Related papers: Towards a Formal Distributional Semantics: Simulat…
To ensure interpretability of extracted sources in tensor decomposition, we introduce in this paper a dictionary-based tensor canonical polyadic decomposition which enforces one factor to belong exactly to a known dictionary. A new…
In compositional model-theoretic semantics, researchers assemble truth-conditions or other kinds of denotations using the lambda calculus. It was previously observed that the lambda terms and/or the denotations studied tend to follow the…
The categorical compositional distributional model of natural language provides a conceptually motivated procedure to compute the meaning of sentences, given grammatical structure and the meanings of its words. This approach has…
A computationally challenging classical elimination theory problem is to compute polynomials which vanish on the set of tensors of a given rank. By moving away from computing polynomials via elimination theory to computing pseudowitness…
Compressed sensing extends from the recovery of sparse vectors from undersampled measurements via efficient algorithms to the recovery of matrices of low rank from incomplete information. Here we consider a further extension to the…
Different from previous surveys in semantic parsing (Kamath and Das, 2018) and knowledge base question answering(KBQA)(Chakraborty et al., 2019; Zhu et al., 2019; Hoffner et al., 2017) we try to takes a different perspective on the study of…
Word embedding is a powerful tool in natural language processing. In this paper we consider the problem of word embedding composition \--- given vector representations of two words, compute a vector for the entire phrase. We give a…
Distributional semantics offers new ways to study the semantics of morphology. This study focuses on the semantics of noun singulars and their plural inflectional variants in English. Our goal is to compare two models for the…
Lexical semantics theories differ in advocating that the meaning of words is represented as an inference graph, a feature mapping or a vector space, thus raising the question: is it the case that one of these approaches is superior to the…
This article presents a natural extension of the tensor algebra. In addition to "left multiplications" by vectors, we can consider "derivations" by covectors as basic operators on this extended algebra. These two types of operators satisfy…
Mathematical notation makes up a large portion of STEM literature, yet finding semantic representations for formulae remains a challenging problem. Because mathematical notation is precise, and its meaning changes significantly with small…
Distributed representations (such as those based on embeddings) and discrete representations (such as those based on logic) have complementary strengths. We explore one possible approach to combining these two kinds of representations. We…
In this paper, we briefly discuss the dynamic and functional approach to computer symbolic tensor analysis. The ccgrg package for Wolfram Language/Mathematica is used to illustrate this approach. Some examples of applications are attached.
This paper gives a broad account of the various sequent-based proof formalisms in the proof-theoretic literature. We consider formalisms for various modal and tense logics, intuitionistic logic, conditional logics, and bunched logics. After…
The question of what kinds of linguistic information are encoded in different layers of Transformer-based language models is of considerable interest for the NLP community. Existing work, however, has overwhelmingly focused on word-level…
Contingency table analysis routinely relies on log linear models, with latent structure analysis providing a common alternative. Latent structure models lead to a low rank tensor factorization of the probability mass function for…
Traditional semantic parsers map language onto compositional, executable queries in a fixed schema. This mapping allows them to effectively leverage the information contained in large, formal knowledge bases (KBs, e.g., Freebase) to answer…
Tarski gave a general semantics for deductive reasoning: a formula a may be deduced from a set A of formulas iff a holds in all models in which each of the elements of A holds. A more liberal semantics has been considered: a formula a may…
Abstract. The purpose of this paper is twofold. We introduce the theory of random tensors, which naturally extends the method of random averaging operators in our earlier work arXiv:1910.08492, to study the propagation of randomness under…
The recent proliferation of richly structured probabilistic models raises the question of how to automatically determine an appropriate model for a dataset. We investigate this question for a space of matrix decomposition models which can…