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Many interesting and useful symbolic computation algorithms manipulate mathematical expressions in mathematically meaningful ways. Although these algorithms are commonplace in computer algebra systems, they can be surprisingly difficult to…
We present a quantum computing approach to analyzing Large Language Model (LLM) embeddings, leveraging complex-valued representations and modeling semantic relationships using quantum mechanical principles. By establishing a direct mapping…
We use a labelled deduction system ( LND$_{ED-}$TRS ) based on the concept of computational paths (sequences of rewrites) as equalities between two terms of the same type, which allowed us to carry out in homotopic theory an approach using…
The increasing adoption of large language models (LLMs) has raised serious concerns about their reliability and trustworthiness. As a result, a growing body of research focuses on evidence-based text generation with LLMs, aiming to link…
We introduce a type system for the Quipper language designed to derive upper bounds on the size of the circuits produced by the typed program. This size can be measured according to various metrics, including width, depth and gate count,…
We introduce Qunity, a new quantum programming language designed to treat quantum computing as a natural generalization of classical computing. Qunity presents a unified syntax where familiar programming constructs can have both quantum and…
Quipper is a domain-specific programming language for the description of quantum circuits. Because it is implemented as an embedded language in Haskell, Quipper is a very practical functional language. However, for the same reason, it lacks…
In this chapter we provide an overview of computational modeling for semantic change using large and semi-large textual corpora. We aim to provide a key for the interpretation of relevant methods and evaluation techniques, and also provide…
Sentence-level Quality estimation (QE) of machine translation is traditionally formulated as a regression task, and the performance of QE models is typically measured by Pearson correlation with human labels. Recent QE models have achieved…
Machine Translation (MT) Quality Estimation (QE) assesses translation reliability without reference texts. This study introduces "textual similarity" as a new metric for QE, using sentence transformers and cosine similarity to measure…
In the e-print is discussed a few steps to introducing of "vocabulary" of relativistic physics in quantum theory of information and computation (QTI&C). The behavior of a few simple quantum systems those are used as models in QTI&C is…
Qualitative Spatial Reasoning (QSR) is well explored area of Commonsense Reasoning and has multiple applications ranging from Geographical Information Systems to Robotics and Computer Vision. Recently many claims have been made for the…
We present the syntax and rules of deduction of QPEL (Quantum Program and Effect Language), a language for describing both quantum programs, and properties of quantum programs - effects on the appropriate Hilbert space. We show how…
Dependent types allow us to express precisely what a function is intended to do. Recent work on Quantitative Type Theory (QTT) extends dependent type systems with linearity, also allowing precision in expressing when a function can run.…
We present an extensive mechanization of the meta-theory of Martin-L\"of Type Theory (MLTT) in the Coq proof assistant. Our development builds on pre-existing work in Agda to show not only the decidability of conversion, but also the…
Quality Estimation (QE) is the task of automatically predicting Machine Translation quality in the absence of reference translations, making it applicable in real-time settings, such as translating online social media conversations. Recent…
The problem of Phase Estimation (or Amplitude Estimation) admits a quadratic quantum speedup. Wang, Higgott and Brierley [2019, Phys. Rev. Lett. 122 140504] have shown that there is a continuous trade-off between quantum speedup and circuit…
Large language models (LLMs) such as ChatGPT are increasingly proficient in understanding and generating a mixture of code and text. Evaluation based on such $\textit{mixture}$ can lead to a more comprehensive understanding of the models'…
The calculus of constructions (CC) is a core theory for dependently typed programming and higher-order constructive logic. Originally introduced in Coquand's 1985 thesis, CC has inspired 25 years of research in programming languages and…
Homotopy type theory is an interpretation of Martin-L\"of's constructive type theory into abstract homotopy theory. There results a link between constructive mathematics and algebraic topology, providing topological semantics for…