Continuous Generative Neural Networks: A Wavelet-Based Architecture in Function Spaces
In this work, we present and study Continuous Generative Neural Networks (CGNNs), namely, generative models in the continuous setting: the output of a CGNN belongs to an infinite-dimensional function space. The architecture is inspired by DCGAN, with one fully connected layer, several convolutional...
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| creator | Alberti, Giovanni S Santacesaria, Matteo Sciutto, Silvia |
| description | In this work, we present and study Continuous Generative Neural Networks (CGNNs), namely, generative models in the continuous setting: the output of a CGNN belongs to an infinite-dimensional function space. The architecture is inspired by DCGAN, with one fully connected layer, several convolutional layers and nonlinear activation functions. In the continuous \(L^2\) setting, the dimensions of the spaces of each layer are replaced by the scales of a multiresolution analysis of a compactly supported wavelet. We present conditions on the convolutional filters and on the nonlinearity that guarantee that a CGNN is injective. This theory finds applications to inverse problems, and allows for deriving Lipschitz stability estimates for (possibly nonlinear) infinite-dimensional inverse problems with unknowns belonging to the manifold generated by a CGNN. Several numerical simulations, including signal deblurring, illustrate and validate this approach. |
| doi_str_mv | 10.48550/arxiv.2205.14627 |
| format | Article |
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| subjects | Computer Science - Learning Continuity (mathematics) Electromagnetic wave filters Inverse problems Mathematical models Multiresolution analysis Neural networks Nonlinearity Statistics - Machine Learning |
| title | Continuous Generative Neural Networks: A Wavelet-Based Architecture in Function Spaces |
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