Efficiently updates vertex representations for dynamic graphs using random walks.
problem Updating vertex representations for dynamic graphs without re-generating them on each update.
method Proposes algorithms that extend random walk-based methods to dynamic graphs, considering the extent and rate of changes.
result Achieves competitive results to state-of-the-art methods while being computationally efficient.
Research tackles learning vertex representations for bipartite networks.
problem Lack of research on learning vertex representations for bipartite networks.
method Apply generic methods like node2vec and LINE, but ignore vertex type information.
result Generic methods are suboptimal for bipartite networks due to different properties and patterns.
Network embedding aims to learn the low-dimensional representations of vertexes in a network, while structure and inherent properties of the network is preserved. Existing network embedding works primarily focus on preserving the microscopic structure, such as the first- and second-order proximity of vertexes, while th…
A new method pools graph vertex representations into a function space for better graph classification.
problem Pooling graph vertex representations for graph-centric tasks.
method Proposes a novel function space pooling method for graph neural networks.
result The proposed method generally outperforms existing pooling methods in graph classification.
Enhances node embeddings in networks using topic modeling.
problem Learning effective node embeddings in network structures.
method Introduces a framework that assigns each node a topic and generates enhanced community representations.
result The method outperforms baseline NRL methods in node classification and link prediction tasks.
DeepMap learns deep graph representations via CNNs, improving graph classification performance.
problem Quantifying graph similarities for tasks like classification.
method Proposes DeepMap framework extending CNNs to arbitrary graphs, learning dense low-dimensional vectors.
result DeepMap achieves state-of-the-art performance on graph classification benchmarks.
For random graphs distributed according to stochastic blockmodels, a special case of latent position graphs, adjacency spectral embedding followed by appropriate vertex classification is asymptotically Bayes optimal; but this approach requires knowledge of and critically depends on the model dimension. In this paper, w…
Network embedding methodologies, which learn a distributed vector representation for each vertex in a network, have attracted considerable interest in recent years. Existing works have demonstrated that vertex representation learned through an embedding method provides superior performance in many real-world applicatio…
The goal of graph representation learning is to embed each vertex in a graph into a low-dimensional vector space. Existing graph representation learning methods can be classified into two categories: generative models that learn the underlying connectivity distribution in the graph, and discriminative models that predi…
The paper tackles scalability issues in Graph Representation Learning.
problem Prohibitive time and memory complexities in Graph Representation Learning.
method Leveraging the K-Core Decomposition property of Graphs to reduce time and memory consumption.
result Proposed techniques significantly reduce computational resources without compromising embedding quality.
Let M be a Riemannian manifold. For p∈M, the tensor algebra of the negative part of the (complex) affinization of the tangent space of M at p has a natural structure of a meromorphic open-string vertex algebra. These meromorphic open-string vertex algebras form a vector bundle over M with a connection. We …
New method for learning on heterogeneous graphs without meta-paths.
problem Learning on heterogeneous graphs is sensitive to meta-paths choice, leading to poor performance.
method Decompose heterogeneous graph into homogeneous relation-type graphs, combine higher-order representations, use attention mechanisms.
result Our model outperforms state-of-the-art baselines in vertex classification tasks on heterogeneous graph datasets.
Mathematical construction of vertex algebra representations from integrable G2 structures.
problem Constructing representations of a specific vertex algebra from geometric input.
method Integrable G2 structures with closed torsion on group manifolds, embedding into superaffine vertex algebra and chiral de Rham complex.
result Embeddings of deformed Shatashvili-Vafa vertex algebra in the chiral algebra of heterotic G2 backgrounds.
We establish a direct map between refined topological vertex and sl(N) homological invariants of the of Hopf link, which include Khovanov-Rozansky homology as a special case. This relation provides an exact answer for homological invariants of the of Hopf link, whose components are colored by arbitrary representations …
Researchers link vertex algebras to non-Kähler solutions of the Hull-Strominger system.
problem Constructing representations of vertex algebras from non-Kähler solutions of the Hull-Strominger system.
method Embedding the N=2 superconformal vertex algebra in the chiral de Rham complex of a string Courant algebroid, with a condition on the Hermitian-Yang-Mills connection.
result Any solution of the Hull-Strominger system satisfying the Hermitian-Yang-Mills condition has an associated N=2 embedding.
Graph neural networks often assume vertex labels are independent, but we show this is rarely true and propose a method to improve predictions.
problem Graph neural networks often assume vertex labels are conditionally independent given their neighborhood features, which is rarely true.
method We model the joint distribution of residuals on vertices with a parameterized multivariate Gaussian and estimate parameters by maximizing the marginal likelihood of the observed labels.
result Our method achieves substantially higher accuracy than competing baselines and can be interpreted as the strength of correlation among connected vertices.
