Related papers: Profunctor Optics, a Categorical Update
Arboreal categories provide an axiomatic framework in which abstract notions of bisimilarity and back-and-forth games can be defined. They act on extensional categories, typically consisting of relational structures, via arboreal…
We introduce a notion of complexity of diagrams (and in particular of objects and morphisms) in an arbitrary category, as well as a notion of complexity of functors between categories equipped with complexity functions. We discuss several…
We construct injective hulls and projective covers in categories of generalized uniform hypergraphs which generalizes the constructions in the category of quivers and the category of undirected graphs. While the constructions are not…
Recurrent Neural Network, Long Short-Term Memory, and Transformer have made great progress in predicting the trajectories of moving objects. Although the trajectory element with the surrounding scene features has been merged to improve…
It is shown that the one-lens system in para-axial optics can serve as an optical computer for contraction of Wigner's little groups and an analogue computer which transforms analytically computations on a spherical surface to those on a…
Category and multicategory theory provide abstract frameworks for describing structures and their compositions, with multicategories extending traditional categories to handle multi-input operations. These theories enable modular reasoning…
Transformation optics (TO) is a new tool for controlling electromagnetic fields. In the context of metamaterial technology, it provides a direct link between a desired electromagnetic (EM) phenomenon and the material response required for…
Some basic features of the simultaneous inclusion of discrete fibrations and discrete opfibrations in categories over a base category X are considered. In particular, we illustrate the formulas (|P)x = ten(x/X,P) ; (P|)x = hom(X/x,P) which…
Free-space optical information transfer through diffusive media is critical in many applications, such as biomedical devices and optical communication, but remains challenging due to random, unknown perturbations in the optical path. In…
Optical resonators enable the generation, manipulation, and storage of electromagnetic waves. They are widely used in technology and fundamental research, in telecommunications, lasers and nonlinear optics, ultra-sensitive measurements in…
The concepts of fuzzy objects and their classes are described that make it possible to structurally represent knowledge about fuzzy and partially-defined objects and their classes. Operations over such objects and classes are also proposed…
This paper introduces a simple type system for combinatory logic in which combinators have at most one type, whose polymorphism is revealed by application. The combinatory types exactly describe the structure of their values, which may be…
How can Transformers model and learn enumerative geometry? What is a robust procedure for using Transformers in abductive knowledge discovery within a mathematician-machine collaboration? In this work, we introduce a Transformer-based…
The usage of transformers has grown from learning about language semantics to forming meaningful visiolinguistic representations. These architectures are often over-parametrized, requiring large amounts of computation. In this work, we…
Many theories of semantic interpretation use lambda-term manipulation to compositionally compute the meaning of a sentence. These theories are usually implemented in a language such as Prolog that can simulate lambda-term operations with…
Metaoptics are thin, planar surfaces consisting of many subwavelength optical resonators that can be designed to simultaneously control the amplitude, phase, and polarization to arbitrarily shape an optical wavefront much in the same manner…
The optical interaction of light and matter is modeled as an oscillating dipole in a plane wave. We analyze absorption, scattering and extinction for this system by the energy flow, which is depicted by streamlines of the Poynting vector.…
This work uses visual knowledge discovery in parallel coordinates to advance methods of interpretable machine learning. The graphic data representation in parallel coordinates made the concepts of hypercubes and hyperblocks (HBs) simple to…
Data integration and migration processes in polystores and multi-model database management systems highly benefit from data and schema transformations. Rigorous modeling of transformations is a complex problem. The data and schema…
Image captioning models typically follow an encoder-decoder architecture which uses abstract image feature vectors as input to the encoder. One of the most successful algorithms uses feature vectors extracted from the region proposals…