Research
Research
Research
Research
87+ open-access research outputs.
Real numbers in constructive mathematics have always seemed to require compromises of one form or another. Classical proofs of Cauchy completeness require countable choice, Bishop's setoid constructio…
In recent years, Homotopy Type Theory (HoTT) has had great success both as a foundation of mathematics and as internal language to reason about $\infty$-groupoids (a.k.a. spaces). However, in many are…
Artificial intelligence (AI) has the potential to transform healthcare, education, governance and socioeconomic equity, but its benefits remain concentrated in a small number of languages (Bender, 201…
Recent progress in large language models and multimodal interaction has made it possible to develop AI companions that can have fluent and emotionally expressive conversations. However, many of these …
We introduce Open Horn Type Theory (OHTT), an extension of dependent type theory with two primitive judgment forms: coherence and gap, subject to a mutual exclusion law. Unlike classical or intuitioni…
VTuber agencies -- multichannel networks (MCNs) that bundle Virtual YouTubers (VTubers) on YouTube -- curate portfolios of channels and coordinate programming, cross appearances, and branding in the l…
Existing speech semantic communication systems mainly based on Joint Source-Channel Coding (JSCC) architectures have demonstrated impressive performance, but their effectiveness remains limited by mod…
The Seifert-van Kampen theorem computes the fundamental group of a space from the fundamental groups of its constituents. We develop a modular SVK framework within the setting of computational paths -…
Some advantages of Cubical Type Theory, as implemented by Cubical Agda, over intensional Martin-L\"of Type Theory include Quotient Inductive Types (QITs), which exist as instances of Higher Inductive …
Categories with families (CwFs) have been used to define the semantics of type theory in type theory. In the setting of Homotopy Type Theory (HoTT), one of the limitations of the traditional notion of…
Bug localisation, the study of developing methods to localise the files requiring changes to resolve bugs, has been researched for a long time to develop methods capable of saving developers' time. Re…
Data trading is one of the key focuses of Web 3.0. However, all the current methods that rely on blockchain-based smart contracts for data exchange cannot support large-scale data trading while ensuri…
Dynamic HoTT (DHoTT) is a conservative extension of Homotopy Type Theory designed for evolving texts in conversational AI. In a chat system, a large language model (LLM) is queried with a growing pref…
This article studies the fundamental problem of using i.i.d. coin tosses from an entropy source to efficiently generate random variables $X_i \sim P_i$ $(i \ge 1)$, where $(P_1, P_2, \dots)$ is a rand…
Recent studies suggest that while generative AI (GenAI) can enhance individual creativity, it often reduces the diversity of collective outputs. A well-known example of this homogenization effect is b…
Noninterference theory supports the analysis of secure computations in multi-level security systems. Classical equivalence-based approaches to noninterference mainly rely on bisimilarity. In a nondete…
Collision-resistant cryptographic hash functions (CRHs) are crucial for security, particularly for message authentication in Zero-knowledge Proof (ZKP) applications. However, traditional CRHs like SHA…
Audio synthesis has broad applications in multimedia. Recent advancements have made it possible to generate relevant audios from inputs describing an audio scene, such as images or texts. However, the…
Awodey, later with Newstead, showed how polynomial functors with extra structure (termed ``natural models'') hold within them the categorical semantics for dependent type theory. Their work presented …
TOTTA outlines the spatial position and rotation guidance of a real/virtual tool (TO) towards a real/virtual target (TA), which is a key task in Mixed Reality applications. The task error can have cri…
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