Graph cross network improves graph classification accuracy.
problem Improving graph classification accuracy.
method Graph cross network (GXN) with vertex infomax pooling (VIPool) and feature-crossing layer.
result Improves graph classification accuracy by 2.12% and 1.15%.
In a dynamic network, the neighborhood of the vertices evolve across different temporal snapshots of the network. Accurate modeling of this temporal evolution can help solve complex tasks involving real-life social and interaction networks. However, existing models for learning latent representation are inadequate for …
Researchers clarify modular group representations and vertex operator algebras for 3d invariants.
problem Understanding the full set of 3d invariants and their modular properties.
method Introducing supersymmetric defects and constructing cone vertex operator algebras.
result The full vector-valued quantum modular form for \(\widetilde{
m SL}_2(\mathbb{Z})\) captures all \(\hat Z\)-invariants of a given three-manifold.
A method for ranking items using distance-based learning from positive and unlabeled data.
problem Learning to rank items without an analytic description of what constitutes a good ranking.
method Combining representations using an integer linear program for ranking items based on nominations.
result The method is effective in simulation and real data examples, especially when supervision is light.
This paper improves nearest neighbor search by learning optimal routing functions.
problem Local minima issues in greedy routing on similarity graphs.
method Learn routing function that considers global graph structure.
result Significant improvement in search performance via learning.
If a knot is represented by an m-strand braid, then HOMFLY polynomial in representation R is a sum over characters in all representations Q\in R^{\otimes m}. Coefficients in this sum are traces of products of quantum R-matrices along the braid, but these matrices act in the space of intertwiners, and their size is equa…
This paper proposes a new Quantum Spatial Graph Convolutional Neural Network (QSGCNN) model that can directly learn a classification function for graphs of arbitrary sizes. Unlike state-of-the-art Graph Convolutional Neural Network (GCNN) models, the proposed QSGCNN model incorporates the process of identifying transit…
Proposes a new method to describe graph vertex features using characteristic functions.
problem Describing the distribution of vertex features at multiple scales on graphs.
method Introduces FEATHER, a computationally efficient algorithm to calculate characteristic functions based on random walk transition probabilities.
result Demonstrates that the proposed method creates high-quality graph representations and is robust to data corruption.
New model learns graph features for classification.
problem Graph classification with structural information loss.
method Transform graphs into vertex grids, apply vertex convolution.
result Model preserves structural information on local vertices.
Given a vertex of interest in a network G1, the vertex nomination problem seeks to find the corresponding vertex of interest (if it exists) in a second network G2. A vertex nomination scheme produces a list of the vertices in G2, ranked according to how likely they are judged to be the corresponding vertex of …
The recently suggested tangle calculus for knot polynomials is intimately related to topological string considerations and can help to build the HOMFLY-PT invariants from the topological vertices. We discuss this interplay in the simplest example of the Hopf link and link L8n8. It turns out that the resolved conif…
Machine learning techniques have recently been adopted in various applications in medicine, biology, chemistry, and material engineering. An important task is to predict the properties of molecules, which serves as the main subroutine in many downstream applications such as virtual screening and drug design. Despite th…
Neural embeddings have been used with great success in Natural Language Processing (NLP). They provide compact representations that encapsulate word similarity and attain state-of-the-art performance in a range of linguistic tasks. The success of neural embeddings has prompted significant amounts of research into appli…
Enhances graph classification with multiple graphs.
problem Improving graph classification accuracy with multiple graphs.
method Graph fusion embedding using encoder embedding.
result The method consistently improves classification accuracy for large vertex sets.
The paper develops a spectral theory for hypergraphs with edge-dependent vertex weights using random walks.
problem Lack of spectral theory for hypergraphs with edge-dependent vertex weights.
method Random walks on hypergraphs with edge-dependent vertex weights, deriving a random walk-based hypergraph Laplacian.
result Random walks on hypergraphs with edge-dependent vertex weights can capture higher-order relationships in data.
New method clusters hypergraphs using weighted random walks and Laplacians.
problem Clustering hypergraph data with edge-dependent weights.
method Random walks with edge-dependent vertex weights, constructing hypergraph Laplacians for clustering.
result Proposed methods outperform existing hypergraph clustering algorithms.
