تقرير
Continuous Generative Neural Networks
| العنوان: | Continuous Generative Neural Networks |
|---|---|
| المؤلفون: | Alberti, Giovanni S., Santacesaria, Matteo, Sciutto, Silvia |
| سنة النشر: | 2022 |
| المجموعة: | Computer Science Statistics |
| مصطلحات موضوعية: | Statistics - Machine Learning, Computer Science - Machine Learning |
| الوصف: | 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. Comment: 40 pages, 8 figures |
| نوع الوثيقة: | Working Paper |
| URL الوصول: | http://arxiv.org/abs/2205.14627 |
| رقم الأكسشن: | edsarx.2205.14627 |
| قاعدة البيانات: | arXiv |
| الوصف غير متاح. |