Related papers: Categorical Foundations for CuTe Layouts

In this paper, we study the notion of smooth $\infty$-categories within the framework of a six-functor formalism. By leveraging the theory of condensed mathematics and analytic stacks, we apply these results to demonstrate that a rigid…

We survey systematic approaches to basis-restricted fragments of propositional logic and modal logics, with an emphasis on how expressive power and computational complexity depend on the allowed operators. The propositional case is…

In typed functional languages, one can typically only manipulate data in a type-safe manner if it first has been deserialised into an in-memory tree represented as a graph of nodes-as-structs and subterms-as-pointers. We demonstrate how we…

The efficacy of deep learning has resulted in its use in a growing number of applications. The Volta graphics processor unit (GPU) architecture from NVIDIA introduced a specialized functional unit, the "tensor core", that helps meet the…

Enormous activity in the Quantum Computing area has resulted in considering them to solve different difficult problems, including those of applied nature, together with classical computers. An attempt is made in this work to nail down a…

Mechanistic interpretability seeks to understand how Large Language Models (LLMs) represent and process information. Recent approaches based on dictionary learning and transcoders enable representing model computation in terms of sparse,…

This paper presents an automatic layout generation framework in advanced CMOS technologies. The framework extends the template-and-grid-based layout generation methodology with the following additional techniques applied to produce optimal…

To respond to the need of efficient training and inference of deep neural networks, a plethora of domain-specific hardware architectures have been introduced, such as Google Tensor Processing Units and NVIDIA Tensor Cores. A common feature…

Scaling modern deep learning workloads demands coordinated placement of data and compute across device meshes, memory hierarchies, and heterogeneous accelerators. We present Axe Layout, a hardware-aware abstraction that maps logical tensor…

Qualitative Choice Logic (QCL) and Conjunctive Choice Logic (CCL) are formalisms for preference handling, with especially QCL being well established in the field of AI. So far, analyses of these logics need to be done on a case-by-case…

In this paper we presented a novel constructive approach for training deep neural networks using geometric approaches. We show that a topological covering can be used to define a class of distributed linear matrix inequalities, which in…

The algebraic zigzag construction has recently been introduced as a combinatorial foundation for a higher dimensional notion of string diagram. For use in a proof assistant, a layout algorithm is required to determine the optimal rendering…

We utilize classical facts from topology to show that the classification problem in machine learning is always solvable under very mild conditions. Furthermore, we show that a softmax classification network acts on an input topological…

Classification is an important goal in many branches of mathematics. The idea is to describe the members of some class of mathematical objects, up to isomorphism or other important equivalence in terms of relatively simple invariants. Where…

Classical AI planners provide solutions to planning problems in the form of long and opaque text outputs. To aid in the understanding transferability of planning solutions, it is necessary to have a rich and comprehensible representation…

Configural processing, the perception of spatial relationships among an object's components, is crucial for object recognition. However, the teleology and underlying neurocomputational mechanisms of such processing are still elusive,…

For a finite-dimensional gentle algebra, it is already known that the functorially finite torsion classes of its category of finite-dimensional modules can be classified using a combinatorial interpretation, called maximal non-crossing sets…

We study the cluster category of a canonical algebra A in terms of the hereditary category of coherent sheaves over the corresponding weighted projective line X. As an application we determine the automorphism group of the cluster category…

This paper unites two research lines. The first involves finding categorical models of quantum programming languages and their type systems. The second line concerns the program of quantization of mathematical structures, which amounts to…

In the present paper, we propose a new axiomatic approach to nonstandard analysis and its application to the general theory of spatial structures in terms of category theory. Our framework is based on the idea of internal set theory, while…