Notes a flaw in a proof about embedding graphs.
problem A flaw in proving Sachs' conjecture about graph embeddings.
method Analyzing Stanfield's proof for gaps.
result Identifies a significant error in the proof.
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arXiv research
A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
168,695 papers · 148 categories
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48 results for “linkless embedding”
A maximally linkless graph is a graph that can be embedded in without any links, but cannot be embedded in such a way if any other edge is added to the graph. Recently, a family of maximally linkless graphs was found with edges. We improve upon this by demonstrating a new family of maximally lin…
Graphs embeddable on torus and linklessly in 3D can be embedded linklessly in standard torus.
problem Embedding linklessly in a standard torus for graphs embeddable on torus and in 3D.
method Analyzing graphs of order 9 and below, showing linkless embedding in standard torus.
result For graphs of order 9 and below, linkless embedding in standard torus is possible.
Classifies intrinsically linked tournaments by their score sequences.
problem Classifying intrinsically linked tournaments using their score sequences.
method Examining the score sequences of tournaments and identifying linkless sequences.
result The vast majority of score sequences for 8-vertex tournaments are linkless.
We announce results about flat (linkless) embeddings of graphs in 3-space. A piecewise-linear embedding of a graph in 3-space is called {\it flat} if every circuit of the graph bounds a disk disjoint from the rest of the graph. We have shown: (i) An embedding is flat if and only if the fundamental group of the compleme…
New bounds on maximal linkless graphs with improved edge-to-vertex ratios.
problem Finding maximal linklessly embeddable graphs with improved edge-to-vertex ratios.
method Constructing families of graphs and proving necessary and sufficient conditions for clique sums.
result Improved edge-to-vertex ratios for maximal linklessly embeddable graphs.
New graphs found that can be drawn without crossing links.
problem Finding graphs that can be drawn without links crossing.
method Provided specific examples for each .
result Infinite family of graphs linklessly embeddable and Tutte-4-connected.
A simpler proof for apex graphs in McCarty and Thomas' conjecture.
problem Proving a conjecture about apex graphs and their linklessly embeddable properties.
method Shorter and simpler proof for the apex case.
result A shorter and simpler proof for the apex case of the conjecture.
We consider intrinsic linking and knotting in the context of directed graphs. We construct an example of a directed graph that contains a consistently oriented knotted cycle in every embedding. We also construct examples of intrinsically 3-linked and 4-linked directed graphs. We introduce two operations, consistent edg…
Constructions stemming from non-separating planar graphs and their Colin de Verdière invariantmath.CO
New constructions from non-separating planar graphs improve understanding of graph linkability and knotability.
problem Understanding linkability and knotability of graph complements.
method Using maximal non-separating planar graphs to construct examples of maximal linkless and knotless graphs, and analyzing their Colin de Verdière invariant.
result The Colin de Verdière invariant of the complement of a maximal non-separating planar graph satisfies μ(cG) ≤ n-4, and equality holds.
Study finds maximal linklessly embeddable graphs up to 11 vertices and their complements.
problem Characterizing linklessly embeddable graphs and their complements.
method Comprehensive search and verification of graphs up to 11 vertices.
result For graphs of order 11, either the graph or its complement is intrinsically linked.
Study embeddability of 2-complexes in 4-space, proving Heawood family's excluded minors.
problem Whether a 2-dimensional CW complex embeds in .
method Operations preserving embeddability, constructions of non-preserving transformations, study of 4-flat graphs.
result Prove 78 graphs of Heawood family are excluded minors for 4-flat graphs.
The dominant graph neural networks (GNNs) over-rely on the graph links, several serious performance problems with which have been witnessed already, e.g., suspended animation problem and over-smoothing problem. What's more, the inherently inter-connected nature precludes parallelization within the graph, which becomes …
We review a cochain-free treatment of the classical van Kampen obstruction θto embeddability of an n-polyhedron into R^{2n} and consider several analogues and generalizations of θ, including an extraordinary lift of θwhich in the manifold case has been studied by J.-P. Dax. The following results are obtained. - The mod…
Embeddings are ubiquitous in machine learning, appearing in recommender systems, NLP, and many other applications. Researchers and developers often need to explore the properties of a specific embedding, and one way to analyze embeddings is to visualize them. We present the Embedding Projector, a tool for interactive v…
Proposes QQE for transforming and embedding data distributions.
problem Transforming and embedding data distributions for better representation or visualization.
method Quantile-Quantile Embedding (QQE) using quantile-quantile plot concept.
result QQE allows for better discrimination of classes in some cases.
