Multigrid methodologies in Deep Learning : from ResNet analogies to spectral analysis of convolutions / submitted by Antonia Maria van Betteray. Wuppertal, 2026
Inhalt
- Acknowledgments
- Foreword
- Introduction
- Fundamentals of Numerical Linear Algebra
- Matrix Decompositions
- Crystalline Structures
- Discrete Fourier Transforms
- Iterative Methods
- Multigrid Methods
- Fundamentals of Machine Learning
- Improving the Accuracy-Weight Trade-off
- Introduction
- Improved Scaling with Respect to all Relevant Dimensions
- Building Blocks Inspired by Polynomial Smoothers
- Related Work
- Reducing the Number of Channels
- Modified Layers
- Multigrid-Inspired Architectures
- Polynomial Neural Networks
- Residual Learning and Multigrid Methods
- Revisiting ResNet and Multigrid
- Resolution Coarsening
- Full Approximation Scheme (FAS) for Resolution Coarsening
- Multigrid in all Dimensions (MGiaD)
- Channel Coarsening
- Multigrid in Resolution and Channel Dimensions
- Experimental Setup and Evaluation
- Conclusion
- Poly-MgNet: Polynomial Building Blocks in Multigrid-Inspired ResNets
- Efficient SVD by Local Fourier Analysis
- Discussion & Outlook
- List of Notations
- Bibliography
- Appendix