Related papers: A Category Theoretic View of Contextual Types: fro…
Graded monads refine traditional monads using effect annotations in order to describe quantitatively the computational effects that a program can generate. They have been successfully applied to a variety of formal systems for reasoning…
The neural architectures of language models are becoming increasingly complex, especially that of Transformers, based on the attention mechanism. Although their application to numerous natural language processing tasks has proven to be very…
As originally proposed, type classes provide overloading and ad-hoc definition, but can still be understood (and implemented) in terms of strictly parametric calculi. This is not true of subsequent extensions of type classes. Functional…
Contextuality is a key feature of quantum mechanics that provides an important non-classical resource for quantum information and computation. Abramsky and Brandenburger used sheaf theory to give a general treatment of contextuality in…
Recent work by Abramsky and Brandenburger used sheaf theory to give a mathematical formulation of non-locality and contextuality. By adopting this viewpoint, it has been possible to define cohomological obstructions to the existence of…
We develop a dependent type theory that is based purely on inductive and coinductive types, and the corresponding recursion and corecursion principles. This results in a type theory with a small set of rules, while still being fairly…
Contextuality is a key distinguishing feature between classical and quantum physics. It expresses a fundamental obstruction to describing quantum theory using classical concepts. In turn, understood as a resource for quantum computation, it…
We present a domain-specific type theory for constructions and proofs in category theory. The type theory axiomatizes notions of category, functor, profunctor and a generalized form of natural transformations. The type theory imposes an…
Dependent Object Types (DOT) is intended to be a core calculus for modelling Scala. Its distinguishing feature is abstract type members, fields in objects that hold types rather than values. Proving soundness of DOT has been surprisingly…
Contextuality is a key distinguishing feature between classical and quantum physics. It expresses a fundamental obstruction to describing quantum theory using classical concepts. In turn, when understood as a resource for quantum…
Quantum theory departs from classical probabilistic theories in foundational ways. These departures--termed quantumness here--power quantum information and computation. This thesis charts the role of discrete structures in assessing…
Commonsense reasoning refers to the ability of evaluating a social situation and acting accordingly. Identification of the implicit causes and effects of a social context is the driving capability which can enable machines to perform…
The purpose of this text is to prove all technical aspects of our model for dependent type theory with parametric quantifiers [Nuyts, Vezzosi and Devriese, 2017]. It is well-known that any presheaf category constitutes a model of dependent…
Linguistic structures exhibit a rich array of global phenomena, however commonly used Markov models are unable to adequately describe these phenomena due to their strong locality assumptions. We propose a novel hierarchical model for…
Contextuality can be understood as the impossibility to construct a globally consistent description of a model even if there is local agreement. In particular, quantum models present this property. We can describe contextuality with the…
We introduce basic notions in category theory to type theorists, including comprehension categories, categories with attributes, contextual categories, type categories, and categories with families along with additional discussions that are…
Transformer with self-attention has led to the revolutionizing of natural language processing field, and recently inspires the emergence of Transformer-style architecture design with competitive results in numerous computer vision tasks.…
We study the relationship between presheaf constructions and free cocompletions in the context of formal category theory, elucidating the coincidence between the two concepts in familiar settings. We show that, in a virtual equipment…
Cognition does not only depend on bottom-up sensor feature abstraction, but also relies on contextual information being passed top-down. Context is higher level information that helps to predict belief states at lower levels. The main…
We introduce MTT, a dependent type theory which supports multiple modalities. MTT is parametrized by a mode theory which specifies a collection of modes, modalities, and transformations between them. We show that different choices of mode…