We show how Ramond free neutral Fermi fields lead to a τ-function theory of BKP type which describes iso-orthogonal deformations of systems of ortogonal curvilinear coordinates. We also provide a vertex operator representation for the classical Ribaucour transformation.
A new method learns text network embeddings by combining generative autoencoder and homophilic priors.
problem Improving performance of network learning applications, especially for textual networks.
method Variational Homophilic Embedding (VHE) - a fully generative model that optimizes a variational autoencoder for semantic information and a homophilic prior for structural information.
result VHE outperforms existing methods in various tasks on real-world textual networks.
We consider the issue of the slice invariance of refined topological string amplitudes, which means that they are independent of the choice of the preferred direction of the refined topological vertex. We work out two examples. The first example is a geometric engineering of five-dimensional U(1) gauge theory with a ma…
Algorithm learns graph ARMA processes for missing signal estimation.
problem Missing signal estimation in time-varying graph signals.
method Learning joint time-vertex power spectral density through convex relaxations.
result High accuracy in time-vertex signal estimation.
Deep learning improves neutrino-nucleus interaction vertex reconstruction.
problem Vertex reconstruction of neutrino-nucleus interaction events.
method Combining energy and timing data for classification and regression tasks using deep learning.
result The model achieves 4.00% higher classification accuracy and 0.9919 higher regression accuracy than previous methods.
The application of deep learning to symbolic domains remains an active research endeavour. Graph neural networks (GNN), consisting of trained neural modules which can be arranged in different topologies at run time, are sound alternatives to tackle relational problems which lend themselves to graph representations. In …
Vertex distortion detects if a knot is unknot.
problem Determining if a knot is the unknot.
method Using Denne-Sullivan's bound on Gromov distortion, the vertex distortion of nontrivial lattice knots is bounded. Then, it is shown that trivial vertex distortion implies the unknot.
result The conjecture that trivial vertex distortion implies the unknot is proven.
Given a flag in each of the vertex-transitive tessellations of the Euclidean plane by regular polygons, we determine the flag stabilizer under the action of the automorphism group of a regular cover. In so doing we give a presentation of these tilings as quotients of regular (infinite) polyhedra.
The study finds the bounds of vertex orbits in maps derived from specific lattices.
problem Determining the bounds of vertex orbits in maps derived from k-vertex-homogeneous lattices. method Analyzing maps as quotients of k-vertex-homogeneous lattices. result Sharp bounds of the number of vertex orbits are identified.
New hypergraph neural network learns variable-sized hyperedges.
problem Learning representations for non-uniform hypergraphs with variable cardinalities.
method Developed a hypergraph neural network exploiting incidence structure.
result Significant improvement in accuracy on real-world hypergraph datasets.
Paper uses neural networks to efficiently compute vertex centrality measures in large networks.
problem Efficiently computing vertex centrality measures in massive real-world networks.
method Neural network learning algorithms to approximate centrality measures.
result Neural network regression model outperforms other techniques in terms of solution quality and computation time.
GRAMPA algorithm recovers latent vertex correspondence in correlated graphs with high probability.
problem Recovering latent vertex correspondence between unlabeled, edge-correlated weighted graphs.
method Spectral graph matching algorithm, GRAMPA, with exact recovery guarantees for Erdős-Rényi graphs.
result GRAMPA exactly recovers latent vertex correspondence with high probability for Erdős-Rényi graphs with edge correlation coefficient 1−σ2 and average degree at least polylog(n) when σ≲1/polylog(n). New method embeds correlation networks to reveal underlying time series patterns.
problem Analyzing correlation networks derived from time series data.
method Spectral embedding of noisy correlation networks, leveraging Fourier basis elements.
result Spectral embedding recovers true vertex-level latent representations under suitable assumptions.
New maps on the plane with specific symmetry properties identified.
problem Characterizing maps with quasi-vertex-transitive properties.
method Analyzing the automorphism groups and vertex orbits of maps on the plane.
result Existence of quasi-vertex-transitive maps of certain types, but not vertex-transitive.
634 vertex-transitive and over 10^103 non-vertex-transitive 27-vertex triangulations of octonionic projective plane.
problem Constructing and classifying triangulations of the octonionic projective plane.
method Combinatorial construction and analysis of symmetry groups.
result Found 634 vertex-transitive and over 10^103 non-vertex-transitive 27-vertex triangulations.
Let Γ be a one-ended, torsion-free hyperbolic group and let G be a semisimple Lie group with finite center. Using the canonical JSJ splitting due to Sela, we define amalgam Anosov representations of Γ into G and prove that they form a domain of discontinuity for the action of Out(Γ). In the appendix,…