Proposes a method for coarse graph alignment using sparse partial least squares.
problem Aligning graphs with community structures when there's no natural one-to-one mapping.
method Sparse partial least squares method incorporating observed graph structures and imposing sparsity.
result Demonstrates effectiveness in simulations.
G-CREWE efficiently aligns large networks using node embeddings and compression.
problem Efficiently aligning large networks for various applications.
method Uses node embeddings and compression to align networks at fine and coarse resolutions.
result G-CREWE achieves efficient and accurate network alignment, twice as fast as existing methods.
Study semi-coarse spaces' homotopy and homology, extending coarse geometry.
problem Extend homotopy and homology concepts to semi-coarse spaces.
method Analyze homotopy and construct homology groups invariant under semi-coarse homotopy equivalence.
result Show semi-coarse homology is isomorphic to Vietoris-Rips homology for graphs.
Study recovers community structure from coarse graph measurements.
problem Community recovery from low-resolution graph measurements.
method Formalized coarsening process of graph measurements, developed conditions for perfect recovery.
result Simple and closed-form asymptotic conditions for perfect recovery of coarse graph communities.
Study of mapping class groups on infinite graphs, focusing on their large-scale geometry.
problem Understanding the large-scale geometry of mapping class groups on infinite graphs.
method Using coarse geometry techniques, classify coarsely bounded groups and compute asymptotic dimension.
result Identify conditions for global and local coarsely bounded pure mapping class groups of infinite rank graphs.
We introduce a new variant of the coarse Baum-Connes conjecture designed to tackle coarsely disconnected metric spaces called the boundary coarse Baum-Connes conjecture. We prove this conjecture for many coarsely disconnected spaces that are known to be counterexamples to the coarse Baum-Connes conjecture. In particula…
The study introduces Cayley--Abels--Rosendal graphs for Polish groups.
problem Understanding the structure of Polish groups through graph theory.
method Developing Cayley--Abels--Rosendal graphs and applying them to Polish groups.
result Groups with Cayley--Abels--Rosendal graphs are topological analogues of finitely generated groups.
Graph machine learning lacks a balanced theory, focusing on expressive power and optimization.
problem Insufficient theoretical understanding of GNNs' generalization behavior.
method Develop a balanced theory focusing on expressive power, generalization, and optimization.
result Theoretical advancements need to align with practical success in graph machine learning.
The study compares lamplighter graphs up to quasi-isometry using coarse topology.
problem When do two lamplighter graphs have the same coarse geometry?
method Inspired by topology, the approach involves techniques to compare lamplighter graphs up to quasi-isometry.
result Efficient comparison methods for lamplighter graphs up to quasi-isometry.
Aspect-level sentiment classification (ASC) aims at identifying sentiment polarities towards aspects in a sentence, where the aspect can behave as a general Aspect Category (AC) or a specific Aspect Term (AT). However, due to the especially expensive and labor-intensive labeling, existing public corpora in AT-level are…
Estimates for graph embeddings into symmetric spaces derived from coarse geometry.
problem Estimating optimal volume of graph embeddings into symmetric spaces.
method Coarse geometric thick embeddings and wiring techniques.
result Optimal and lower bounds for graph embeddings in symmetric spaces of different ranks.
This paper addresses questions of quasi-isometric rigidity and classification for fundamental groups of finite graphs of groups, under the assumption that the Bass-Serre tree of the graph of groups has finite depth. The main example of a finite depth graph of groups is one whose vertex and edge groups are coarse Poinca…
We show that the arc graph of Sg1 is a coarse Lipschitz retract of the free splitting complex of F2g. We also show that the arc and curve graph of Sg1 is a coarse Lipschitz retract of both the cyclic splitting graph of F2g and the maximally cyclic splitting graph of F2g.
We introduce a notion of fibred coarse embedding into Hilbert space for metric spaces, which is a generalization of Gromov's notion of coarse embedding into Hilbert space. It turns out that a large class of expander graphs admit such an embedding. We show that the maximal coarse Baum-Connes conjecture holds for metric …
Machine learning generates coarse-grained force fields for molecular dynamics.
problem Creating thermodynamically consistent coarse-grained models for larger systems.
method Hybrid architecture using graph neural networks to learn molecular features.
result Framework reproduces thermodynamics for small biomolecular systems.
Unique median structures found in hyperbolic spaces.
problem Uniqueness of median structures in hyperbolic spaces.
method Analyzing product of hyperbolic spaces and properties of relative hyperbolicity.
result Non-hyperbolic pants graphs can have unique median structures.
