Related papers: Towards a Formal Distributional Semantics: Simulat…
Vector space models have become popular in distributional semantics, despite the challenges they face in capturing various semantic phenomena. We propose a novel probabilistic framework which draws on both formal semantics and recent…
Tensors, or multi-linear forms, are important objects in a variety of areas from analytics, to combinatorics, to computational complexity theory. Notions of tensor rank aim to quantify the "complexity" of these forms, and are thus also…
Functional Distributional Semantics is a framework that aims to learn, from text, semantic representations which can be interpreted in terms of truth. Here we make two contributions to this framework. The first is to show how a type of…
In this paper, we present a partial survey of the tools borrowed from tensor algebra, which have been utilized recently in Statistics and Signal Processing. It is shown why the decompositions well known in linear algebra can hardly be…
The notion of a tensor captures three great ideas: equivariance, multilinearity, separability. But trying to be three things at once makes the notion difficult to understand. We will explain tensors in an accessible and elementary way…
This thesis is about the problem of compositionality in distributional semantics. Distributional semantics presupposes that the meanings of words are a function of their occurrences in textual contexts. It models words as distributions over…
Computer algebra is widely used in various fields of mathematics, physics and other sciences. The simplification of tensor expressions is an important special case of computer algebra. In this paper, we consider the reduction of tensor…
Categorical compositional distributional semantics provide a method to derive the meaning of a sentence from the meaning of its individual words: the grammatical reduction of a sentence automatically induces a linear map for composing the…
Many studies were recently done for investigating the properties of contextual language models but surprisingly, only a few of them consider the properties of these models in terms of semantic similarity. In this article, we first focus on…
We present a new framework for compositional distributional semantics in which the distributional contexts of lexemes are expressed in terms of anchored packed dependency trees. We show that these structures have the potential to capture…
Distributional tensor fields can be regarded as multilinear mappings with distributional values or as (classical) tensor fields with distributional coefficients. We show that the corresponding isomorphisms hold also in the bornological…
We propose a new linear algebraic approach to the computation of Tarskian semantics in logic. We embed a finite model M in first-order logic with N entities in N-dimensional Euclidean space R^N by mapping entities of M to N dimensional…
A grammar logic refers to an extension to the multi-modal logic K in which the modal axioms are generated from a formal grammar. We consider a proof theory, in nested sequent calculus, of grammar logics with converse, i.e., every modal…
NLP tasks differ in the semantic information they require, and at this time no single se- mantic representation fulfills all requirements. Logic-based representations characterize sentence structure, but do not capture the graded aspect of…
Distributional word representation methods exploit word co-occurrences to build compact vector encodings of words. While these representations enjoy widespread use in modern natural language processing, it is unclear whether they accurately…
As we continue to collect and store textual data in a multitude of domains, we are regularly confronted with material whose largely unknown thematic structure we want to uncover. With unsupervised, exploratory analysis, no prior knowledge…
We define new norms for symmetric tensors over ordered normed spaces; these norms are defined by considering linear combinations of tensor products or powers of positive elements only. Relations between the different norms are studied. The…
This paper shows how to derive nested calculi from labelled calculi for propositional intuitionistic logic and first-order intuitionistic logic with constant domains, thus connecting the general results for labelled calculi with the more…
We present a fit-for-purpose introduction to tensors and their operations. It is envisaged to help the reader become acquainted with its underpinning concepts for the study of path signatures. The text includes exercises, solutions and many…
In the literature, tensors have been effectively used for capturing the context information in language models. However, the existing methods usually adopt relatively-low order tensors, which have limited expressive power in modeling…