Related papers: Kantorovich--Kernel Neural Operators: Approximatio…
In this paper, we introduce a Kantorovich version of the Bernstein-type logarithmic operators. The idea comes from the wide literature concerning exponential polynomials that preserve exponential functions: here, the exponential weights are…
In this work we apply deep neural networks to find the non-equilibrium steady state solution to correlated open quantum many-body systems. Motivated by the ongoing search to find more powerful representations of (mixed) quantum states, we…
In this paper, we derive an inverse result for bivariate Kantorovich type sampling series for the space of all continuous functions with upto second order partial derivatives are continuous and bounded on $R^2.$ Further, we prove the rate…
In this chapter we review the main literature related to the recent advancement of deep neural-kernel architecture, an approach that seek the synergy between two powerful class of models, i.e. kernel-based models and artificial neural…
This work explains in detail the theory behind Complex-Valued Neural Network (CVNN), including Wirtinger calculus, complex backpropagation, and basic modules such as complex layers, complex activation functions, or complex weight…
Here we research the univariate quantitative approximation of real and complex valued continuous functions on a compact interval or all the real line by quasi-interpolation, Baskakov type and quadrature type neural network operators. We…
This paper develops a novel operator theoretic framework to study the contraction properties of Markov semigroups with respect to a general class of Kantorovich semi-distances, which notably includes Wasserstein distances. The rather simple…
We consider the problem of deep neural net compression by quantization: given a large, reference net, we want to quantize its real-valued weights using a codebook with $K$ entries so that the training loss of the quantized net is minimal.…
This paper presents novel generalization bounds for vector-valued neural networks and deep kernel methods, focusing on multi-task learning through an operator-theoretic framework. Our key development lies in strategically combining a…
In the present paper, we studied the voronovskaja type theorem for general Gamma type operators. Also, we obtain an error estimate for general Gamma type operators.
In recent years, Orthogonal Recurrent Neural Networks (ORNNs) have gained popularity due to their ability to manage tasks involving long-term dependencies, such as the copy-task, and their linear complexity. However, existing ORNNs utilize…
The Chernoff approximation method is a powerful and flexible tool of functional analysis, which allows in many cases to express exp(tL) in terms of variable coefficients of a linear differential operator L. In this paper, we prove a theorem…
In this paper, we introduce Durrmeyer type modification of Meyer-Konig-Zeller operators based on (p,q)-integers. Rate of convergence of these operators are explored with the help of Korovkin type theorems. We establish some direct results…
Deep learning based on deep neural networks of various structures and architectures has been powerful in many practical applications, but it lacks enough theoretical verifications. In this paper, we consider a family of deep convolutional…
For the past 30 years or so, machine learning has stimulated a great deal of research in the study of approximation capabilities (expressive power) of a multitude of processes, such as approximation by shallow or deep neural networks,…
The Kantorovich exponential sampling series at jump discontinuities of the bounded measurable signal f has been analysed. A representation lemma for the series is established and using this lemma certain approximation theorems for…
The present paper deals with the Stancu type generalization of the Kantorovich discrete $q$-Beta operators. We establish some direct results, which include the asymptotic formula and error estimation in terms of the modulus of continuity…
The successive approximations method allows us to solve problems concerning existence and uniqueness of fixed points of wide classes of operators. The classical result in this field, such as Banach -- Caccioppoli principle together with…
Deep neural networks generalize well on unseen data though the number of parameters often far exceeds the number of training examples. Recently proposed complexity measures have provided insights to understanding the generalizability in…
Motivated by structures that appear in deep neural networks, we investigate nonlinear composite models alternating proximity and affine operators defined on different spaces. We first show that a wide range of activation operators used in…