Characterizes quasiconformal homeomorphisms on surfaces.
problem Understanding the group of quasiconformal homeomorphisms on surfaces.
method Combinatorial characterization of quasiconformal homeomorphisms via graphs of essential quasicircles.
result Quasiconformal homeomorphisms are automorphisms of a graph of essential quasicircles on a surface.
New framework learns labels at both bag and graph levels.
problem Learning multi-label classifiers from multi-graph bags.
method Designing scoring functions and rank-loss objective for graph and bag levels; developing sub-gradient descent algorithm.
result Superior performance over state-of-the-art algorithms.
The paper explores non-amenability in infinite-type surfaces and graphs.
problem Determining non-amenability in mapping class groups of infinite-type surfaces and graphs.
method Analyzes mapping class groups of infinite-type surfaces and graphs, provides examples and exhibits classes of groups.
result Completely determines non-amenability of mapping class groups of infinite-type surfaces and graphs.
Graph neural network predicts optimal coarse-grained mapping operators.
problem Optimal coarse-grained mapping operators selection for molecular dynamics simulations.
method Graph Neural Network (DSGPM) trained on expert-annotated data.
result DSGPM outperforms state-of-the-art methods in graph segmentation.
The study combines graph-minors and metric spaces, answering some questions and conjectures.
problem Whether geodesic metric spaces without a fat H minor are quasi-isometric to graphs without H minor. method Combining graph-minors and coarse geometry, answering affirmatively for small H. result Affirmative answer for small H in the problem statement. Detecting correlated trees helps align sparse graphs.
problem Detecting correlation between trees for sparse random graphs.
method MPAlign message-passing algorithm for graph alignment.
result MPAlign succeeds in polynomial time for partial alignment.
Graph alignment in two correlated random graphs refers to the task of identifying the correspondence between vertex sets of the graphs. Recent results have characterized the exact information-theoretic threshold for graph alignment in correlated Erdős-Rényi graphs. However, very little is known about the existence of e…
Recent research in coarse geometry revealed similarities between certain concepts of analysis, large scale geometry, and topology. Property A of G.Yu is the coarse analog of amenability for groups and its generalization (exact spaces) was later strengthened to be the large scale analog of paracompact spaces using parti…
The study explores ends in coarse homotopy of proper geodesic spaces.
problem Understanding ends in coarse homotopy of proper geodesic spaces.
method Recontextualizing ends as a functor and proving properties of coarse path components.
result Existence of a natural surjection from coarse path components to ends, not always an injection.
New model generates larger molecules more effectively.
problem Previous graph generation techniques struggle with larger molecules.
method Hierarchical graph encoder-decoder using structural motifs.
result Model significantly outperforms previous baselines on molecule generation tasks.
Study on hyperbolic groups, focusing on separability and splittings.
problem Coarse separability and splittings in hyperbolic groups.
method Quantitative analysis of volume growth and cut-sets, focusing on thickened spheres.
result One-ended hyperbolic groups that are not virtually surface groups are coarsely separable by a subset of subexponential growth if and only if they split over a virtually cyclic subgroup.
Groups with specific properties have similar cubulations and coarse median structures.
problem Understanding the structure of certain groups through cubical coarsening.
method Analyzing right-angled Artin and Coxeter groups, focusing on automorphisms and cubulations.
result Automorphisms of specific groups preserve coarse median structures and have nice fixed subgroups.
The pants graph of a free group is constructed and studied.
problem Understanding the structure of free groups through graph theory.
method Developed a pants graph and studied its properties.
result The pants graph of a free group is connected and unbounded.
Study of pure mapping class groups on infinite graphs.
problem Classifying graphs with specific mapping class groups.
method Completely classified graphs with pure mapping class groups.
result Established semidirect product decomposition and computed first integral cohomology.
Classifies homeomorphism groups of countable Stone spaces up to coarse equivalence.
problem Classifying non-locally compact topological groups using geometric group theory.
method Classification based on coarsely bounded sets and quasi-isometry.
result Groups in the second class are quasi-isometric to the Hamming cube.
A novel method for comparing graphs of different sizes using Wasserstein distance.
problem Comparing non-aligned graphs of varying sizes.
method Optimal transport in graph comparison framework, solving a one-to-many assignment problem.
result Significant improvements in graph alignment and classification tasks.
