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Continuous vector representations of words and objects appear to carry surprisingly rich semantic content. In this paper, we advance both the conceptual and theoretical understanding of word embeddings in three ways. First, we ground…

A sememe is defined as the minimum semantic unit of human languages. Sememe knowledge bases (KBs), which contain words annotated with sememes, have been successfully applied to many NLP tasks, and we believe that by learning the smallest…

Using a vocabulary that is shared across languages is common practice in Multilingual Neural Machine Translation (MNMT). In addition to its simple design, shared tokens play an important role in positive knowledge transfer, assuming that…

Typically an ontology matching technique is a combination of much different type of matchers operating at various abstraction levels such as structure, semantic, syntax, instance etc. An ontology matching technique which employs matchers at…

The collapse of a vapor bubble near a flat solid boundary results in the formation of a jet that is directed towards the boundary. In more complex geometries such as corners, predictions of the collapse cannot be made in a straightforward…

Unfoldings are a well known partial-order semantics of P/T Petri nets that can be applied to various model checking or verification problems. For high-level Petri nets, the so-called symbolic unfolding generalizes this notion. A complete…

Rotational symmetry plays a central role in physics, providing an elegant framework to describe how the properties of 3D objects -- from atoms to the macroscopic scale -- transform under the action of rigid rotations. Equivariant models of…

We propose to achieve explainable neural machine translation (NMT) by changing the output representation to explain itself. We present a novel approach to NMT which generates the target sentence by monotonically walking through the source…

We introduce in this article a new method to estimate the minimum distance of codes from algebraic surfaces. This lower bound is generic, i.e. can be applied to any surface, and turns out to be ``liftable'' under finite morphisms, paving…

We introduce a recurrent neural network language model (RNN-LM) with long short-term memory (LSTM) units that utilizes both character-level and word-level inputs. Our model has a gate that adaptively finds the optimal mixture of the…

Jumping automata are finite automata that read their input in a non-consecutive manner, disregarding the order of the letters in the word. We introduce and study jumping automata over infinite words. Unlike the setting of finite words,…

We show the details of certain computations that are described in [BMW19].

Large Language Models (LLMs) perform internal computations in continuous vector spaces yet produce discrete tokens -- a fundamental mismatch whose geometric consequences remain poorly understood. We develop a mathematical framework that…

To determine whether an $n\times n$-matrix has rank at most $r$ it suffices to check that the $(r+1)\times (r+1)$-minors have rank at most $r$. In other words, to describe the set of $n\times n$-matrices with the property of having rank at…

We propose a new technique for computational language representation called elementwise embedding, in which a material (semantic unit) is abstracted into a horizontal concatenation of lower-dimensional element (character) embeddings. While…

We examine the various linkings in space-time of ``ball-like'' and ``ring-like'' topological solitons in certain nonlinear sigma models in 2+1 and 3+1 dimensions. By going to theories where soliton overlaps are forbidden, these linkings…

We develop a mathematical theory of symmetry protected trivial (SPT) orders and anomaly-free symmetry enriched topological (SET) orders in all dimensions via two different approaches with an emphasis on the second approach. The first…

Word Sense Disambiguation (WSD) is one of the hardest tasks in natural language understanding and knowledge engineering. The glass ceiling of 80% F1 score is recently achieved through supervised deep-learning, enriched by a variety of…

Existing algorithms for aligning cross-lingual word vector spaces assume that vector spaces are approximately isomorphic. As a result, they perform poorly or fail completely on non-isomorphic spaces. Such non-isomorphism has been…

We show that three- and four-stage Bott manifolds are classified up to diffeomorphism by their integral cohomology rings. In addition, any cohomology ring isomorphism between two three-stage Bott manifolds can be realized by a…