arXiv research

SLiCE learns contextual node embeddings for link prediction in heterogeneous networks.

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.

ProbETA models travel time correlations between trips for better navigation.

GAP learns node representations by attending to different parts of its neighborhood.

Link groups can only have certain SU(2) representations.

Satellite links with many twists have simpler companions.

GOAT learns multiple node representations from graph structure alone.

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.

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 …

Learning knowledge representation is an increasingly important technology applicable in many domain-specific machine learning problems. We discuss the effectiveness of traditional Link Prediction or Knowledge Graph Completion evaluation protocol when embedding knowledge representation for categorised multi-relational d…

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.

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.

The paper connects Apollonian packings to knot theory and improves link representations.

Given a link $L$, a representation $π_1(S^{3}-L)\to {\rm SL}(2,\mathbb{C})$ 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.

GRADE models evolving graph dynamics by learning node and community representations.

Given a link $L\subset S^3$, a representation $π_1(S^3-L)\to{\rm SL}(2,\mathbb{C})$ is {\it trace-free} if it sends each meridian to an element with trace zero. We present a method for completely determining trace-free ${\rm SL}(2,\mathbb{C})$-representations for arborescent links. Concrete computations are done for a …

New findings clarify the link between distributional closeness and representational similarity.

Stratifies representation varieties of twisted Hopf links.

New invariants for virtual knots and links defined via quiver representations.

The paper defines new representations and groups related to virtual links.

We study an $A_\infty$ category associated to Legendrian links in $\mathbb{R}^3$ 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.

We introduce a multivariable Casson-Lin type invariant for links in $S^3$. This invariant is defined as a signed count of irreducible $\operatorname{SU}(2)$ 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.

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 …

Learning knowledge representation is an increasingly important technology that supports a variety of machine learning related applications. However, the choice of hyperparameters is seldom justified and usually relies on exhaustive search. Understanding the effect of hyperparameter combinations on embedding quality is …

We describe a family of representations in SL(3,$\mathbb C$) 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,$\mathbb C$) and can be seen as factorising through a quotient of $π$ defined by a certain exception…

Study links using Soergel bimodules and Serre duality.

The paper studies parabolic representations of 2-bridge links using symplectic quandles.

Method learns hierarchical representations of samples and features simultaneously.

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.

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.

This paper learns graph node representations using global context prediction.

The paper enhances representations to show left-orderability of certain 3-manifold groups.

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 $K_6$, t…

GraphCL learns node representations by maximizing similarity between perturbed node features.

New 2-representations link spectral enhancements in link homology.