Related papers: Categorical Foundations for CuTe Layouts
Categorical data does not have an intrinsic definition of distance or order, and therefore, established visualization techniques for categorical data only allow for a set-based or frequency-based analysis, e.g., through Euler diagrams or…
As the text databases available to users become larger and more heterogeneous, genre becomes increasingly important for computational linguistics as a complement to topical and structural principles of classification. We propose a theory of…
We take a novel lattice-theoretic approach to the $\tau$-cluster morphism category $\mathfrak{T}(A)$ of a finite-dimensional algebra $A$ and define the category via the lattice of torsion classes $\mathrm{tors } A$. Using the lattice…
Based on Gandy's principles for models of computation we give category-theoretic axioms describing locally deterministic updates to finite objects. Rather than fixing a particular category of states, we describe what properties such a…
Non-deterministic constraint logic (NCL) is a simple model of computation based on orientations of a constraint graph with edge weights and vertex demands. NCL captures \PSPACE\xspace and has been a useful tool for proving algorithmic…
We define a model for linear logic based on two well-known ingredients: games and simulations. This model is interesting in the following respect: while it is obvious that the objects interpreting formulas are games and that everything is…
We describe LEGO, a new approach to optimizing data movement whereby code is expressed as a layout-independent computation and composed with layouts for data and computation. This code generator organization derives complex indexing…
Software Categorization is the task of organizing software into groups that broadly describe the behavior of the software, such as "editors" or "science." Categorization plays an important role in several maintenance tasks, such as…
Clustering is a fundamental learning task widely used as a first step in data analysis. For example, biologists use cluster assignments to analyze genome sequences, medical records, or images. Since downstream analysis is typically…
A large amount of research on Convolutional Neural Networks has focused on flat Classification in the multi-class domain. In the real world, many problems are naturally expressed as problems of hierarchical classification, in which the…
Most of the current explainability techniques focus on capturing the importance of features in input space. However, given the complexity of models and data-generating processes, the resulting explanations are far from being `complete', in…
We examine various categorical structures that can and cannot be constructed. We show that total computable functions can be mimicked by constructible functors. More generally, whatever can be done by a Turing machine can be constructed by…
In this paper, we describe a general class of $C^1$ smooth rational splines that enables, in particular, exact descriptions of ellipses and ellipsoids - some of the most important primitives for CAD and CAE. The univariate rational splines…
The categorified theories known as "doctrines" specify a category equipped with extra structure, analogous to how ordinary theories specify a set with extra structure. We introduce a new framework for doctrines based on double category…
We propose Neural Turtle Graphics (NTG), a novel generative model for spatial graphs, and demonstrate its applications in modeling city road layouts. Specifically, we represent the road layout using a graph where nodes in the graph…
We propose a type-theoretic framework for describing and proving properties of quantum computations, in particular those presented as quantum circuits. Our proposal is based on an observation that, in the polymorphic type system of Coq,…
Whether it be source code in a programming language, prose in natural language, or otherwise, text is highly structured. Currently, text visualizations are confined either to _flat, line-based_ decorations, which can convey only limited…
Harnessing the potential computational advantage of quantum computers for machine learning tasks relies on the uploading of classical data onto quantum computers through what are commonly referred to as quantum encodings. The choice of such…
We review the categorical approach to the BPS sector of a 4d $\mathcal{N}=2$ QFT, clarifying many tricky issues and presenting a few novel results. To a given $\mathcal{N}=2$ QFT one associates several triangle categories: they describe…
Condensed mathematics, developed by Clausen and Scholze over the last few years, proposes a generalization of topology with better categorical properties. It replaces the concept of a topological space by that of a condensed set, which can…