CaGAT learns context-aware edge representations for graph data.
problem Ignoring edge representation in GNNs.
method Unified Context-aware Adaptive Graph Attention Network (CaGAT) that learns both node and edge representations.
result CaGAT improves performance on semi-supervised learning tasks.
This paper proposes a method to learn graph representations by partitioning edges into communities.
problem Graph neural networks ignore how edges are formed, leading to suboptimal representation learning.
method Introduces a generative model to partition edges into community-specific weighted edges, then uses these for GNN-based inference and classification.
result The method learns discriminative representations for both node-level and graph-level classification tasks.
ACERL embeds networks into a low-dimensional space preserving structural and semantic properties.
problem Challenges in brain connectivity data analysis with subject-specific, high-dimensional, and sparse networks.
method Contrastive learning of augmented network pairs with adaptive random masking.
result Achieves minimax optimal convergence rate for edge representation learning.
New method preserves directed edge info in graph embeddings.
problem Learning accurate node embeddings for directed graphs.
method Low-rank asymmetric projections with graph likelihood objective.
result Significant improvement in link prediction accuracy.
New framework for disentangling graph node and edge features.
problem Learning disentangled representations for attributed graphs with node and edge features.
method Proposes a novel variational objective and architecture for node and edge deconvolutions to disentangle latent factors.
result Demonstrates effectiveness of the proposed model and its extensions on synthetic and real-world datasets.
UniNet efficiently learns network representations from large graphs.
problem Efficiently learning network representations from large graphs.
method Metropolis-Hastings sampling for efficient edge sampling and random walk model abstraction.
result UniNet outperforms existing NRL models on billion-edge networks.
Graph neural networks improve with edge similarity constraints in RNA structure analysis.
problem Lack of edge similarity constraints in graph neural networks.
method Introduced a graph neural network layer that leverages prior information about edge similarities.
result Edge similarity constraints do not enhance performance in graph neural networks.
The Weierstrass representation of discrete isotropic surfaces in R2,1, R3,1 and R2,2math.DG Using an integrable discrete Dirac operator, we construct a discrete version of the Weierstrass representation of time-like surfaces parametrized along isotropic directions in R2,1, R3,1 and R2,2. The corresponding discrete surfaces have isotropic edges. We show that any discrete surface satisfying a gen…
GTEA learns node representations in temporal interaction graphs.
problem Inductive representation learning on temporal interaction graphs.
method Integrates sequence model with time encoder and self-attention scheme for edge and node embeddings.
result GTEA learns comprehensive node representations capturing temporal and structural characteristics.
Friend recommendation system using heterogeneous edge embeddings.
problem Inadequate performance of existing network embedding techniques on multi-graph social networks.
method Proposes a method to mine network representation exploiting heterogeneity in multi-graphs.
result Outperforms state-of-the-art baselines on Hike's social network in terms of accuracy and user satisfaction.
New method pools graphs with edge features for molecular data.
problem Pooling graphs with edge features for molecular data.
method Proposes two types of pooling layers compatible with edge-feature graph-convolutional architecture.
result Significantly outperforms previous benchmarks on three out of four MoleculeNet datasets.
Improved KAN model explains brain dynamics through edge learning and synaptic strength.
problem Explaining brain dynamics and frequencies in different brain regions.
method ELKAN (Edge Learning KNN) model with edge learning and trimming, inspired by brain science.
result ELKAN model outperforms KAN in explaining brain frequencies and dynamics.
HGT models heterogeneous graphs with dedicated node and edge representations.
problem Infeasibility of existing GNNs for heterogeneous graphs.
method Node- and edge-type dependent parameters, relative temporal encoding, heterogeneous mini-batch graph sampling.
result HGT outperforms state-of-the-art GNNs by 9%--21% on various downstream tasks.
