Related papers: Quick introduction to tensor analysis
Research on summarization has mainly been driven by empirical approaches, crafting systems to perform well on standard datasets with the notion of information Importance remaining latent. We argue that establishing theoretical models of…
Decision theories offer principled methods for making choices under various types of uncertainty. Algorithms that implement these theories have been successfully applied to a wide range of real-world problems, including materials and drug…
Compositionality is a key property for dealing with complexity, which has been studied from many points of view in diverse fields. Particularly, the composition of individual computations (or programs) has been widely studied almost since…
The tensor self energy is computed at one loop order in a model in which a vector and tensor interact in a way that eliminates all tensor degrees of freedom. Divergencies arise which cannot be eliminated without introducing a kinetic term…
This book can be seen either as a text on theorem proving that uses techniques from general algebra, or else as a text on general algebra illustrated and made concrete by practical exercises in theorem proving. The book considers several…
This paper studies a tensor-structured linear regression model with a scalar response variable and tensor-structured predictors, such that the regression parameters form a tensor of order $d$ (i.e., a $d$-fold multiway array) in…
In this paper, we describe an approach that enables an autonomous system to infer the semantics of a command (i.e. a symbol sequence representing an action) in terms of the relations between changes in the observations and the action…
This is the second part in a series of papers in which we introduce and develop a natural, general tensor category theory for suitable module categories for a vertex (operator) algebra. In this paper (Part II), we develop logarithmic formal…
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…
These lecture notes concern the basics of the theory of process behaviour. First the concept of a (labelled) transition system receives ample treatment and then the following issues concerning process behaviour are elaborated in the setting…
Theory revision integrates inductive learning and background knowledge by combining training examples with a coarse domain theory to produce a more accurate theory. There are two challenges that theory revision and other theory-guided…
This chapter provides a tutorial overview of first principles methods to describe the properties of matter at the ground state or equilibrium. It begins with a brief introduction to quantum and statistical mechanics for predicting the…
Tensor decomposition methods are popular tools for learning latent variables given only lower-order moments of the data. However, the standard assumption is that we have sufficient data to estimate these moments to high accuracy. In this…
We introduce a tensor-based model of shared representation for meta-learning from a diverse set of tasks. Prior works on learning linear representations for meta-learning assume that there is a common shared representation across different…
We provide an overview of the hybrid compositional distributional model of meaning, developed in Coecke et al. (arXiv:1003.4394v1 [cs.CL]), which is based on the categorical methods also applied to the analysis of information flow in…
Simple type theory is formulated for use with the generic theorem prover Isabelle. This requires explicit type inference rules. There are function, product, and subset types, which may be empty. Descriptions (the eta-operator) introduce the…
In this lecture note, we discuss a fundamental concept, referred to as the {\it characteristic rank}, which suggests a general framework for characterizing the basic properties of various low-dimensional models used in signal processing.…
Higher-order data with high dimensionality arise in a diverse set of application areas such as computer vision, video analytics and medical imaging. Tensors provide a natural tool for representing these types of data. Although there has…
Definition Modeling, the task of generating definitions, was first proposed as a means to evaluate the semantic quality of word embeddings-a coherent lexical semantic representations of a word in context should contain all the information…
In this paper we propose an efficient method to compress a high dimensional function into a tensor ring format, based on alternating least-squares (ALS). Since the function has size exponential in $d$ where $d$ is the number of dimensions,…