Related papers: Word-Representation of Melon Graphs
Molecular representation learning (MRL) is a key step to build the connection between machine learning and chemical science. In particular, it encodes molecules as numerical vectors preserving the molecular structures and features, on top…
Multi-layer graphs consist of several graphs (layers) over the same vertex set. They are motivated by real-world problems where entities (vertices) are associated via multiple types of relationships (edges in different layers). We chart the…
Idiomatic expressions are an integral part of human languages, often used to express complex ideas in compressed or conventional ways (e.g. eager beaver as a keen and enthusiastic person). However, their interpretations may not be…
Recent literature shows that large-scale language modeling provides excellent reusable sentence representations with both recurrent and self-attentive architectures. However, there has been less clarity on the commonalities and differences…
We consider two graph models of semantic change. The first is a time-series model that relates embedding vectors from one time period to embedding vectors of previous time periods. In the second, we construct one graph for each word: nodes…
We present a family of neural-network--inspired models for computing continuous word representations, specifically designed to exploit both monolingual and multilingual text. This framework allows us to perform unsupervised training of…
Isomorphisms allow human cognition to transcribe a potentially unsolvable problem from one domain to a different domain where the problem might be more easily addressed. Current approaches only focus on transcribing structural information…
The representation space of pretrained Language Models (LMs) encodes rich information about words and their relationships (e.g., similarity, hypernymy, polysemy) as well as abstract semantic notions (e.g., intensity). In this paper, we…
We consider the problems of finding optimal identifying codes, (open) locating-dominating sets and resolving sets (denoted IDENTIFYING CODE, (OPEN) LOCATING-DOMINATING SET and METRIC DIMENSION) of an interval or a permutation graph. In…
Many finite groups, including all finite non-abelian simple groups, can be symmetrically generated by involutions. In this paper we give an algorithm to symmetrically represent elements of finite groups and to transform symmetrically…
In this paper, we consider representations of integers as sums of at most four distinct $m$-gonal numbers (allowing a fixed number of repeats of each polygonal number occurring in the sum). We show that the number of such representations…
A segment representation of a graph is an assignment of line segments in 2D to the vertices in such a way that two segments intersect if and only if the corresponding vertices are adjacent. Not all graphs have such segment representations,…
An {\it overlap representation} of a graph $G$ assigns sets to vertices so that vertices are adjacent if and only if their assigned sets intersect with neither containing the other. The {\it overlap number} $\ol(G)$ (introduced by Rosgen)…
The distinguishing number of a permutation group $G\leqslant\Sym(\Omega)$ is the minimum number of colours needed to colour $\Omega$ in such a way that the only colour preserving element of $G$ is the identity. The distinguishing number of…
In this purely experimental work we try to represent the set of plane maps with 3 vertices and 3 faces as a bipartite ribbon graph. In particular, this construction allows one to estimate the genus of the initial set.
Graphical models capture relations between entities in a wide range of applications including social networks, biology, and natural language processing, among others. Graph neural networks (GNN) are neural models that operate over graphs,…
Large language models have evolved to process multiple modalities beyond text, such as images and audio, which motivates us to explore how to effectively leverage them for graph reasoning tasks. The key question, therefore, is how to…
Semantic word clouds visualize the semantic relatedness between the words of a text by placing pairs of related words close to each other. Formally, the problem of drawing semantic word clouds corresponds to drawing a rectangle contact…
We introduce proof terms for string rewrite systems and, using these, show that various notions of equivalence on reductions known from the literature can be viewed as different perspectives on the notion of causal equivalence. In…
Semantic Heterogeneity is conventionally understood as the existence of variance in the representation of a target reality when modelled, by independent parties, in different databases, schemas and/ or data. We argue that the mere encoding…