Related papers: Reasoning About Vectors using an SMT Theory of Seq…
Given vector representations for individual words, it is necessary to compute vector representations of sentences for many applications in a compositional manner, often using artificial neural networks. Relatively little work has explored…
Chain-of-Thought (CoT) prompting has emerged as a powerful approach to enhancing the reasoning capabilities of Large Language Models (LLMs). However, existing implementations, such as in-context learning and fine-tuning, remain costly and…
Predicting future behavior of other traffic participants is an essential task that needs to be solved by automated vehicles and human drivers alike to achieve safe and situationaware driving. Modern approaches to vehicles trajectory…
Recently, decision trees (DT) have been used as an explainable representation of controllers (a.k.a. strategies, policies, schedulers). Although they are often very efficient and produce small and understandable controllers for discrete…
An important component of achieving language understanding is mastering the composition of sentence meaning, but an immediate challenge to solving this problem is the opacity of sentence vector representations produced by current neural…
In this paper we describe an approach to construct large extendable collections of vectors in predefined spaces of given dimensions. These collections are useful for neural network latent space configuration and training. For classification…
Vector representations of graphs and relational structures, whether hand-crafted feature vectors or learned representations, enable us to apply standard data analysis and machine learning techniques to the structures. A wide range of…
We introduce the Vector Fitting algorithm for the creation of reduced-order models from the sampled response of a linear time-invariant system. This data-driven approach to reduction is particularly useful when the system under modeling is…
Techniques in which words are represented as vectors have proved useful in many applications in computational linguistics, however there is currently no general semantic formalism for representing meaning in terms of vectors. We present a…
A vector composition of a vector $\mathbf{\ell}$ is a matrix $\mathbf{A}$ whose rows sum to $\mathbf{\ell}$. We define a weighted vector composition as a vector composition in which the column values of $\mathbf{A}$ may appear in different…
Machine learning systems regularly deal with structured data in real-world applications. Unfortunately, such data has been difficult to faithfully represent in a way that most machine learning techniques would expect, i.e. as a real-valued…
Techniques in which words are represented as vectors have proved useful in many applications in computational linguistics, however there is currently no general semantic formalism for representing meaning in terms of vectors. We present a…
This paper introduces a new mathematical framework for analysis and optimization of tensor expressions within an enclosing loop. Tensors are multi-dimensional arrays of values. They are common in high performance computing (HPC) and machine…
Reasoning about array data structures is a key requirement for many applications in hardware and software verification, especially in combination with machine integers. The Satisfiability Modulo Theories (SMT) theory of extensional arrays…
Vector models of language are based on the contextual aspects of language, the distributions of words and how they co-occur in text. Truth conditional models focus on the logical aspects of language, compositional properties of words and…
Vector addition systems are an important model in theoretical computer science and have been used for the analysis of systems in a variety of areas. Termination is a crucial property of vector addition systems and has received considerable…
We present a compact data structure to represent both the duration and length of homogeneous segments of trajectories from moving objects in a way that, as a data warehouse, it allows us to efficiently answer cumulative queries. The…
Regular sequences are natural generalisations of fixed points of constant-length substitutions on finite alphabets, that is, of automatic sequences. Using the harmonic analysis of measures associated with substitutions as motivation, we…
Vector representations have become a central element in semantic language modelling, leading to mathematical overlaps with many fields including quantum theory. Compositionality is a core goal for such representations: given representations…
Machine learning methods based on statistical principles have proven highly successful in dealing with a wide variety of data analysis and analytics tasks. Traditional data models are mostly concerned with independent identically…