Visualizing Optimizers using Chebyshev Proxies and Fatou Sets
| dc.contributor.author | Winchenbach, Rene | en_US |
| dc.contributor.author | Thuerey, Nils | en_US |
| dc.contributor.editor | Bender, Jan | en_US |
| dc.contributor.editor | Botsch, Mario | en_US |
| dc.contributor.editor | Keim, Daniel A. | en_US |
| dc.date.accessioned | 2022-09-26T09:28:52Z | |
| dc.date.available | 2022-09-26T09:28:52Z | |
| dc.date.issued | 2022 | |
| dc.description.abstract | With recent advances in optimization many different optimization approaches have been proposed, especially regarding the optimization of weights for neural networks. However, comparing these approaches in a visually succinct and intuitive manner is difficult to do, especially without relying on simplified toy examples that may not be representative. In this paper, we present a visualization toolkit using a modified variant of Fatou sets of functions in the complex domain to directly visualize the convergence behavior of an optimizer across a large range of input values. Furthermore, we propose an approach of generating test functions based on polynomial Chebyshev proxies, with polynomial degrees up to 11217, and a modification of these proxies to yield functions that are strictly positive with known global minima, i.e., roots. Our proposed toolkit is provided as a cross platform open source framework in C++ using OpenMP for parallelization. Finally, for menomorphic functions the process generates visually interesting fractals, which might also be interesting from an artistic standpoint. | en_US |
| dc.description.sectionheaders | Session II | |
| dc.description.seriesinformation | Vision, Modeling, and Visualization | |
| dc.identifier.doi | 10.2312/vmv.20221206 | |
| dc.identifier.isbn | 978-3-03868-189-2 | |
| dc.identifier.pages | 75-82 | |
| dc.identifier.pages | 8 pages | |
| dc.identifier.uri | https://doi.org/10.2312/vmv.20221206 | |
| dc.identifier.uri | https://diglib.eg.org:443/handle/10.2312/vmv20221206 | |
| dc.publisher | The Eurographics Association | en_US |
| dc.rights | Attribution 4.0 International License | |
| dc.rights.uri | https://creativecommons.org/licenses/by/4.0/ | |
| dc.subject | CCS Concepts: Mathematics of computing --> Computations on polynomials; Human-centered computing --> Scientific visualization | |
| dc.subject | Mathematics of computing | |
| dc.subject | Computations on polynomials | |
| dc.subject | Human centered computing | |
| dc.subject | Scientific visualization | |
| dc.title | Visualizing Optimizers using Chebyshev Proxies and Fatou Sets | en_US |