Related papers: Unifying cubical and multimodal type theory
By extending the advantage of chain-of-thought (CoT) reasoning in human-like step-by-step processes to multimodal contexts, multimodal CoT (MCoT) reasoning has recently garnered significant research attention, especially in the integration…
This paper gives a uniform-theoretic refinement of classical homotopy theory. Both cubical sets (with connections) and uniform spaces admit classes of weak equivalences, special cases of classical weak equivalences, appropriate for the…
We construct a model of type theory enjoying parametricity from an arbitrary one. A type in the new model is a semi-cubical type in the old one, illustrating the correspondence between parametricity and cubes. Our construction works not…
Martin-L\"of's Intuitionistic Theory of Types is becoming popular for formal reasoning about computer programs. To handle recursion schemes other than primitive recursion, a theory of well-founded relations is presented. Using primitive…
A type theory is presented that combines (intuitionistic) linear types with type dependency, thus properly generalising both intuitionistic dependent type theory and full linear logic. A syntax and complete categorical semantics are…
Several different topoi have played an important role in the development and applications of synthetic guarded domain theory (SGDT), a new kind of synthetic domain theory that abstracts the concept of guarded recursion frequently employed…
Multimodal learning has mainly focused on learning large models on, and fusing feature representations from, different modalities for better performances on downstream tasks. In this work, we take a detour from this trend and study the…
Human perception of the empirical world involves recognizing the diverse appearances, or 'modalities', of underlying objects. Despite the longstanding consideration of this perspective in philosophy and cognitive science, the study of…
As humans, we experience the world with all our senses or modalities (sound, sight, touch, smell, and taste). We use these modalities, particularly sight and touch, to convey and interpret specific meanings. Multimodal expressions are…
We present a new model of Guarded Dependent Type Theory (GDTT), a type theory with guarded recursion and multiple clocks in which one can program with, and reason about coinductive types. Productivity of recursively defined coinductive…
This book is the result of a seminar in which we reviewed multimodal approaches and attempted to create a solid overview of the field, starting with the current state-of-the-art approaches in the two subfields of Deep Learning individually.…
Algebraic datatypes, and among them lists and trees, have attracted a lot of interest in automated reasoning and Satisfiability Modulo Theories (SMT). Since its latest stable version, the SMT-LIB standard defines a theory of algebraic…
${\rm CTT}_{\rm qe}$ is a version of Church's type theory with global quotation and evaluation operators that is engineered to reason about the interplay of syntax and semantics and to formalize syntax-based mathematical algorithms. ${\rm…
With the exponential surge in diverse multi-modal data, traditional uni-modal retrieval methods struggle to meet the needs of users seeking access to data across various modalities. To address this, cross-modal retrieval has emerged,…
Nakano's "later" modality, inspired by G\"{o}del-L\"{o}b provability logic, has been applied in type systems and program logics to capture guarded recursion. Birkedal et al modelled this modality via the internal logic of the topos of…
Cubical type theory is an extension of Martin-L\"of type theory recently proposed by Cohen, Coquand, M\"ortberg and the author which allows for direct manipulation of $n$-dimensional cubes and where Voevodsky's Univalence Axiom is provable.…
This paper presents preliminary work on a general system for integrating dependent types into substructural type systems such as linear logic and linear type theory. Prior work on this front has generally managed to deliver type systems…
Reasoning over multiple modalities, e.g. in Visual Question Answering (VQA), requires an alignment of semantic concepts across domains. Despite the widespread success of end-to-end learning, today's multimodal pipelines by and large…
While accurate and user-friendly Computer-Aided Design (CAD) is crucial for industrial design and manufacturing, existing methods still struggle to achieve this due to their over-simplified representations or architectures incapable of…
We present three examples of \textit{multi-topological} semantics for intuitionistic modal logic with one modal operator $\Box$ (which behaves in some sense like necessity). We show that it is possible to treat neighborhood models,…