Bayesian framework proves thresholds for multi-graph alignment feasibility.
problem Determining when multi-graph alignment is statistically possible.
method Developed a Bayesian estimation framework over metric spaces.
result Identified thresholds for Gaussian and sparse Erdős-Rényi models.
This paper studies aligning knowledge graphs from different sources or languages. Most existing methods train supervised methods for the alignment, which usually require a large number of aligned knowledge triplets. However, such a large number of aligned knowledge triplets may not be available or are expensive to obta…
We study the geometry of warped cones over free, minimal isometric group actions and related constructions of expander graphs. We prove a rigidity theorem for the coarse geometry of such warped cones: Namely, if a group has no abelian factors, then two such warped cones are quasi-isometric if and only if the actions ar…
New method aligns brain surfaces based on functional signatures.
problem Inter-individual variability in neuroimaging data.
method Fused Unbalanced Gromov-Wasserstein (FUGW) based on Optimal Transport.
result FUGW significantly increases between-subject correlation of activity.
Graph-Relational Domain Adaptation (GRDA) adapts domains based on their graph structure.
problem Uniform alignment of domains ignores topological structures.
method Uses a domain graph to encode adjacency and a novel graph discriminator.
result Empirically shows improved generalization and domain information incorporation.
We introduce a novel definition of curvature for hypergraphs, a natural generalization of graphs, by introducing a multi-marginal optimal transport problem for a naturally defined random walk on the hypergraph. This curvature, termed \emph{coarse scalar curvature}, generalizes a recent definition of Ricci curvature for…
LP-SparseMAP relaxes SparseMAP for more complex structures.
problem SparseMAP's tractable MAP inference oracle limits its applicability.
method Local polytope relaxation for factor graphs.
result LP-SparseMAP outperforms SparseMAP and Structured SVM in structured prediction tasks.
Study on connectivity and geometry of random Coxeter groups.
problem Connectivity threshold for square percolation on random graphs.
method Probabilistic combinatorics and techniques from geometric group theory.
result Determines connectivity threshold and cubical coarse median structure for random Coxeter groups.
Statistical-computational gap found in aligning multiple Gaussian graphs.
problem Aligning multiple Gaussian graphs with unknown signals.
method Generalized informational threshold and computational barrier analysis.
result Existence of a statistical-computational gap in multiple Gaussian graph alignment.
Study on matching nodes between graphs to preserve edges, focusing on limits and algorithms.
problem Matching nodes between graphs to preserve most edges, especially in random graphs.
method Investigates fundamental limits and designs algorithms to recover alignments in planted graphs.
result High probability guarantees on the success or failure of graph alignment algorithms.
A new neural network model for molecular graphs that learns efficiently and accurately.
problem Learning on molecular graphs with cycles and complex structures.
method Hierarchical inter-message passing using raw graph and junction tree representations.
result The model outperforms classical GNNs in detecting cycles and is efficient to train.
DHGAK aligns substructures for better graph kernel performance.
problem Limited performance of traditional graph kernels due to missing substructure similarities.
method Hierarchically aligns relational substructures in deep embedding space, assigning same feature maps in RKHS.
result DHGAK outperforms state-of-the-art graph kernels on various benchmarks.
New method calculates Ricci curvature from distances between weighted volumes.
problem Calculating Ricci curvature for weighted Riemannian manifolds.
method Asymptotic retrieval of generalized Ricci tensor from scaled metric derivatives of Wasserstein 1-distances.
result Limiting coarse curvature of random graphs converges to generalized Ricci tensor.
New method separates graph structure from node attributes to recover lost signal.
problem Standard representation learning on attributed graphs merges incompatible metric spaces, leading to geometrically flawed alignment.
method Custom variational autoencoder that separates manifold learning from structural alignment.
result Transforms geometric conflict into interpretable structural descriptor, uncovering connectivity patterns and anomalies.
In this paper, we prove that certain spaces are not quasi-isometric to Cayley graphs of finitely generated groups. In particular, we answer a question of Woess and prove a conjecture of Diestel and Leader by showing that certain homogeneous graphs are not quasi-isometric to a Cayley graph of a finitely generated group.…
Researchers prove it's impossible to partially recover graph alignments in certain conditions.
problem Recovering vertex correspondence between two random graphs with correlated edges.
method Used the probabilistic method to build automorphisms between tree components of a subcritical Erdös-Rényi graph.
result Proved an impossibility result for partial recovery in the sparse regime with constant average degree and correlation.