Graph products inherit Morse local-to-global property from their components.
problem Generalizing local-to-global property to graph products of infinite groups.
method Generalizing maximization procedure for relatively hierarchically hyperbolic groups and showing stable embeddings.
result Graph products of infinite Morse local-to-global groups have the Morse local-to-global property.
This thesis explores GNNs, categorizing them into local and global approaches.
problem Understanding the convergence of global GNNs and connecting local and global approaches.
method Categorization of GNNs into local and global, study of Invariant Graph Networks, connecting local and global approaches, and using local MPNN for graph coarsening.
result Established a connection between local and global GNN approaches.
LCNs use Lovasz embeddings to capture global graph properties.
problem Semi-supervised learning on graph data.
method LCNs use Lovasz embeddings to incorporate global graph properties.
result LCNs outperform GCNs on various graph models and real-world datasets.
We introduce a new graph kernel combining local and global properties.
problem Graph kernels focusing on local properties often fail on large graphs.
method Weisfeiler-Lehman algorithm with stochastic approximation.
result Our kernel outperforms state-of-the-art on graph classification benchmarks.
In this paper, we unify the Markov theory of a variety of different types of graphs used in graphical Markov models by introducing the class of loopless mixed graphs, and show that all independence models induced by m-separation on such graphs are compositional graphoids. We focus in particular on the subclass of rib…
New graph kernel scales well with graph size and number, achieving state-of-the-art performance.
problem Graph kernels lose structure information when representing graphs.
method Proposes a positive-definite global alignment graph kernel using random features and random graph embeddings.
result Achieves quasi-linear scalability with respect to graph size and number.
PAGTN improves molecular property prediction by leveraging longer-range graph dependencies.
problem Local aggregation in GCNs misses higher-order graph properties.
method PAGTN uses path features and global attention layers to capture longer-range dependencies.
result PAGTN outperforms GCNs on various molecular property prediction datasets.
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…
Geometric approach monitors dynamic large graphs, detects major events.
problem Monitoring dynamic large graphs is challenging due to local changes affecting global properties.
method Developed a geometric approach using Ollivier-Ricci curvature for real-time monitoring.
result Detects major events and changes via graph embedding geometry.
Graphs from knot types help identify unique knots.
problem Identifying knots uniquely.
method Created Reidemeister graphs from knot types and analyzed their properties.
result Graph isomorphism type is a complete knot invariant.
Study shows how discrete graph curvature relates to manifold curvature.
problem Relating discrete graph curvature to intrinsic manifold curvature.
method Continuum limits of Ollivier's Ricci curvature on data clouds.
result Random geometric graphs inherit global curvature properties of manifolds.
We present an equivalent criterion for the global existence of Euler's multiplier for an integrable one-form taking into account the corresponding codim-1-foliation. In particular, the impact of inseparable leaves is considered. Here, we suppose that the foliation can be reduced to a graph; we also discuss obstructions…
Embeds directed graphs into statistical manifolds for better geodesic preservation.
problem Preserving global geodesic information in directed graphs.
method Global minimization of pairwise relative entropy and graph geodesics.
result Our embedding outperforms existing models in various evaluation metrics.
A new readout layer improves graph property prediction.
problem Graph property prediction challenges due to information loss.
method Introduces a novel generalized global pooling layer for Message-Passing Neural Networks.
result New state-of-the-art results in graph property prediction.
The paper tests properties of trees in graphical models using covariance queries.
problem Testing properties of trees in graphical models.
method Covariance queries model, randomized tests for tree properties.
result Efficient testing of global tree properties using sub-quadratic number of queries.
A reinforcement learning algorithm improves graph construction for robustness.
problem Improving graph construction for specific objectives.
method Reinforcement learning and graph neural networks.
result The approach outperforms existing methods in robustness.
New graph models relax constraints for acyclic directed mixed graphs.
problem Modeling directed cycles and correlated errors in mixed graphs.
method Introducing new Markov and causal properties, interpreting as structural equations, and developing an exact algorithm.
result New models can be interpreted as systems of structural equations with correlated errors.
