Related papers: Word-Representation of Melon Graphs
The representation of graphs is commonly based on the adjacency matrix concept. This formulation is the foundation of most algebraic and computational approaches to graph processing. The advent of deep learning language models offers a wide…
We study a geometric representation problem, where we are given a set $\cal R$ of axis-aligned rectangles with fixed dimensions and a graph with vertex set $\cal R$. The task is to place the rectangles without overlap such that two…
A graph $G = (V, E)$ is word-representable, if there exists a word $w$ over the alphabet $V$ such that for letters $\{x,y\}\in V$, $x$ and $y$ alternate in $w$ if and only if $xy \in E$. A graph is co-bipartite if its complement is a…
In many ways, graphs are the main modality of data we receive from nature. This is due to the fact that most of the patterns we see, both in natural and artificial systems, are elegantly representable using the language of graph structures.…
Many models learn representations of knowledge graph data by exploiting its low-rank latent structure, encoding known relations between entities and enabling unknown facts to be inferred. To predict whether a relation holds between…
A graph G(V, E) is word-representable if there exists a word w over V such that distinct letters x and y alternate in w iff $xy \in E$. We introduce p-complete squares and p-complete square-free word-representable graphs. A word is…
While the problem of determining the representation number of an arbitrary word-representable graph is NP-hard, this problem is open even for bipartite graphs. The representation numbers are known for certain bipartite graphs including all…
Researchers have relegated natural language processing tasks to Transformer-type models, particularly generative models, because these models exhibit high versatility when performing generation and classification tasks. As the size of these…
A permutiple is a natural number whose representation in some base is an integer multiple of a number whose representation has the same collection of digits. A previous paper utilizes a finite-state-machine construction and its state graph…
Distinct letters $x$ and $y$ alternate in a word $w$ if after deleting in $w$ all letters but the copies of $x$ and $y$ we either obtain a word of the form $xyxy\cdots$ (of even or odd length) or a word of the form $yxyx\cdots$ (of even or…
Simple conceptual graphs are considered as the kernel of most knowledge representation formalisms built upon Sowa's model. Reasoning in this model can be expressed by a graph homomorphism called projection, whose semantics is usually given…
A graph $G = (V, E)$ is word-representable, if there exists a word w over the alphabet V such that for letters ${x, y} \in V$ , $x$ and $y$ alternate in $w$ if and only if $xy \in E$. In this paper, we prove that any non-empty…
In this paper, we discuss a method for identifying a seed word that would best represent a class of named entities in a graphical representation of words and their similarities. Word networks, or word graphs, are representations of…
A graph $G$ with vertex set $V(G)$ and edge set $E(G)$ is said to be word-representable if there exists a word $w$ over the alphabet $V(G)$ such that, for any two distinct letters $x,y \in V(G)$, the letters $x$ and $y$ alternate in $w$ if…
Learning to fuse vision and language information and representing them is an important research problem with many applications. Recent progresses have leveraged the ideas of pre-training (from language modeling) and attention layers in…
A graph is called $k$-representable if there exists a word $w$ over the nodes of the graph, each node occurring exactly $k$ times, such that there is an edge between two nodes $x,y$ if and only after removing all letters distinct from…
Recent findings in neuroscience suggest that the human brain represents information in a geometric structure (for instance, through conceptual spaces). In order to communicate, we flatten the complex representation of entities and their…
The popular bag of words assumption represents a document as a histogram of word occurrences. While computationally efficient, such a representation is unable to maintain any sequential information. We present a continuous and…
One major deficiency of most semantic representation techniques is that they usually model a word type as a single point in the semantic space, hence conflating all the meanings that the word can have. Addressing this issue by learning…
Network or graph structures are ubiquitous in the study of complex systems. Often, we are interested in complexity trends of these system as it evolves under some dynamic. An example might be looking at the complexity of a food web as…