Related papers: Categorical Foundations for CuTe Layouts
Despite ample evidence that our concepts, our cognitive architecture, and mathematics itself are all deeply compositional, few models take advantage of this structure. We therefore propose a radically compositional approach to computational…
Solving classification with graph methods has gained huge popularity in recent years. This is due to the fact that the data can be intuitively modeled with graphs to utilize high level features to aid in solving the classification problem.…
Locales have been studied as "topologies without points", mainly by tools of category theory. While traditional topology presents a space as a set of points with specified neighborhoods, localic topology presents a space as a lattice of…
We define a symmetric monoidal category modelling fuzzy concepts and fuzzy conceptual reasoning within G\"ardenfors' framework of conceptual (convex) spaces. We propose log-concave functions as models of fuzzy concepts, showing that these…
A discriminative structured analysis dictionary is proposed for the classification task. A structure of the union of subspaces (UoS) is integrated into the conventional analysis dictionary learning to enhance the capability of…
We classify mobile Pauli stabilizer codes up to gapped interfaces and coarse-graining using the framework of algebraic $\mathrm{L}$-theory. We compare this classification with that of framed TQFTs, theories that arise naturally in the…
The categorical compositional approach to meaning has been successfully applied in natural language processing, outperforming other models in mainstream empirical language processing tasks. We show how this approach can be generalized to…
Classical deep networks are effective because depth enables adaptive geometric deformation of data representations. In quantum neural networks (QNNs), however, depth or state reachability alone does not guarantee this feature-learning…
Structured layouts are preferable in many 2D visual contents (\eg, GUIs, webpages) since the structural information allows convenient layout editing. Computational frameworks can help create structured layouts but require heavy labor input.…
We develop a general framework for working with structured lifting problems, establishing closure and uniqueness properties of their solutions. In a subsequent paper, we apply these results to axiomatize computation rules of cubical type…
This paper proposes a formal cognitive framework for problem solving based on category theory. We introduce cognitive categories, which are categories with exactly one morphism between any two objects. Objects in these categories are…
In many applications of neural network, it is common to introduce huge amounts of input categorical features, as well as output labels. However, since the required network size should have rapid growth with respect to the dimensions of…
We develop a learning framework for building deformable templates, which play a fundamental role in many image analysis and computational anatomy tasks. Conventional methods for template creation and image alignment to the template have…
The emergent dynamics in spacetime diagrams of cellular automata (CAs) is often organised by means of a number of behavioural classes. Whilst classification of elementary CAs is feasible and well-studied, non-elementary CAs are generally…
Over the last decade, Convolutional Neural Networks (CNN) saw a tremendous surge in performance. However, understanding what a network has learned still proves to be a challenging task. To remedy this unsatisfactory situation, a number of…
The purpose of this paper is to show that the dual notions of elements & distinctions are the basic analytical concepts needed to unpack and analyze morphisms, duality, and universal constructions in the Sets, the category of sets and…
For a small quantaloid $\mathcal{Q}$, a $\mathcal{Q}$-closure space is a small category enriched in $\mathcal{Q}$ equipped with a closure operator on its presheaf category. We investigate $\mathcal{Q}$-closure spaces systematically with…
We present a new model of computation, described in terms of monoidal categories. It conforms the Church-Turing Thesis, and captures the same computable functions as the standard models. It provides a succinct categorical interface to most…
We propose a categorial grammar based on classical multiplicative linear logic. This can be seen as an extension of abstract categorial grammars (ACG) and is at least as expressive. However, constituents of {\it linear logic grammars (LLG)}…
We introduce idris-ct, a Idris library providing verified type definitions of categorical concepts.idris-ct strives to be a bridge between academy and industry, catering both to category theorists who want to implement and try their ideas…