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Large Language Models (LLMs) encode semantic relationships in high-dimensional vector embeddings. This paper explores the analogy between LLM embedding spaces and quantum mechanics, positing that LLMs operate within a quantized semantic…
This dissertation is concerned with the study of program equivalence and algebraic effects as they arise in the theory of programming languages. Algebraic effects represent impure behaviour in a functional programming language, such as…
Despite their remarkable ability to capture linguistic nuances across diverse languages, questions persist regarding the degree of alignment between languages in multilingual embeddings. Drawing inspiration from research on high-dimensional…
Quantum based systems are a relatively new research area for that different modelling languages including process calculi are currently under development. Encodings are often used to compare process calculi. Quality criteria are used then…
In this paper we present an alternative approach to formalize the theory of logic programming. In this formalization we allow existential quantified variables and equations in queries. In opposite to standard approaches the role of answer…
Embedding words in high-dimensional vector spaces has proven valuable in many natural language applications. In this work, we investigate whether similarly-trained embeddings of integers can capture concepts that are useful for mathematical…
Using the category of metric spaces as a template, we develop a metric analogue of the categorical semantics of classical/intuitionistic logic, and show that the natural notion of predicate in this "continuous semantics" is equivalent to…
We present an algebraic framework for interacting extended quantum systems to study complex phenomena characterized by the coexistence and competition of different states of matter. We start by showing how to connect different…
The evaluation of text-generative vision-language models is a challenging yet crucial endeavor. By addressing the limitations of existing Visual Question Answering (VQA) benchmarks and proposing innovative evaluation methodologies, our…
We prove a general congruence result for bisimilarity in higher-order languages, which generalises previous work to languages specified by a labelled transition system in which programs may occur as labels, and which may rely on operations…
In order to reason about effects, we can define quantitative formulas to describe behavioural aspects of effectful programs. These formulas can for example express probabilities that (or sets of correct starting states for which) a program…
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…
This invited paper presents an overview of an ongoing research program aimed at extending the Curry-Howard-Lambek correspondence to quantum computation. We explore two key frameworks that provide both logical and computational foundations…
We introduce a proof language for Intuitionistic Multiplicative Additive Linear Logic (IMALL), extended with a modality B to capture mixed-state quantum computation. The language supports algebraic constructs such as linear combinations,…
We explore the possibility of extending Mardare et al. quantitative algebras to the structures which naturally emerge from Combinatory Logic and the lambda-calculus. First of all, we show that the framework is indeed applicable to those…
Runtime efficiency and termination are crucial properties in the studies of program verification. Instead of dealing with these issues in an ad hoc manner, it would be useful to develop a robust framework in which such properties are…
As large language models (LLMs) become integral to code-related tasks, a central question emerges: Do LLMs truly understand program semantics? We introduce EquiBench, a new benchmark for evaluating LLMs through equivalence checking, i.e.,…
This paper proposes appropriate sound and complete proof systems for algebraic structures over metric spaces by combining the development of Quantitative Equational Theories (QET) with the Enriched Lawvere Theories. We extend QETs to Metric…
We propose a method that learns a discriminative yet semantic space for object categorization, where we also embed auxiliary semantic entities such as supercategories and attributes. Contrary to prior work which only utilized them as side…
In a recent work, arXiv:2503.05884, we proposed a unified notion of nonclassicality that applies to arbitrary processes in quantum theory, including individual quantum states, measurements, channels, set of these, etc. This notion is…