Maps can be embedded in higher dimensions if they lift to embeddings in product spaces.
problem Embedding maps in higher dimensions without self-intersections.
method Lifting maps to embeddings in product spaces.
result Maps can be embedded in higher dimensions if they lift to embeddings in product spaces.
New embeddings for manifolds using heat kernels.
problem Constructing canonical conformal embeddings for manifolds.
method Employing heat kernel embedding from Bérard-Besson-Gallot'94 to find canonical conformal embeddings.
result Intrinsic construction of canonical conformal embeddings with dimensions growing exponentially with .
Introduces PELP for graph-enhanced word embeddings.
problem Combining graph side-information into static word embeddings.
method Probabilistic embeddings using Laplacian priors.
result Unified and flexible approach to various embedding methods.
Curvature regularization prevents distortion in graph embeddings.
problem Graph topology patterns distort in Euclidean space, making detection difficult.
method Proposes curvature regularization to enforce flatness in embedding manifolds.
result Significant improvements in five embedding methods on open graph datasets.
Word embeddings are a powerful approach for unsupervised analysis of language. Recently, Rudolph et al. (2016) developed exponential family embeddings, which cast word embeddings in a probabilistic framework. Here, we develop dynamic embeddings, building on exponential family embeddings to capture how the meanings of w…
Proposes cone embedding for better graph hierarchical structure representation.
problem Lack of natural and interpretable hierarchical indicators in graph embeddings.
method Metric cone embedding method to capture hierarchical structure.
result Extracts hierarchical structure from other graph embedding outputs.
Classifies linear embeddings of grassmannians and ind-grassmannians.
problem Understanding linear embeddings of grassmannians and ind-grassmannians.
method Classification through isomorphism of Picard groups and direct limits.
result Most linear embeddings of grassmannians are equivariant.
BC-Aligner maintains backward compatibility of embeddings after frequent updates.
problem Updating embeddings without requiring consumer teams to retrain their models.
method Learning backward compatible embeddings through BC-Aligner.
result BC-Aligner maintains backward compatibility with existing unintended tasks after multiple model version updates.
Embedding calculus proves convergence for surfaces.
problem Proving convergence of embedding calculus for surfaces.
method Goodwillie-Weiss' embedding calculus for spaces of embeddings into a manifold of dimension at most two.
result Relates Johnson filtration of mapping class group to embedding calculus.
Unified framework for word embedding models using noise examples.
problem Improving word embedding models with negative sampling.
method Formulated a Word-Context Classification (WCC) framework that generalizes SkipGram word embedding models.
result The best noise distribution is the data distribution, improving both performance and training speed.
Models use embeddings and attention for better claim severity prediction.
problem Improving predictive modeling of claim severity with categorical data.
method Developed neural networks and attention-based architectures with embeddings.
result Attention-based models enhance predictive performance with contextual augmentation.
A fast graph embedding method for large graphs.
problem Efficiently embedding large graphs for various applications.
method One-hot graph encoder embedding with linear complexity.
result Graph encoder embedding is approximately normally distributed and converges to its mean.
Paper proves impossibility of three desirable properties in node embedding.
problem Understanding limitations of node embedding methods.
method Axiomatic approach to node embedding, proving impossibility of three properties.
result No node embedding method can satisfy all three desirable properties simultaneously.
The study characterizes and verifies equivariant embeddings of symmetric Kählerian manifolds.
problem Characterizing and verifying equivariant embeddings of symmetric Kählerian manifolds.
method Investigation motivated by Cartan and Wallach's theorem on symmetric spaces, focusing on and parallel plurimean curvature.
result If an equivariant embedding has parallel plurimean curvature, it is the extrinsically symmetric one.
Proves uniqueness of embedding complex manifold into infinite-dimensional space.
problem Balanced embedding of non-compact complex manifold into infinite-dimensional projective space.
method Fine estimates of asymptotics of a balanced embedding.
result Uniqueness of embedding proven.