It is known that for each combinatorial type of convex 3-dimensional polyhedra, there is a representative with edges tangent to the unit sphere. This representative is unique up to projective transformations that fix the unit sphere. We show that there is a unique representative (up to congruence) with edges tangent to…
In this article we give an explicit description of the representation matrix of a Heisenberg type action constructed by Blanchet, Habegger, Masbaum and Vogel. We give the matrix in terms of a ribbon graph and its admissible colorings. We show that components of the representation matrix satisfies the {\it external edge…
Proposes a new CNN using DTCWT ScatterNet for efficient learning.
problem Training efficiency and feature extraction in CNNs.
method Replaces CNN's first layers with a parametric log based DTCWT ScatterNet.
result Improves training efficiency and learns complex patterns early.
New stabilization method in graph braid homology yields polynomial growth.
problem Stabilization in graph braid homology.
method Introduced a stabilization map on graph configuration spaces, leading to a polynomial ring action on homology.
result Homology module is finitely generated and shows polynomial growth in Betti numbers.
This paper presents a method to summarize directed graphs while preserving edge information.
problem Summarizing directed graphs while maintaining edge directionality.
method A model based on minimizing reconstruction error with non-negative constraints, related to Max-Cut criterion, using multiplicative update algorithms.
result The proposed method identifies compressed nodes and directed compressed relations, providing a more accurate representation of directed graphs.
Develops methods for clustering hypergraphs with categorical edge labels.
problem Complex graph representations with multiple interaction types.
method Combinatorial objective function, polynomial-time algorithm for two types, linear programming relaxations for more types.
result Efficient algorithms for clustering hypergraphs with categorical edge labels.
We show that for a representation of the fundamental group of a triangulated closed 3-manifold (not necessarily hyperbolic) into $\PSL$ so that any edge loop has non-trivial image under the representation, there exist uncountably many solutions to the hyperbolic gluing equation whose associated representations are conj…
Posits improve DNN training efficiency on edge devices.
problem Training deep neural networks with low-precision formats.
method Used posits (5-8 bit) for DNN training compared to floating point.
result 16-bit posits outperform 16-bit floating point for end-to-end training.
Spectral embedding improves with edge weight transformations.
problem Improving spectral embedding for weighted networks.
method Analyzed edge weight transformations for spectral embedding quality.
result Transformations like tempering or thresholding can significantly enhance spectral embedding.
EHNA learns node embeddings from historical network neighborhoods.
problem Capturing temporal information in evolving networks.
method Temporal random walk and deep learning model with attention mechanism.
result EHNA outperforms existing methods in network reconstruction and link prediction tasks.
This work estimates edge weights of edge-reinforced random walks using observed data.
problem Statistical estimation of edge weights in edge-reinforced random walks.
method Proposes an estimator based on the generalized method of moments using the magic formula and hyperbolic Gaussian structure.
result Analyzes the sample complexity of the proposed estimator.
In this article we determine the structure of a twisted first cohomology group of the first homology of a trivalent graph with a coefficient associated with the quantum Clebsch-Gordan condition. As an application we give a characterization of a combinatorial property, the external edge condition, which is defined by th…
We give algorithms with provable guarantees that learn a class of deep nets in the generative model view popularized by Hinton and others. Our generative model is an n node multilayer neural net that has degree at most nγ for some γ<1 and each edge has a random edge weight in [−1,1]. Our algorithm learns {\em …
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.
Graph embedding method captures both local and global network structure.
problem Representing and analyzing complex graph networks.
method Spectral embedding based on a generalized graph Laplacian.
result Significant improvement in data analysis tasks.
MeshCNN analyzes 3D shapes using edges, overcoming irregularities.
problem Irregularities in mesh representations hinder neural network analysis.
method MeshCNN uses specialized convolution and pooling layers on mesh edges, collapsing them to focus on important features.
result MeshCNN effectively analyzes 3D shapes, learning which edges to collapse.
GNN-FiLM uses feature-wise linear modulation to improve graph neural networks.
problem Improving graph neural networks for better performance.
method Feature-wise linear modulation applied to target node representations in GNNs.
result GNN-FiLM outperforms baseline methods on a regression task for molecular graphs.
New model for network analysis using functional data.
problem Existing network models treat nodes as functions, but this paper introduces functional edges.
method Transform adjacency matrix into functional adjacency tensor, apply Tucker decomposition, regularize basis matrices, and solve tensor completion problem.
result The model effectively captures community structure and handles irregular functional edge data.
