Related papers: Image and Transfer Functions
Neural network systems describe complex mappings that can be very difficult to understand. In this paper, we study the inverse problem of determining the input images that get mapped to specific neural network classes. Ultimately, we expect…
We present a novel usage of Transformers to make image classification interpretable. Unlike mainstream classifiers that wait until the last fully connected layer to incorporate class information to make predictions, we investigate a…
We study Translation functors and Wall-Crossing functors on infinite dimensional representations of a complex semisimple Lie algebra using D-modules. This functorial machinery is then used to prove the Endomorphism-theorem and the…
We outline the theory of reflections for prederivators, derivators and stable derivators. In order to parallel the classical theory valid for categories, we outline how reflections can be equivalently described as categories of fractions,…
The results presented in this paper are refinements of some results presented in a previous paper. Three such refined results are presented. The first one relaxes one of the basic hypotheses assumed in the previous paper, and thus extends…
In Musilak-Orlicz type spaces ${\mathcal S}_{\bf M}$, direct and inverse approximation theorems are obtained in terms of the best approximations of functions and generalized moduli of smoothness. The question of the exact constants in…
The theory of generalized inverses of matrices and operators is closely connected with projections, i.e., idempotent (bounded) linear transformations. We show that a similar situation occurs in any associative ring $\mathcal{R}$ with a unit…
Understanding the mechanisms underlying deep neural networks remains a fundamental challenge in machine learning and computer vision. One promising, yet only preliminarily explored approach, is feature inversion, which attempts to…
We review three examples of functors from Lorentzian categories and their applications in finiteness results, singularity theorems and boundary constructions. The third example is a novel functor from the category of ordered measure spaces…
We develop a transfer matrix formalism for four-flux radiative transfer models, which is ideally suited for studying transport through multiple scattering layers. The model, derived for spherical particles within the diffusion…
The notions of faithfully projective, faithfully flat, and faithfully injective modules--defined as modules for which the three classical homological functors are both faithful and exact--play fundamental roles across various areas of…
An inventory of all possible homogenous Hilbert curves in two dimensions are reported. Six new Hilbert curves are described by introducing the reversion operation in the construction algorithm. For each curve, the set of affine…
Optics, aka functional references, are classes of tools that allow composable access into compound data structures. Usually defined as programming language libraries, they provide combinators to manipulate different shapes of data such as…
We study the properties of different type of transforms by means of operational methods and discuss the relevant interplay with many families of special functions. We consider in particular the binomial transform and its generalizations. A…
The translation operator $T^A$ associated with the special affine Fourier transform (SAFT) $\mathscr{F}_A$ is introduced from harmonic analysis point of view. The analogues of Wendel's theorem, Wiener theorem, Weiner-Tauberian theorem and…
In this paper, we propose a numerical method of Fourier transform based on hyperfunction theory. In the proposed method, we compute analytic functions called the defining functions, which give the desired Fourier transform as a…
We give a natural notion of (non-exact) integral functor in the context of k-linear and graded categories. In this broader sense, we prove that every k-linear and graded functor is integral.
A discrete complexified quaternion Fourier transform is introduced. This is a generalization of the discrete quaternion Fourier transform to the case where either or both of the signal/image and the transform kernel are complex…
We introduce a new concept of s-recollements of extriangulated categories, which generalizes recollements of abelian categories, recollements of triangulated categories, as well as recollements of extriangulated categories. Moreover, some…
This paper considers some open questions related to the inverse problem of pure point diffraction, in particular, what types of objects may diffract, and which of these may exhibit the same diffraction. Some diverse objects with the same…