Winchenbach, ReneThuerey, NilsBender, JanBotsch, MarioKeim, Daniel A.2022-09-262022-09-262022978-3-03868-189-2https://doi.org/10.2312/vmv.20221206https://diglib.eg.org:443/handle/10.2312/vmv20221206With 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.Attribution 4.0 International LicenseCCS Concepts: Mathematics of computing --> Computations on polynomials; Human-centered computing --> Scientific visualizationMathematics of computingComputations on polynomialsHuman centered computingScientific visualization10.2312/vmv.2022120675-828 pages