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Word embeddings are a powerful approach for capturing semantic similarity among terms in a vocabulary. In this paper, we develop exponential family embeddings, a class of methods that extends the idea of word embeddings to other types of…
We specify the frontier of decidability for fragments of the first-order theory of ordinal multiplication. We give a NEXPTIME lower bound for the complexity of the existential fragment of $\langle \omega^{\omega^\lambda}; \times, \omega,…
To represent anything from mathematical concepts to real-world objects, we have to resort to an encoding. Encodings, such as written language, usually assume a decoder that understands a rich shared code. A semantic embedding is a form of…
In this paper, we explore the usage of Word Embedding semantic resources for Information Retrieval (IR) task. This embedding, produced by a shallow neural network, have been shown to catch semantic similarities between words (Mikolov et…
A non-deterministic recursion scheme recognizes a language of finite trees. This very expressive model can simulate, among others, higher-order pushdown automata with collapse. We show decidability of the diagonal problem for schemes. This…
Complex reasoning over text requires understanding and chaining together free-form predicates and logical connectives. Prior work has largely tried to do this either symbolically or with black-box transformers. We present a middle ground…
We introduce a new notion of a relational word as a finite totally ordered set of positions endowed with three binary relations that describe which positions are labeled by equal data, by unequal data and those having an undefined relation…
We study two modifications of the Post Correspondence Problem (PCP), namely 1) the bi-infinite version, where it is asked whether there exists a bi-infinite word such that two given morphisms agree on it, and 2) the conjugate version, where…
Word embeddings are effective intermediate representations for capturing semantic regularities between words, when learning the representations of text sequences. We propose to view text classification as a label-word joint embedding…
An $\ell$-page stack layout (also known as an $\ell$-page book embedding) of a graph is a linear order of the vertex set together with a partition of the edge set into $\ell$ stacks (or pages), such that the endpoints of no two edges on the…
Sequential word order is important when processing text. Currently, neural networks (NNs) address this by modeling word position using position embeddings. The problem is that position embeddings capture the position of individual words,…
This paper discusses limitations of reflexive and diagonal arguments as methods of proof of limitative theorems (e.g. G\"odel's theorem on Entscheidungsproblem, Turing's halting problem or Chaitin-G\"odel's theorem). The fact, that a formal…
In this paper, we consider the minimal doubly resolving set problem in Hamming graphs, hypercubes and folded hypercubes. We prove that the minimal doubly resolving set problem in hypercubes is equivalent to the coin weighing problem. Then…
We investigate the problem of inducing word embeddings that are tailored for a particular bilexical relation. Our learning algorithm takes an existing lexical vector space and compresses it such that the resulting word embeddings are good…
Word embedding algorithms produce very reliable feature representations of words that are used by neural network models across a constantly growing multitude of NLP tasks. As such, it is imperative for NLP practitioners to understand how…
Rademacher complexity is often used to characterize the learnability of a hypothesis class and is known to be related to the class size. We leverage this observation and introduce a new technique for estimating the size of an arbitrary…
The problem of constructing explicit functions which cannot be approximated by low degree polynomials has been extensively studied in computational complexity, motivated by applications in circuit lower bounds, pseudo-randomness,…
Pre-trained language models such as BERT have become a more common choice of natural language processing (NLP) tasks. Research in word representation shows that isotropic embeddings can significantly improve performance on downstream tasks.…
Answer Set Programming (ASP) is an increasingly popular framework for declarative programming that admits the description of problems by means of rules and constraints that form a disjunctive logic program. In particular, many AI problems…
We study $d$-dimensional simplicial complexes that are PL embeddable in $\mathbb{R}^{d+1}$. It is shown that such a complex must satisfy a certain homological condition. The existence of this obstruction allows us to provide a systematic…