Related papers: Kantorovich-Type Stochastic Neural Network Operato…

In this paper we study stochastic quasi-Newton methods for nonconvex stochastic optimization, where we assume that noisy information about the gradients of the objective function is available via a stochastic first-order oracle (SFO). We…

This paper explores the asymptotic behavior of univariate neural network operators, with an emphasis on both classical and fractional differentiation over infinite domains. The analysis leverages symmetrized and perturbed hyperbolic tangent…

The lacking of analytic solutions of diverse partial differential equations (PDEs) gives birth to a series of computational techniques for numerical solutions. Although numerous latest advances are accomplished in developing neural…

The aim of this research is to examine various statistical approximation properties with respect to Kantorovich \textit{\text{\texthtq}}-Baskakov operators using wavelets. We discuss and investigate a weighted statistical approximation…

Machine learning provides algorithms that can learn from data and make inferences or predictions on data. Stochastic acceptors or probabilistic automata are stochastic automata without output that can model components in machine learning…

Neural operators generalize neural networks to learn mappings between function spaces from data. They are commonly used to learn solution operators of parametric partial differential equations (PDEs) or propagators of time-dependent PDEs.…

Energy efficiency in computation is ultimately limited by noise, with quantum limits setting the fundamental noise floor. Analog physical neural networks hold promise for improved energy efficiency compared to digital electronic neural…

Recently, there has been a growing interest in distributionally robust optimization (DRO) as a principled approach to data-driven decision making. In this paper, we consider a distributionally robust two-stage stochastic optimization…

Mechanistic modeling provides a biophysically grounded framework for studying the spread of pathological tau protein in tauopathies like Alzheimer's disease. Existing approaches typically model tau propagation as a diffusive process on the…

Random Neural Networks (RNNs) are a class of Neural Networks (NNs) that can also be seen as a specific type of queuing network. They have been successfully used in several domains during the last 25 years, as queuing networks to analyze the…

This work develops a new method for estimating and optimizing the directed information rate between two jointly stationary and ergodic stochastic processes. Building upon recent advances in machine learning, we propose a recurrent neural…

In this paper we construct Stancu type q-Kantrovich-Sz\'asz-Mirakjan operators generated by Dunkl generalization of the exponential function. We obtain some approximation results using the Korovkin approximation theorem and the weighted…

Stochastic variance reduction has proven effective at accelerating first-order algorithms for solving convex finite-sum optimization tasks such as empirical risk minimization. Incorporating second-order information has proven helpful in…

This work introduces a neural operator based surrogate modeling framework for neutron transport computation. Two architectures, the Deep Operator Network (DeepONet) and the Fourier Neural Operator (FNO), were trained for fixed source…

We consider solving a probably infinite dimensional operator equation, where the operator is not modeled by physical laws but is specified indirectly via training pairs of the input-output relation of the operator. Neural operators have…

In this paper, we study the order of approximation for max-product Kantorovich sampling operators based upon generalized kernels in the setting of Orlicz spaces. We establish a quantitative estimate for the considered family of…

Multiplicative stochasticity such as Dropout improves the robustness and generalizability of deep neural networks. Here, we further demonstrate that always-on multiplicative stochasticity combined with simple threshold neurons are…

In the present article, we introduce and study the behaviour of the new family of exponential type neural network operators activated by the sigmoidal functions. We establish the point-wise and uniform approximation theorems for these NN…

Fourier Neural Operators (FNOs) excel on tasks using functional data, such as those originating from partial differential equations. Such characteristics render them an effective approach for simulating the time evolution of quantum…

Stochastic equations play an important role in computational science, due to their ability to treat a wide variety of complex statistical problems. However, current algorithms are strongly limited by their sampling variance, which scales…