Related papers: Neural Network Operators on fuzzy number valued co…
Infinite order differential operators appear in different fields of Mathematics and Physics and in the last decades they turned out to be of fundamental importance in the study of the evolution of superoscillations as initial datum for…
Some fractals -- for instance those associated with the Mandelbrot and quadratic Julia sets -- are computed by iterating a function, and identifying the boundary between hyperparameters for which the resulting series diverges or remains…
Traditional Recurrent Neural Networks assume vectorized data as inputs. However many data from modern science and technology come in certain structures such as tensorial time series data. To apply the recurrent neural networks for this type…
In this paper, we consider the locally convex spaces of entire functions with growth given by proximate orders, and study the representation as a differential operator of a continuous homomorphism from such a space to another one. As a…
Operator learning refers to the application of ideas from machine learning to approximate (typically nonlinear) operators mapping between Banach spaces of functions. Such operators often arise from physical models expressed in terms of…
We study asynchronous federated learning mechanisms with nodes having potentially different computational speeds. In such an environment, each node is allowed to work on models with potential delays and contribute to updates to the central…
We consider a class of linear differential operators acting on vector-valued function spaces with general coupled boundary conditions. Unlike in the more usual case of so-called quantum graphs, the boundary conditions can be nonlinear.…
Traditional convolutional neural networks are limited to handling Euclidean space data, overlooking the vast realm of real-life scenarios represented as graph data, including transportation networks, social networks, and reference networks.…
Artificial neural networks can learn complex, salient data features to achieve a given task. On the opposite end of the spectrum, mathematically grounded methods such as topological data analysis allow users to design analysis pipelines…
This work proposes a Neural Network model that can control its depth using an iterate-to-fixed-point operator. The architecture starts with a standard layered Network but with added connections from current later to earlier layers, along…
We develop a phenomenological coarse--graining procedure for activity in a large network of neurons, and apply this to recordings from a population of 1000+ cells in the hippocampus. Distributions of coarse--grained variables seem to…
A scale of the Frechet spaces of exponential type entire functions of one complex variable is considered. Certain special properties of subsets of these spaces consisting of Laguerre entire functions, which are obtained as uniform limits on…
In this paper, we investigate Durrmeyer-type generalizations of maximum-minimum neural network operators. The primary objective of this study is to establish the convergence of these operators in the $L^{p}$ norm for functions $f\in…
In this paper, a new self-organizing fuzzy neural network model is presented which is able to learn and reproduce different sequences accurately. Sequence learning is important in performing skillful tasks, such as writing and playing…
We consider half-line Dirac operators with operator data of Wigner-von Neumann type. If the data is a finite linear combination of Wigner-von Neumann functions, we show absence of singular continuous spectrum and provide an explicit set…
In this note, we consider the space of all continuous operators with respect to the unbounded topology on locally solid vector lattices. We investigate whether this space forms a band. In addition, we look into some situations under which,…
Neural operators (NOs) are designed to learn maps between infinite-dimensional function spaces. We propose a novel reframing of their use. By introducing an auxiliary base-space, any finite-dimensional function can be viewed as an operator…
Derivatives and integration operators are well-studied examples of linear operators that commute with scaling up to a fixed multiplicative factor; i.e., they are scale-invariant. Fractional order derivatives (integration operators) also…
In this paper we study the theory of the so-called Kantorovich max-product neural network operators in the setting of Orlicz spaces $L^{\varphi}$. The results here proved, extend those given by Costarelli and Vinti in Result Math., 2016, to…
Recently, graph neural networks have attracted great attention and achieved prominent performance in various research fields. Most of those algorithms have assumed pairwise relationships of objects of interest. However, in many real…