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pro vyhledávání: '"Smets, Bart"'
We introduce a class of trainable nonlinear operators based on semirings that are suitable for use in neural networks. These operators generalize the traditional alternation of linear operators with activation functions in neural networks. Semirings
Externí odkaz:
http://arxiv.org/abs/2405.18805
PDE-based Group Convolutional Neural Networks (PDE-G-CNNs) utilize solvers of geometrically meaningful evolution PDEs as substitutes for the conventional components in G-CNNs. PDE-G-CNNs offer several key benefits all at once: fewer parameters, inher
Externí odkaz:
http://arxiv.org/abs/2403.15182
Autor:
Smets, Bart M. N.
These are the lecture notes that accompanied the course of the same name that I taught at the Eindhoven University of Technology from 2021 to 2023. The course is intended as an introduction to neural networks for mathematics students at the graduate
Externí odkaz:
http://arxiv.org/abs/2403.04807
Group equivariant convolutional neural networks (G-CNNs) have been successfully applied in geometric deep learning. Typically, G-CNNs have the advantage over CNNs that they do not waste network capacity on training symmetries that should have been ha
Externí odkaz:
http://arxiv.org/abs/2210.00935
We introduce a data-driven version of the plus Cartan connection on the homogeneous space $\mathbb{M}_2$ of 2D positions and orientations. We formulate a theorem that describes all shortest and straight curves (parallel velocity and parallel momentum
Externí odkaz:
http://arxiv.org/abs/2208.11004
We present a PDE-based framework that generalizes Group equivariant Convolutional Neural Networks (G-CNNs). In this framework, a network layer is seen as a set of PDE-solvers where geometrically meaningful PDE-coefficients become the layer's trainabl
Externí odkaz:
http://arxiv.org/abs/2001.09046
Total variation regularization and total variation flows (TVF) have been widely applied for image enhancement and denoising. To include a generic preservation of crossing curvilinear structures in TVF we lift images to the homogeneous space $M = \mat
Externí odkaz:
http://arxiv.org/abs/1902.08145
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Akademický článek
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Autor:
Smets, Bart
This paper investigates how concepts from game theory and ICT can contribute to solve challenges in demand side management, an important concept in the upcoming smart grid. Demand side management is about modifying the energy load distribution on the
Externí odkaz:
http://arxiv.org/abs/1409.0547