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Extending the lambda-calculus with a construct for sharing, such as let expressions, enables a special representation of terms: iterated applications are decomposed by introducing sharing points in between any two of them, reducing to the…
This paper presents the Pi-graphs, a visual paradigm for the modelling and verification of mobile systems. The language is a graphical variant of the Pi-calculus with iterators to express non-terminating behaviors. The operational semantics…
Vector Symbolic Architectures (VSAs) are one approach to developing Neuro-symbolic AI, where two vectors in $\mathbb{R}^d$ are `bound' together to produce a new vector in the same space. VSAs support the commutativity and associativity of…
Linear conjunctive grammars are a family of formal grammars with an explicit conjunction operation allowed in the rules, which is notable for its computational equivalence fo one-way real-time cellular automata, also known as trellis…
Logic programming (LP) is a programming language based on first-order Horn clause logic that uses SLD-resolution as a semi-decision procedure. Finite SLD-computations are inductively sound and complete with respect to least Herbrand models…
This is Part II of the two-part comprehensive survey devoted to a computing framework most commonly known under the names Hyperdimensional Computing and Vector Symbolic Architectures (HDC/VSA). Both names refer to a family of computational…
String diagrams are a powerful tool for reasoning about composite structures in symmetric monoidal categories. By representing string diagrams as graphs, equational reasoning can be done automatically by double-pushout rewriting. !-graphs…
We investigate the properties of linear primitive liftings $\rho\colon \mathcal{L}^p(\mu)\to \mathcal{L}^p(\mu)$ for probability spaces $(X,\Sigma,\mu)$, which are linear maps selecting a representative from each class for almost everywhere…
We present LINSPECTOR WEB, an open source multilingual inspector to analyze word representations. Our system provides researchers working in low-resource settings with an easily accessible web based probing tool to gain quick insights into…
In this paper, we present an approach, namely Lexical Semantic Image Completion (LSIC), that may have potential applications in art, design, and heritage conservation, among several others. Existing image completion procedure is highly…
In this paper we present a deep learning architecture for extracting word embeddings for visual speech recognition. The embeddings summarize the information of the mouth region that is relevant to the problem of word recognition, while…
One hallmark of human language is its combinatoriality -- reusing a relatively small inventory of building blocks to create a far larger inventory of increasingly complex structures. In this paper, we explore the idea that combinatoriality…
Contrastive language-image pre-training (CLIP) is a powerful vision-language model that has shown great benefits for various tasks. However, we have identified some issues with its explainability, which undermine its credibility and limit…
Visual representation learning has been a cornerstone in computer vision, involving typical forms such as visual embeddings, structural symbols, and text-based representations. Despite the success of CLIP-type visual embeddings, they often…
Mapping words into a fixed-dimensional vector space is the backbone of modern NLP. While most word embedding methods successfully encode semantic information, they overlook phonetic information that is crucial for many tasks. We develop…
I'll outline the latest version of my limits of math course. The purpose of this course is to illustrate the proofs of the key information-theoretic incompleteness theorems of algorithmic information theory by means of algorithms written in…
This paper describes an abstract machine for linguistic formalisms that are based on typed feature structures, such as HPSG. The core design of the abstract machine is given in detail, including the compilation process from a high-level…
Visual speech recognition (VSR), also known as lip reading, is the task of recognizing speech from silent video. Despite significant advancements in VSR over recent decades, most existing methods pay limited attention to real-world visual…
Several abstract machines that operate on symbolic input alphabets have been proposed in the last decade, for example, symbolic automata or lattice automata. Applications of these types of automata include software security analysis and…
Vision-language model (VLM) encoders such as CLIP enable strong retrieval and zero-shot classification in a shared image-text embedding space, yet the semantic organization of this space is rarely inspected. We present a post-hoc framework…