Related papers: Unifying cubical and multimodal type theory
This paper introduces Relational Type Theory (RelTT), a new approach to type theory with extensionality principles, based on a relational semantics for types. The type constructs of the theory are those of System F plus relational…
Unified multimodal models (UMMs) aim to integrate understanding and generation within a single architecture. However, it remains underexplored how to effectively coordinate these two capabilities for more effective and efficient reasoning.…
As observed recently by various people the topos $\mathbf{sSet}$ of simplicial sets appears as essential subtopos of a topos $\mathbf{cSet}$ of cubical sets, namely presheaves over the category $\mathbf{FL}$ of finite lattices and monotone…
The connectional brain template (CBT) captures the shared traits across all individuals of a given population of brain connectomes, thereby acting as a fingerprint. Estimating a CBT from a population where brain graphs are derived from…
We present an abstract unifying framework for interpreting Stone-type dualities; several known dualities are seen to be instances of just one topos-theoretic phenomenon, and new dualities are introduced. In fact, infinitely many new…
This paper presents a new scalable algorithm for cross-modal similarity preserving retrieval in a learnt manifold space. Unlike existing approaches that compromise between preserving global and local geometries, the proposed technique…
We define and develop two-level type theory (2LTT), a version of Martin-L\"of type theory which combines two different type theories. We refer to them as the inner and the outer type theory. In our case of interest, the inner theory is…
In the systems and software modeling field, a conceptual model involves modeling with concepts to support development and design. An example of a conceptual model is a description developed using the Unified Modeling Language (UML). UML…
The goal of this article is to emphasize the role of cubical sets in enriched categories theory and infinity-categories theory. We show in particular that categories enriched in cubical sets provide a convenient way to describe many…
Containers capture the concept of strictly positive data types in programming. The original development of containers is done in the internal language of locally cartesian closed categories (LCCCs) with disjoint coproducts and W-types, and…
Contrastive learning has become one of the most impressive approaches for multi-modal representation learning. However, previous multi-modal works mainly focused on cross-modal understanding, ignoring in-modal contrastive learning, which…
We present a unifying framework for type systems for process calculi. The core of the system provides an accurate correspondence between essentially functional processes and linear logic proofs; fragments of this system correspond to…
Universal Multimodal embedding models built on Multimodal Large Language Models (MLLMs) have traditionally employed contrastive learning, which aligns representations of query-target pairs across different modalities. Yet, despite its…
Recent years have seen remarkable progress in both multimodal understanding models and image generation models. Despite their respective successes, these two domains have evolved independently, leading to distinct architectural paradigms:…
Behavior Trees (BTs) got the robotics society attention not least thanks to their modularity and reusability. The subtrees of BTs could be treated as separate behaviors and therefore reused. We address the following research question: do we…
We explore a quantitative interpretation of 2-dimensional intuitionistic type theory (ITT) in which the identity type is interpreted as a "type of differences". We show that a fragment of ITT, that we call difference type theory (dTT),…
We prove normalization for (univalent, Cartesian) cubical type theory, closing the last major open problem in the syntactic metatheory of cubical type theory. Our normalization result is reduction-free, in the sense of yielding a bijection…
Integrating multiple generative foundation models, especially those trained on different modalities, into something greater than the sum of its parts poses significant challenges. Two key hurdles are the availability of aligned data…
We propose a new cubical type theory, termed (self-deprecatingly) the naive cubical type theory, and study its semantics using the universe category framework, which is similar to Uemura's categories with representable morphisms. In…
We intend to investigate the metalogical property of 'omitting types' for a wide variety of quantifier logics (that can also be seen as multimodal logics upon identifying existential quantifiers with modalities syntactically and…