SLiCE learns contextual node embeddings for link prediction in heterogeneous networks.
problem Link prediction requires specific contextual information not captured by static node embeddings.
method Self-supervised pre-training with localized attention mechanisms.
result SLiCE significantly outperforms existing methods on link prediction tasks.
We examine two fundamental tasks associated with graph representation learning: link prediction and semi-supervised node classification. We present a novel autoencoder architecture capable of learning a joint representation of both local graph structure and available node features for the multi-task learning of link pr…
The Tong-Yang-Ma representations are extended to string links and welded string links.
problem Extending Tong-Yang-Ma representations to string links and welded string links.
method Using the method of Silver and Williams, the authors extend the Tong-Yang-Ma representations.
result The kernels of the extended representations can be described using linking numbers.
Proposes clustering as a new evaluation method for clinical knowledge embedding.
problem Traditional Link Prediction evaluation protocol loses information and harms model accuracy.
method Proposes Clustering Evaluation Protocol as an alternative.
result Experimental results show the proposed protocol can potentially replace Link Prediction.
ProbETA models travel time correlations between trips for better navigation.
problem Trip correlations not captured by existing methods.
method Deep hierarchical joint probabilistic model with learnable link representations.
result ProbETA outperforms state-of-the-art methods with 12.60% MAPE reduction.
GAP learns node representations by attending to different parts of its neighborhood.
problem Context-free learning of node representations in graph representation learning.
method Graph Neighborhood Attentive Pooling (GAP) using attentive pooling networks.
result GAP outperforms 10 state-of-the-art methods on link prediction and clustering tasks.
Link groups can only have certain SU(2) representations.
problem Characterizing SU(2) representations of link groups.
method Analyzing the structure of link groups and their representations in SU(2).
result Irreducible SU(2) representations of link groups are restricted to specific configurations.
GOAT learns multiple node representations from graph structure alone.
problem Context-free graph representation learning limits model performance.
method Inspired by gossip and mutual attention, GOAT learns multiple node representations.
result GOAT outperforms 12 SOTA baselines on link prediction and clustering tasks.
Satellite links with many twists have simpler companions.
problem Relationship between satellite and companion links' complexity.
method Constructing satellite links with multiple full twists and analyzing their companion links.
result Satellite links with many twists have simpler companion links.
Relational data representations have become an increasingly important topic due to the recent proliferation of network datasets (e.g., social, biological, information networks) and a corresponding increase in the application of statistical relational learning (SRL) algorithms to these domains. In this article, we exami…
We construct the augmentation representation. It is a representation of the fundamental group of the link complement associated to an augmentation of the framed cord algebra. This construction connects representations of two link invariants of different types. We also study properties of the augmentation representation…
Study representation varieties of twisted Hopf links using combinatorial and Hodge theory.
problem Representation theory of Hopf link complements with n twists.
method Combinatorial problem and equivariant Hodge theory.
result Close formulas for E-polynomials of representation and character varieties for ranks 2 and 3.
A realization of a virtual link diagram is obtained by choosing over/under markings for each virtual crossing. Any realization can also be obtained from some representation of the virtual link. (A representation of a virtual link is a link diagram on an oriented 2-dimensional surface.) We prove that if a minimal genus …
We examine two fundamental tasks associated with graph representation learning: link prediction and node classification. We present a new autoencoder architecture capable of learning a joint representation of local graph structure and available node features for the simultaneous multi-task learning of unsupervised link…
The paper introduces two-tone colorings for links and shows conditions for surjective dihedral representations.
problem The challenge is to find conditions for links to admit surjective dihedral representations.
method The method involves introducing two-tone colorings and providing conditions for the link groups to admit such representations.
result Any link with at least 3 components admits a surjective homomorphism to the dihedral group of arbitrary degree.
Learning latent representations of nodes in graphs is an important and ubiquitous task with widespread applications such as link prediction, node classification, and graph visualization. Previous methods on graph representation learning mainly focus on static graphs, however, many real-world graphs are dynamic and evol…
Persona2vec learns multiple node roles in graphs.
problem Graphs often have nodes with multiple overlapping roles.
method Persona2vec learns multiple node representations based on structural contexts.
result Persona2vec outperforms state-of-the-art models in link prediction.
