Related papers: Translational tilings: structured or wild?
Code-Switching, a common phenomenon in written text and conversation, has been studied over decades by the natural language processing (NLP) research community. Initially, code-switching is intensively explored by leveraging linguistic…
This paper surveys the theory of multiple packings and coverings. The study of multiple arrangements started in the 60s of the last century, and it was restricted mostly to lattice arrangements on the plane or of general arrangements of…
Asymmetric combination of logics is a formal process that develops the characteristic features of a specific logic on top of another one. Typical examples include the development of temporal, hybrid, and probabilistic dimensions over a…
Rigidity is an emergent property of materials - it is not a feature of individual components that comprise the structure, but instead arises from interactions between many constituent parts. Recently, it has been recognized that…
This paper is about the tiling dynamical systems approach to the study of aperiodic order. We compare and contrast four related types of systems: ordinary (one-dimensional) symbolic systems, one-dimensional tiling systems, multidimensional…
Convergence is a fundamental topic in analysis that is most commonly modelled using topology. However, there are many natural convergences that are not given by any topology; e.g., convergence almost everywhere of a sequence of measurable…
A finite set of integers $A$ tiles the integers by translations if $\mathbb{Z}$ can be covered by pairwise disjoint translated copies of $A$. Restricting attention to one tiling period, we have $A\oplus B=\mathbb{Z}_M$ for some…
As the intermediate-level representations bridging the two levels, structured representations of visual scenes, such as visual relationships between pairwise objects, have been shown to not only benefit compositional models in learning to…
Transformer architectures have brought about fundamental changes to computational linguistic field, which had been dominated by recurrent neural networks for many years. Its success also implies drastic changes in cross-modal tasks with…
In recent years, much of the research on clustering algorithms has primarily focused on enhancing their accuracy and efficiency, frequently at the expense of interpretability. However, as these methods are increasingly being applied in…
Alignments, i.e., position-wise comparisons of two or more strings or ordered lists are of utmost practical importance in computational biology and a host of other fields, including historical linguistics and emerging areas of research in…
We study the construction of substitution tilings of the plane based on certain simplicial configurations of tangents of the deltoid with evenly distributed orientations. The random tiling ensembles are obtained as a result of tile…
In the last 30 years, the mathematical theory of aperiodic order has developed enormously. Many new tilings and properties have been discovered, few of which are covered or anticipated by the early papers and books. Here, we start from the…
Cross-lingual alignment, the meaningful similarity of representations across languages in multilingual language models, has been an active field of research in recent years. We survey the literature of techniques to improve cross-lingual…
Efforts to apply transformer-based language models (TLMs) to the problem of reasoning in natural language have enjoyed ever-increasing success in recent years. The most fundamental task in this area to which nearly all others can be reduced…
Given a tiling of a 2D grid with several types of tiles, we can count for every row and column how many tiles of each type it intersects. These numbers are called the_projections_. We are interested in the problem of reconstructing a tiling…
Typology is a subfield of linguistics that focuses on the study and classification of languages based on their structural features. Unlike genealogical classification, which examines the historical relationships between languages, typology…
Along with the great success of deep neural networks, there is also growing concern about their black-box nature. The interpretability issue affects people's trust on deep learning systems. It is also related to many ethical problems, e.g.,…
The physics of disordered media, from metallic glasses to colloidal suspensions, granular matter and biological tissues, offers difficult challenges because it often occurs far from equilibrium, in materials lacking symmetries and evolving…
We survey a decade worth of work pertaining to the nodal structures of random fields, with emphasis on the transformative techniques that shaped the field.