QCNN layers equivariant under pixel cyclic shifts are exactly characterized as Fourier-mode multiplexers after QFT, enabling a deep network with constant expected gradient norm at initialization.
Discovering transforms: A tutorial on circulant matrices, circular convolution, and the discrete fourier transform.arXiv:1805.05533
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Geometric deep learning provides a unified mathematical framework based on grids, groups, graphs, geodesics, and gauges to explain and extend neural network architectures by incorporating physical regularities.
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Pixel-Translation-Equivariant Quantum Convolutional Neural Networks via Fourier Multiplexers
QCNN layers equivariant under pixel cyclic shifts are exactly characterized as Fourier-mode multiplexers after QFT, enabling a deep network with constant expected gradient norm at initialization.
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Geometric Deep Learning: Grids, Groups, Graphs, Geodesics, and Gauges
Geometric deep learning provides a unified mathematical framework based on grids, groups, graphs, geodesics, and gauges to explain and extend neural network architectures by incorporating physical regularities.