Study evaluates margin parameter effects on knowledge embedding quality.
problem Understanding margin parameter's impact on embedding quality.
method Examined margin parameter values for multi-relational categorized data.
result Lower margin values are insufficient, while larger values cause noise.
The paper connects Apollonian packings to knot theory and improves link representations.
problem Realizing algebraic links in Apollonian packings.
method Introducing new representations of links in tangency graphs of sphere packings, proving link realizability, and improving upper bounds.
result Any algebraic link can be realized in the cubic section of the orthoplicial Apollonian packing.
GRADE models evolving graph dynamics by learning node and community representations.
problem Lack of tools to study temporal community dynamics in evolving graphs.
method GRADE is a probabilistic model that learns evolving node and community representations via a random walk prior and variational inference.
result GRADE outperforms baselines in dynamic link prediction and dynamic community detection.
Given a link L, a representation π1(S3−L)→SL(2,C) is {\it tracefree} if the image of each meridian has trace zero. We determine the conjugacy classes of tracefree representations when L is a Montesinos link.
Study multiplicity of non-acyclic SL2-representations and L-functions of Whitehead links.
problem Understanding the multiplicity of non-acyclic SL2-representations and their L-functions.
method Geometric interpretation of Reidemeister torsion divisors and application to L-functions.
result Prove multiplicity two for odd-twisted Whitehead links.
Given a link L⊂S3, a representation π1(S3−L)→SL(2,C) is {\it trace-free} if it sends each meridian to an element with trace zero. We present a method for completely determining trace-free SL(2,C)-representations for arborescent links. Concrete computations are done for a …
New findings clarify the link between distributional closeness and representational similarity.
problem When and why do different neural network representations become similar?
method Identifiability theory, focusing on model families including autoregressive language models.
result Small Kullback-Leibler divergence does not guarantee similar representations.
Stratifies representation varieties of twisted Hopf links.
problem Stratifying representation varieties of twisted Hopf links.
method Using stratification of AGLr(C)-representation varieties of the fundamental group of the complement of a twisted Hopf link. result Explicit description and computation of motives for ranks 1 and 2.
New invariants for virtual knots and links defined via quiver representations.
problem Defining new invariants for virtual knots and links.
method Quiver representations associated to virtual biquandles and rings.
result New polynomial invariants for virtual knots and links.
The paper defines new representations and groups related to virtual links.
problem Defining and studying new representations of virtual braid groups and link groups.
method Introducing virtually symmetric representations, virtual link groups, and marked Gauss diagrams.
result Established equivalence of many known representations to virtually symmetric representations.
We study an A∞ category associated to Legendrian links in R3 whose objects are n-dimensional representations of the Chekanov-Eliashberg differential graded algebra of the link. This representation category generalizes the positive augmentation category and we conjecture that it is equivalent to a …
This is an expository article on diagrammatic representations of knots and links in various settings via braids.
FakeEdge tackles dataset shift in link prediction tasks.
problem Dataset shift between training and testing sets in link prediction.
method Model-agnostic technique to mitigate graph topological gap.
result Extensive experiments show FakeEdge's superiority on multiple datasets.
We introduce a multivariable Casson-Lin type invariant for links in S3. This invariant is defined as a signed count of irreducible SU(2) representations of the link group with fixed meridional traces. For 2-component links with linking number one, the invariant is shown to be a sum of multivariable …
In this paper we investigate the virtual string links via a probabilistic interpretation. This representation can be used to distinguish some virtual string links from classical string links. In order to study the algebraic structure behind this probabilistic interpretation we introduce the notion of virtual flat biqua…
Extends Benard-Conway invariant to all two-component links.
problem Counting irreducible SU(2) representations for two-component links.
method Counting irreducible SU(2) representations with fixed meridional traces.
result Invariant equals symmetrized multivariable link signature for (2, 2n)-torus links.
