Related papers: Unifying cubical and multimodal type theory
The category of Cartesian cubical sets is introduced and endowed with a Quillen model structure using ideas coming from recent constructions of cubical systems of univalent type theory.
A conceptual model can be used to manage complexity in both the design and implementation phases of the system development life cycle. Such a model requires a firm grasp of the abstract principles on which a system is based, as well as an…
We propose a new bi-intuitionistic type theory called Dualized Type Theory (DTT). It is a simple type theory with perfect intuitionistic duality, and corresponds to a single-sided polarized sequent calculus. We prove DTT strongly…
Multiple clustering aims to discover various latent structures of data from different aspects. Deep multiple clustering methods have achieved remarkable performance by exploiting complex patterns and relationships in data. However, existing…
Multimodal representation learning poses significant challenges in capturing informative and distinct features from multiple modalities. Existing methods often struggle to exploit the unique characteristics of each modality due to unified…
Multimodal models often experience a significant performance drop when one or more modalities are missing during inference. To address this challenge, we propose a simple yet effective approach that enhances robustness to missing modalities…
Random tensor models are generalizations of random matrix models which admit $1/N$ expansions. In this article we show that the topological recursion, a modern approach to matrix models which solves the loop equations at all orders, is also…
Generative recommendation (GR) has become a powerful paradigm in recommendation systems that implicitly links modality and semantics to item representation, in contrast to previous methods that relied on non-semantic item identifiers in…
Tabular reasoning involves multi-step information extraction and logical inference over tabular data. While recent advances have leveraged large language models (LLMs) for reasoning over structured tables, such high-quality textual…
Using Butz and Moerdijk's topological groupoid representation of a topos with enough points, a `syntax-semantics' duality for geometric theories is constructed. The emphasis is on a logical presentation, starting with a description of the…
Naturally, humans use multiple modalities to convey information. The modalities are processed both sequentially and in parallel for communication in the human brain, this changes when humans interact with computers. Empowering computers…
Cube categories are used to encode higher-dimensional categorical structures. They have recently gained significant attention in the community of homotopy type theory and univalent foundations, where types carry the structure of such higher…
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 construction introduces persistent bookkeeping…
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…
Homotopy type theory (HoTT) can be seen as a generalisation of structural set theory, in the sense that 0-types represent structural sets within the more general notion of types. For material set theory, we also have concrete models as…
Recent studies have demonstrated advantages of information fusion based on sparsity models for multimodal classification. Among several sparsity models, tree-structured sparsity provides a flexible framework for extraction of…
Humans construct internal world models and reason by manipulating the concepts within these models. Recent advances in AI, particularly chain-of-thought (CoT) reasoning, approximate such human cognitive abilities, where world models are…
The development of cubical type theory inspired the idea of "extension types" which has been found to have applications in other type theories that are unrelated to homotopy type theory or cubical type theory. This article describes these…
This article contains an overview of the results of the author in a field of algebraic topology used in computer science. The relationship between the cubical homology groups of generalized tori and homology groups of partial trace monoid…
This paper is primarily intended as an introduction for the mathematically inclined to some of the rich algebraic combinatorics arising in for instance CFT. It is essentially self-contained, apart from some of the background motivation and…