Related papers: Word-Representation of Melon Graphs

Representations of sets are challenging to learn because operations on sets should be permutation-invariant. To this end, we propose a Permutation-Optimisation module that learns how to permute a set end-to-end. The permuted set can be…

We give an overview of combinatorial methods to represent 3D data, such as graphs and meshes, from the viewpoint of their amenability to analysis using machine learning algorithms. We highlight pros and cons of various representations and…

In this short note, we first associate a new simple undirected graph with a given word over an ordered alphabet of $n$-letters. We will call it the Lyndon graph of that word. Then, we introduce the concept of the Lyndon-word representable…

We study contact representations for graphs, which we call pixel representations in 2D and voxel representations in 3D. Our representations are based on the unit square grid whose cells we call pixels in 2D and voxels in 3D. Two pixels are…

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…

Over the last few years, machine learning over graph structures has manifested a significant enhancement in text mining applications such as event detection, opinion mining, and news recommendation. One of the primary challenges in this…

We obtain an upper and lower bound for the number of reduced words for a permutation in terms of the number of braid classes and the number of commutation classes of the permutation. We classify the permutations that achieve each of these…

This paper proposes a learning model, based on rank-fusion graphs, for general applicability in multimodal prediction tasks, such as multimodal regression and image classification. Rank-fusion graphs encode information from multiple…

(1) There is a finitely presented group with a word problem which is a uniformly effectively inseparable equivalence relation. (2) There is a finitely generated group of computable permutations with a word problem which is a universal…

We investigate topological, combinatorial, statistical, and enumeration properties of finite graphs with high Kolmogorov complexity (almost all graphs) using the novel incompressibility method. Example results are: (i) the mean and variance…

A few steps are made towards representation theory of embeddability among uncountable graphs. A monotone class of graphs is defined by forbidding countable subgraphs, related to the graph's end-structure. Using a combinatorial theorem of…

We develop the technique of reduced word manipulation to give a range of results concerning reduced words and permutations more generally. We prove a broad connection between pattern containment and reduced words, which specializes to our…

Referring expression comprehension aims to locate the object instance described by a natural language referring expression in an image. This task is compositional and inherently requires visual reasoning on top of the relationships among…

Multiword expressions (MWEs) are composed of multiple words and exhibit variable degrees of compositionality. As such, their meanings are notoriously difficult to model, and it is unclear to what extent this issue affects transformer…

Representing words by vectors, or embeddings, enables computational reasoning and is foundational to automating natural language tasks. For example, if word embeddings of similar words contain similar values, word similarity can be readily…

A visibility representation is a classical drawing style of planar graphs. It displays the vertices of a graph as horizontal vertex-segments, and each edge is represented by a vertical edge-segment touching the segments of its end vertices;…

Distributed representations of words have boosted the performance of many Natural Language Processing tasks. However, usually only one representation per word is obtained, not acknowledging the fact that some words have multiple meanings.…

In this work, we introduce a new notion for representing graph classes with formal languages. In contrast to the seminal work by Kitaev and Pyatkin to represent graphs by words, we use formal binary languages in order to have a set of…

Given the success of Graph Neural Networks (GNNs) for structure-aware machine learning, many studies have explored their use for text classification, but mostly in specific domains with limited data characteristics. Moreover, some…

Interpretability is a key challenge in fostering trust for Large Language Models (LLMs), which stems from the complexity of extracting reasoning from model's parameters. We present the Frame Representation Hypothesis, a theoretically robust…