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pro vyhledávání: '"41A65"'
Autor:
Ismailov, Vugar
We study feedforward neural networks with inputs from a topological vector space (TVS-FNNs). Unlike traditional feedforward neural networks, TVS-FNNs can process a broader range of inputs, including sequences, matrices, functions and more. We prove a
Externí odkaz:
http://arxiv.org/abs/2409.12913
We characterize rotund, uniformly rotund, locally uniformly rotund and compactly locally uniformly rotund spaces in terms of sets of (almost) farthest points from the unit sphere using the generalized diameter. For this we introduce few remotality pr
Externí odkaz:
http://arxiv.org/abs/2409.08697
Property~(A) is a week symmetry condition that plays a fundamental role in the characterization of greedy-type bases in the isometric case, i.e., when the constants involved in the study of the efficiency of the thresholding greedy algorithm in Banac
Externí odkaz:
http://arxiv.org/abs/2409.04883
For non-empty sets X we define notions of distance and pseudo metric with values in a partially ordered set that has a smallest element $\theta $. If $h_X$ is a distance in $X$ (respectively, a pseudo metric in $X$), then the pair $(X,h_X)$ is called
Externí odkaz:
http://arxiv.org/abs/2408.15579
In this paper, we examine a discrete dynamical system defined by x(n+1) = Ax(n)+ w(n), where x takes values in a Hilbert space H and w is a periodic source with values in a fixed closed subspace W of H. Our goal is to identify conditions on some spat
Externí odkaz:
http://arxiv.org/abs/2408.06934
Autor:
Moser, Bernhard A., Lunglmayr, Michael
The linearly inseparable XOR problem and the related problem of representing binary logical gates is revisited from the point of view of temporal encoding and its solvability by spiking neural networks with minimal configurations of leaky integrate-a
Externí odkaz:
http://arxiv.org/abs/2408.05845
Autor:
Chen, Deliang
The Machado--Bishop theorem for weighted vector-valued functions vanishing at infinity has been extensively studied. In this paper, we give an analogue of Machado's distance formula for bounded weighted vector-valued functions. A number of applicatio
Externí odkaz:
http://arxiv.org/abs/2407.19925
Publikováno v:
Monatsh. Math.204 (2024), no.4, 969-987
We study the best coapproximation problem in Banach spaces, by using Birkhoff-James orthogonality techniques. We introduce two special types of subspaces, christened the anti-coproximinal subspaces and the strongly anti-coproximinal subspaces. We obt
Externí odkaz:
http://arxiv.org/abs/2407.14471
Autor:
Trunschke, Philipp, Nouy, Anthony
This manuscript addresses the problem of approximating an unknown function from point evaluations. When obtaining these point evaluations is costly, minimising the required sample size becomes crucial, and it is unreasonable to reserve a sufficiently
Externí odkaz:
http://arxiv.org/abs/2407.06674
Autor:
Morina, Erion, Holler, Martin
This work focuses on the analysis of fully connected feed forward ReLU neural networks as they approximate a given, smooth function. In contrast to conventionally studied universal approximation properties under increasing architectures, e.g., in ter
Externí odkaz:
http://arxiv.org/abs/2406.14936