The paper defines invariants for almost graph embeddings and explores their properties.
problem Understanding the properties and limitations of almost graph embeddings in the plane.
method Introducing and analyzing integer invariants (winding number, Wu numbers) for almost embeddings.
result Some values of invariants are realizable for almost embeddings but not for embeddings.
Recently, click-through rate (CTR) prediction models have evolved from shallow methods to deep neural networks. Most deep CTR models follow an Embedding\&MLP paradigm, that is, first mapping discrete id features, e.g. user visited items, into low dimensional vectors with an embedding module, then learn a multi-layer pe…
This work analyzes PPR-based node embeddings and their topological information.
problem Understanding and interpreting PPR-based node embeddings.
method Unified framework and two methods for topology recovery.
result PPR-based embeddings maintain more topological information than random walk-based embeddings.
Network representation learning in low dimensional vector space has attracted considerable attention in both academic and industrial domains. Most real-world networks are dynamic with addition/deletion of nodes and edges. The existing graph embedding methods are designed for static networks and they cannot capture evol…
For leveled spatial graphs, we find a surface embedding that allows cellular embedding.
problem Finding a surface embedding for general spatial graphs is not always possible.
method Define leveled property, decompose graph into subgraphs, and construct surface.
result For leveled spatial graphs with a small number of levels, a surface can always be found.
Long spacelike embeddings can be approximated by isometric ones.
problem Approximating long embeddings to isometric embeddings in Lorentzian spaces.
method Proving approximation by constructing isometric embeddings.
result Long spacelike embeddings can be -approximated by isometric embeddings.
Wrinkled Embeddingsmath.GT
A {\it wrinkled embedding} is a topological embedding which is a smooth embedding everywhere on except a set of -dimensional spheres, where has cuspidal corners. In this paper we prove that any rotation of the tangent plane field of a {\it smoothly embedded} submanifold $V\s…
Graph embeddings have become a key and widely used technique within the field of graph mining, proving to be successful across a broad range of domains including social, citation, transportation and biological. Graph embedding techniques aim to automatically create a low-dimensional representation of a given graph, whi…
Geometrically transforms word embeddings into a common space for better comparison.
problem Comparing embeddings from different sources is challenging.
method Applies orthogonal rotations and Mahalanobis scaling to transform embeddings into a shared latent space.
result The method improves word similarity and analogy tasks.
Obtaining continuous representations of structural data such as directed acyclic graphs (DAGs) has gained attention in machine learning and artificial intelligence. However, embedding complex DAGs in which both ancestors and descendants of nodes are exponentially increasing is difficult. Tackling in this problem, we de…
The paper proves nonexistence and existence results for minimal surfaces in R^4.
problem Proving nonexistence and existence of minimal surfaces in R^4.
method Analyzing complete minimal immersions with finite total curvature and embedded planar ends.
result Existence of embedded minimal spheres in R^4 with 3 embedded planar ends.
Recent works reveal that network embedding techniques enable many machine learning models to handle diverse downstream tasks on graph structured data. However, as previous methods usually focus on learning embeddings for a single network, they can not learn representations transferable on multiple networks. Hence, it i…
MCE reduces embedding instability in nonlinear dimensionality reduction.
problem Embedding instability caused by random initialization.
method Median of multiple embeddings (MCE) based on large deviation theory.
result MCE achieves consistency at an exponential rate and effectively mitigates instability.
Natural language processing has improved tremendously after the success of word embedding techniques such as word2vec. Recently, the same idea has been applied on source code with encouraging results. In this survey, we aim to collect and discuss the usage of word embedding techniques on programs and source code. The a…
Paper uses JIVE to decompose word embeddings, improving sentiment analysis performance.
problem Improving sentiment analysis performance on word embeddings.
method Joint and individual variance explained (JIVE) method for decomposition.
result Mapping word embeddings into joint components improves sentiment analysis performance.
Well-quasi-orders proved on embedded planar graphs.
problem Proving well-quasi-orders on embedded planar graphs.
method Careful analysis and extensions of classical methods for embedded minor relations.
result Embedded minor relations are well-quasi-orders on various classes of embedded planar graphs.
We seek to better understand the difference in quality of the several publicly released embeddings. We propose several tasks that help to distinguish the characteristics of different embeddings. Our evaluation of sentiment polarity and synonym/antonym relations shows that embeddings are able to capture surprisingly nua…