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dc.contributor.authorWinchenbach, Reneen_US
dc.contributor.authorThuerey, Nilsen_US
dc.contributor.editorBender, Janen_US
dc.contributor.editorBotsch, Marioen_US
dc.contributor.editorKeim, Daniel A.en_US
dc.date.accessioned2022-09-26T09:28:52Z
dc.date.available2022-09-26T09:28:52Z
dc.date.issued2022
dc.identifier.isbn978-3-03868-189-2
dc.identifier.urihttps://doi.org/10.2312/vmv.20221206
dc.identifier.urihttps://diglib.eg.org:443/handle/10.2312/vmv20221206
dc.description.abstractWith 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.publisherThe Eurographics Associationen_US
dc.rightsAttribution 4.0 International License
dc.rights.urihttps://creativecommons.org/licenses/by/4.0/
dc.subjectCCS Concepts: Mathematics of computing --> Computations on polynomials; Human-centered computing --> Scientific visualization
dc.subjectMathematics of computing
dc.subjectComputations on polynomials
dc.subjectHuman centered computing
dc.subjectScientific visualization
dc.titleVisualizing Optimizers using Chebyshev Proxies and Fatou Setsen_US
dc.description.seriesinformationVision, Modeling, and Visualization
dc.description.sectionheadersSession II
dc.identifier.doi10.2312/vmv.20221206
dc.identifier.pages75-82
dc.identifier.pages8 pages


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Attribution 4.0 International License
Except where otherwise noted, this item's license is described as Attribution 4.0 International License