Learning Fractals by Gradient Descent

• URL: http://arxiv.org/abs/2303.12722v1
• Date: Tue, 14 Mar 2023 17:20:25 GMT
• Title: Learning Fractals by Gradient Descent
• Authors: Cheng-Hao Tu, Hong-You Chen, David Carlyn, Wei-Lun Chao
• Abstract summary: Recent works in visual recognition have leveraged this property to create random fractal images for model pre-training. We propose a novel approach that learns the parameters underlying a fractal image via gradient descent. We show that our approach can find fractal parameters of high visual quality and be compatible with different loss functions.
• Score: 19.93434604598185
• License: http://creativecommons.org/licenses/by-nc-nd/4.0/
• Abstract: Fractals are geometric shapes that can display complex and self-similar patterns found in nature (e.g., clouds and plants). Recent works in visual recognition have leveraged this property to create random fractal images for model pre-training. In this paper, we study the inverse problem -- given a target image (not necessarily a fractal), we aim to generate a fractal image that looks like it. We propose a novel approach that learns the parameters underlying a fractal image via gradient descent. We show that our approach can find fractal parameters of high visual quality and be compatible with different loss functions, opening up several potentials, e.g., learning fractals for downstream tasks, scientific understanding, etc.

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