This paper gives a connection between well chosen reductions of the Links-Gould invariants of oriented links and powers of the Alexander-Conway polynomial. We prove these formulas by showing the representations of the braid groups we derive the specialized Links-Gould polynomials from can be seen as exterior powers of …
We describe a family of representations in SL(3,C) of the fundamental group π of the Whitehead link complement. These representations are obtained by considering pairs of regular order three elements in SL(3,C) and can be seen as factorising through a quotient of π defined by a certain exception…
The paper studies parabolic representations of 2-bridge links using symplectic quandles.
problem Parabolic representations of 2-bridge links.
method Convert conjugation quandle equations to symplectic quandle equations, using a polynomial PK(u) to find arc coloring vectors. result Explicit formulas for parabolic representations of 2-bridge links are derived, including complex volume and cusp shape.
Study links using Soergel bimodules and Serre duality.
problem Computing the triply-graded homology of the Whitehead link.
method Representability of partial trace functors and diagrammatics for Hochschild cohomology.
result Computed the triply-graded homology of the Whitehead link.
Method learns hierarchical representations of samples and features simultaneously.
problem Hierarchical structures in samples and features not considered by existing methods.
method Jointly learns hierarchical representations via Tree-Wasserstein Distance alternating between samples and features.
result Method improves performance in link prediction and node classification tasks.
Using the recently proposed differential hierarchy (Z-expansion) technique, we obtain a general expression for the HOMFLY polynomials in two arbitrary symmetric representations of link families, including Whitehead and Borromean links. Among other things, this allows us to check and confirm the recent conjecture of arX…
Obtaining colored HOMFLY-PT polynomials for knots from 3-strand braid carrying arbitrary SU(N) representation is still tedious. For a class of rank r symmetric representations, [r]-colored HOMFLY-PT H[r] evaluation becomes simpler. Recently it was shown that H[r], for such knots from 3-strand braid, can…
Proposes a comprehensive framework for financial product lead recommendations using graph representation learning and link prediction.
problem Challenges in surface lead recommendations for financial products due to changing market scenarios and difficulty in capturing holder's mindset.
method Bi-partite graph representation of financial holders and funds, GraphSage model for learning representations, link prediction model for ranking recommendations.
result The proposed graph ML solution outperforms baseline by 42%, 22%, and 14% in hit rate for top-k recommendations (50, 100, 200) and 18%, 19%, and 18% on unseen holders.
We present a new link invariant which depends on a representation of the link group in SO(3). The computer calculations indicate that an abelian version of this invariant is expressed in terms of the Alexander polynomial of the link. On the other hand, if we use non abelian representation, we get the squared non abelia…
Model learns evolving network relationships over time.
problem Dimension reduction for dynamic network data.
method Metric functional space for vector-valued functions.
result Effective link prediction and role identification in dynamic networks.
This paper learns graph node representations using global context prediction.
problem Efficiently learning useful node representations from unlabeled graph data.
method Randomly selects node pairs, trains a neural net to predict contextual positions.
result Our approach outperforms many unsupervised methods and sometimes supervised ones.
The paper enhances representations to show left-orderability of certain 3-manifold groups.
problem Left-orderability of 3-manifold groups using enhanced representations.
method Recalibration of Calegari and Dunfield's flipping construction for $\mbox{Homeo}_+(S^1)$-representations.
result Branched covers of links are left-orderable, generalizing known results.
A book representation of a graph is a particular way of embedding a graph in three dimensional space so that the vertices lie on a circle and the edges are chords on disjoint topological disks. We describe a set of operations on book representations that preserves ambient isotopy, and apply these operations to K6, t…
GraphCL learns node representations by maximizing similarity between perturbed node features.
problem Learning node representations in graph data without labeled data.
method Contrastive learning of node embeddings using graph neural networks and a loss function.
result Significantly outperforms state-of-the-art in unsupervised node classification benchmarks.
New 2-representations link spectral enhancements in link homology.
problem Spectral enhancements in link homology.
method Skew Howe duality, frames, and multifunctors.
result Spectral 2-representations of categorified quantum groups.