Tag: operators
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Learning graphons from data: Random walks, transfer operators, and spectral clustering
Learning graphons from data: Random walks, transfer operators, and spectral clustering arXiv:2507.18147v1 Announce Type: new Abstract: Many signals evolve in time as a stochastic process, randomly switching between states over discretely sampled time points. Here we make an explicit link between the underlying stochastic process of a signal that can take on a bounded continuum…
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Learning Operators by Regularized Stochastic Gradient Descent with Operator-valued Kernels
Learning Operators by Regularized Stochastic Gradient Descent with Operator-valued Kernels arXiv:2504.18184v1 Announce Type: new Abstract: This paper investigates regularized stochastic gradient descent (SGD) algorithms for estimating nonlinear operators from a Polish space to a separable Hilbert space. We assume that the regression operator lies in a vector-valued reproducing kernel Hilbert space induced by an operator-valued…
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Mathematical Foundation of Interpretable Equivariant Surrogate Models
Mathematical Foundation of Interpretable Equivariant Surrogate Models arXiv:2503.01942v1 Announce Type: new Abstract: This paper introduces a rigorous mathematical framework for neural network explainability, and more broadly for the explainability of equivariant operators called Group Equivariant Operators (GEOs) based on Group Equivariant Non-Expansive Operators (GENEOs) transformations. The central concept involves quantifying the distance between GEOs by…