SIGNet creates embeddings for signed networks respecting social balance.
problem Lack of methods to embed signed networks considering edge polarities.
method SIGNet uses a targeted node sampling strategy to model social balance in signed networks.
result SIGNet outperforms existing methods on real-world signed network datasets.
FairDrop improves fairness in graph representation learning by counteracting homophily.
problem Ensuring fairness in graph representation learning, especially in scenarios with protected attributes.
method Proposes a biased edge dropout algorithm (FairDrop) to counteract homophily and improve fairness.
result Successfully improves fairness in all models up to a small or negligible drop in accuracy.
FoSR adds edges to graphs to prevent oversquashing and oversmoothing in GNNs.
problem Oversquashing and oversmoothing in graph neural networks (GNNs).
method First-order spectral rewiring to add edges based on spectral expansion, combined with a relational architecture.
result Our algorithm outperforms existing graph rewiring methods in graph classification tasks.
GTNs learn new graph structures and improve node representation learning.
problem Learning node representations on misspecified or heterogeneous graphs.
method Graph Transformer Networks (GTNs) that generate new graph structures and learn effective node representations.
result GTNs achieve state-of-the-art performance in node classification tasks without predefined meta-paths.
Maximizes mutual information to improve graph neural networks performance.
problem Loss of information between nodes in GNNs aggregation and iteration schemes.
method Explores mutual information maximization in the aggregation and iteration scheme of GNNs.
result Improves state-of-the-art performance on graph tasks.
Study of colored triangulations linked to symmetric groups.
problem Enumeration of permutations up to conjugation.
method Analysis of checker triangulated surfaces and their Belyi data.
result Links between triangulations and infinite symmetric groups.
Enhances graph comparison by incorporating edge features using Fused Gromov-Wasserstein distance.
problem Graph distances overlook edge attributes, limiting their effectiveness.
method Introduced Fused Gromov-Wasserstein distance for graph comparison with edge features. Proposed algorithms for distance and barycenter computation.
result Empirically validated the effectiveness of the novel distance in graph learning tasks.
Extends graph theory to hypergraphs with manifold-valued nodes.
problem Representing complex N-ary relationships on manifolds.
method Defined function spaces and symmetric products for manifold-valued nodes and edges.
result Generalized hypergraph Laplacians to manifold-valued hypergraphs.
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.
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.
New method identifies latent causal graphs without parametric assumptions.
problem Identifying latent causal graphs without parametric assumptions.
method Constructive proofs with new graphical concepts.
result Conditions for nonparametric identification of latent causal graphs.
The paper analyzes deep neural networks' expressivity and training, revealing critical expressivity issues.
problem Critical expressivity issues in deep neural networks.
method Quantitative analysis using Hilbert space and Hermite polynomials for feature mapping and activation function design.
result Deep neural networks evolve to the edge of chaos, but expressivity depends on overcoming convergence.
We model microbiome interactions as graphs to interpret complex dynamics.
problem Understanding the differences in microbiome profiles between healthy and ill individuals.
method Developed a method to learn low-dimensional graph representations of time-evolving microbiome interactions.
result Extracted graph features that highlight microbes and interactions strongly correlated with clinical diseases.
New edge features improve GNN performance in biological datasets.
problem Inefficient use of edge features in GNNs.
method Self-supervised and unsupervised learning for new edge features, incorporating Forman-Ricci curvature.
result Improved node classification performance over baseline GNN models.
Tiered graph autoencoders improve molecular graph representation.
problem Representing and utilizing groups in molecular graphs.
method Adapting tiered graph autoencoders for PyTorch Geometric.
result Molecular graphs have tiered latent representations.
Shifu2 discovers advisor-advisee relationships in collaboration networks.
problem Discovering hidden advisor-advisee relationships in scientific collaboration networks.
method Network Representation Learning (NRL) model, considering both network structure and node/edge semantics.
result Improved stability and effectiveness compared to state-of-the-art methods.
Novel multigraph network improves chemical classification tasks.
problem Learning from variable graphs with multiple relationships.
method Proposed a multigraph network using Chebyshev GCNs to handle variable graphs and learned edges.
result Achieved competitive results on chemical classification benchmarks.