New spectral conditions ensure graph rigidity and global rigidity in the Euclidean plane.
problem Ensuring graph rigidity and global rigidity in the Euclidean plane.
method Improving algebraic connectivity bounds for graph rigidity and global rigidity.
result Every 6-connected graph is rigid and globally rigid if its algebraic connectivity exceeds specific thresholds.
Stable cylinders found in hyperbolic groups and curve graphs.
problem Torsionfree hyperbolic groups and curve graphs of surfaces have globally stable cylinders.
method Generalised Sageev's construction to improve fine properties of hyperbolic spaces.
result Proved curve graphs of surfaces admit equivariant quasi-isometric embeddings in finite products of quasitrees.
New graph model relaxes acyclic constraint for better flexibility.
problem Graphical model constraints limit flexibility.
method Introduces new graphical models with relaxed constraints.
result New models allow directed cycles and up to two edges between nodes.
This paper improves GNNs' generalization by adding a Low-Rank Global Attention module.
problem Improving the generalization power of Graph Neural Networks (GNNs).
method Incorporating a Low-Rank Global Attention (LRGA) module into GNNs.
result Augmenting GNNs with LRGA aligns them with a powerful graph isomorphism test, 2-Folklore Weisfeiler-Lehman (2-FWL).
New graph model handles cycles and latent variables.
problem Models for cycles and latent variables.
method Directed graphs with hyperedges (HEDGes), Markov properties.
result Markov properties for HEDGes are not equivalent.
A new method classifies signals on irregular domains using convolutional cluster pooling.
problem Classifying signals on irregular domains with shared properties.
method Convolutional Cluster Pooling layer exploiting multi-scale clustering.
result Generalizes CNNs for graph data, capturing both local and global patterns.
Large graphs abound in machine learning, data mining, and several related areas. A useful step towards analyzing such graphs is that of obtaining certain summary statistics - e.g., or the expected length of a shortest path between two nodes, or the expected weight of a minimum spanning tree of the graph, etc. These sta…
A new graph model HMG and neural network HMGNN improve molecule property predictions.
problem Predicting quantum mechanical properties of molecules with limited consideration of many-body interactions.
method Introducing heterogeneous molecular graphs (HMG) and building HMGNN on neural message passing scheme.
result HMGNN achieves state-of-the-art performance in 9 out of 12 tasks on the QM9 dataset.
Study inverse mean curvature flow on entire graphs, proving finite time existence for certain asymptotic cases.
problem Analyzing the evolution of entire graphs under inverse mean curvature flow.
method Global existence for starshaped graphs, critical case analysis for asymptotically conical graphs.
result Existence of a finite time \( T \) for certain asymptotically conical graphs, convergence to a flat plane as \( t o T \).
New G-GNN models learn global graph info for better node learning.
problem Learning distant node info and handling plain graphs.
method Unsupervised pre-training for global features, parallel GNN framework.
result G-GNNs outperform other models on standard graphs.
Graph coloring is explained using a topological field theory with defects.
problem Graph coloring as a combinatorial problem is quantum in nature.
method Topological field theory with defects to interpret graph coloring.
result Graph coloring is related to sections of a certain bundle.
Study continuity of phi-invariant for degenerating graphs.
problem Continuity of phi-invariant for degenerating graphs.
method Use Yuan--Zhang's adelic divisors and follow Yuan's globalization of phi-invariants.
result Asymptotic expression of Zhang--Kawazumi's invariants for Riemann surfaces near the boundary of the moduli space.
We define a new notion of total curvature, called net total curvature, for finite graphs embedded in Rn, and investigate its properties. Two guiding principles are given by Milnor's way of measuring the local crookedness of a Jordan curve via a Crofton-type formula, and by considering the double cover of a given graph …
Model forecasts global stock market volatility using dynamic graphs and all trading days.
problem Enhance forecasting accuracy and practical utility in global stock market volatility.
method Spatial-temporal graph neural network architecture to capture volatility spillover effect.
result Forecasting performance surpasses baseline models in all scenarios.
Global graph structure improves GNN performance.
problem Limited graph structure in GNNs leads to indistinguishable node embeddings.
method Empirically tested the impact of global graph information on GNN performance.
result Global information can significantly improve GNN performance by more than 5%.
