be effective for capturing network structure information, and the learned representations can achieve the state-of-the-art performanc…

New bounds on diameters and generators for specific lattices and graphs.

We present a new random sampling strategy for k-bandlimited signals defined on graphs, based on determinantal point processes (DPP). For small graphs, ie, in cases where the spectrum of the graph is accessible, we exhibit a DPP sampling scheme that enables perfect recovery of bandlimited signals. For large graphs, ie, …

The study of networks leads to a wide range of high dimensional inference problems. In many practical applications, one needs to draw inference from one or few large sparse networks. The present paper studies hypothesis testing of graphs in this high-dimensional regime, where the goal is to test between two populations…

Generative model captures hubs and dense communities in social networks.

We show that there are minimal graphs in R^{n+1} whose intersection with the portion of the horizontal hyperplane contained in the unit ball has any prescribed geometry, up to a small deformation. The proof hinges on the construction of minimal graphs that are almost flat but have small oscillations whose geometry we c…

NPGNN improves graph link prediction by adapting to new graphs.

Unified framework sparsifies GNNs for faster inference on large graphs.

Meta-Graph learns to predict missing edges quickly from few samples.

A new algorithm for robust causal discovery in small sample sizes.

Automorphisms of curve graphs and systolic complexes are isomorphic to mapping class groups for small k.

The paper classifies virtual knot polynomials and trivalent graph invariants using skein theory.

This work analyzes the stability of graph filters under large perturbations.

PASCO speeds up graph clustering for large graphs.

This paper uses the relationship between graph conductance and spectral clustering to study (i) the failures of spectral clustering and (ii) the benefits of regularization. The explanation is simple. Sparse and stochastic graphs create a lot of small trees that are connected to the core of the graph by only one edge. G…

Estimates smooth graph signals from partial measurements.

This paper focuses on spectral filters on graphs, namely filters defined as elementwise multiplication in the frequency domain of a graph. In many graph signal processing settings, it is important to transfer a filter from one graph to another. One example is in graph convolutional neural networks (ConvNets), where the…

Estimates CATEs for structured treatments using a new decomposition method.

Deep generative models for graph-structured data offer a new angle on the problem of chemical synthesis: by optimizing differentiable models that directly generate molecular graphs, it is possible to side-step expensive search procedures in the discrete and vast space of chemical structures. We introduce MolGAN, an imp…

We prove that a strictly stable minimal $C^2_h$ intrinsic graph G is locally area-minimizing, i.e. given any $C^1_h$ graph $S$ with the same boundary, $\text{Area}(G)<\text{Area}(S)$ unless $G=S$. As a consequence we show the existence and the uniqueness of $C^\infty$ minimal graphs with prescribed small boundary datum…

HeteGCN improves text classification with efficient, scalable graph models.

We prove that any isometry of the graph of cyclic splittings of a finitely generated free group $F_N$ of rank $N\ge 3$ is induced by an outer automorphism of $F_N$. The same statement also applies to the graphs of maximally-cyclic splittings, and of very small splittings.

Graph-based semi-supervised learning is the problem of propagating labels from a small number of labelled data points to a larger set of unlabelled data. This paper is concerned with the consistency of optimization-based techniques for such problems, in the limit where the labels have small noise and the underlying unl…

In this paper, we proved the mass angular momentum inequality\cite{D1}\cite{ChrusLiWe}\cite{SZ} for axisymmetric, asymptotically flat, vacuum constraint data sets with small trace. Given an initial data set with small trace, we construct a boost evolution spacetime of the Einstein vacuum equations as \cite{ChOM}. Then …

Method detects anomalies on attributed graphs with few labeled instances.

Analyzes Willmore flow for graphs with boundary data, proving existence and convergence.

Minor changes in the exposition and small corrections on the previous version.

Summarizing large-scaled directed graphs into small-scale representations is a useful but less studied problem setting. Conventional clustering approaches, which based on "Min-Cut"-style criteria, compress both the vertices and edges of the graph into the communities, that lead to a loss of directed edge information. O…

We demonstrate that graphs embedded on surfaces are a powerful and practical tool to generate, characterize and simulate networks with a broad range of properties. Remarkably, the study of topologically embedded graphs is non-restrictive because any network can be embedded on a surface with sufficiently high genus. The…

COMRECGC finds common recourse for global counterfactual explanations in GNNs.

GraphTEE estimates treatment effects on graph-structured targets, mitigating bias.

The study combines graph-minors and metric spaces, answering some questions and conjectures.

It has been shown recently that graph signals with small total variation can be accurately recovered from only few samples if the sampling set satisfies a certain condition, referred to as the network nullspace property. Based on this recovery condition, we propose a sampling strategy for smooth graph signals based on …

SpaPool combines dense and sparse techniques for efficient graph pooling.