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…
GNNs may be limited by graph topology, affecting their learning outcomes.
problem Understanding how graph topology influences GNN behavior and performance.
method Investigating the interaction between local topological features and GNN message-passing schemes.
result Locally similar neighborhoods can lead to consistent node representations, affecting GNN performance.
Sharp global Poincaré inequality on graphs via curvature-dimension conditions.
problem Finding a sharp global Poincaré inequality on graphs.
method Introducing and studying the conical curvature-dimension condition, CCD(K,N). result Sharp global Poincaré inequality and eigenvalue bounds on graphs.
Graph Signal Processing improves stock market volatility forecasting.
problem Forecasting realized volatility in a global stock market context.
method Integrating Graph Signal Processing into the HAR model.
result The proposed model outperforms HAR-type benchmarks.
New MLG kernels account for multi-scale graph structures.
problem Existing graph kernels are either local or global, ignoring multi-scale structures.
method Builds a hierarchy of nested subgraphs and uses Feature Space Laplacian Graph kernels.
result MLG kernels can capture structure at multiple scales.
Dynamic Embedding learns text node representations in evolving graphs.
problem Learning text node embeddings in dynamic graphs.
method DetGP model using Gaussian process for non-parametric structure learning.
result DetGP efficiently updates embeddings for dynamic graphs without re-training.
Develops a model for causal discovery in path spaces.
problem Discover causal relationships in path spaces using asymmetric independence.
method Theory linking E-separation in DMGs to conditional independence in SDEs, proving global Markov property, characterizing equivalence classes of graphs.
result Each equivalence class of graphs has a greatest element as a parsimonious representation, which can be identified from data.
Classifies collective motions in biological networks using graph dynamic mode decomposition.
problem Classifying complex collective motions in biological networks based on transient and complexly changing network properties.
method Data-driven spectral analysis (graph dynamic mode decomposition) to extract dynamical properties.
result Contextual node information and physical properties are crucial for classifying collective motions.
New centrality-based graph shift operators improve graph neural networks.
problem Improving graph neural networks by enhancing graph shift operators.
method Proposed Centrality Graph Shift Operators (CGSOs) using global centrality metrics.
result CGSOs lead to improved performance in graph neural networks on real-world datasets.
Two ML frameworks predict antibody properties using structural data.
problem Predicting antibody properties using sequence and structural data.
method ANTIPASTI and INFUSSE models using graph representations and neural networks.
result ANTIPASTI predicts binding affinity; INFUSSE predicts residue flexibility.
The paper conjectures and proves fixed points for certain group actions on nonpositively curved spaces.
problem Actions by automorphisms of finitely generated groups on nonpositively curved complexes without fixed points.
method Use of Helly graphs and geodesic clique paths to prove ellipticity results.
result Finitely generated torsion groups cannot act without fixed points on nonpositively curved spaces.
Optimizes edge coloring in graph bundling for better edge differentiation.
problem Difficulty in identifying origins and destinations of individual edges in strongly bundled graphs.
method Optimizes edge coloring based on pairwise edge strength and origin-destination dissimilarity, solving a nonlinear optimization problem.
result Peacock bundles enhance graph layout comprehensibility with edge differentiation.
We discuss two parameterizations of models for marginal independencies for discrete distributions which are representable by bi-directed graph models, under the global Markov property. Such models are useful data analytic tools especially if used in combination with other graphical models. The first parameterization, i…
COMRECGC finds common recourse for global counterfactual explanations in GNNs.
problem Finding common recourse for global counterfactual explanations in GNNs.
method Formalized the common recourse explanation problem and designed COMRECGC algorithm.
result COMRECGC outperforms strong baselines on four real-world graph datasets.
DMGI embeds multiplex networks with node attributes without supervision.
problem Existing methods fail to handle node attributes and multiple relation types in multiplex networks.
method Inspired by DGI, DMGI maximizes mutual information between local and global graph representations, integrating node embeddings from multiple graphs.
result DMGI outperforms state-of-the-art methods on various downstream tasks.
We present a new family of models that is based on graphs that may have undirected, directed and bidirected edges. We name these new models marginal AMP (MAMP) chain graphs because each of them is Markov equivalent to some AMP chain graph under marginalization of some of its nodes. However, MAMP chain graphs do not onl…