Formula-driven supervised learning (FDSL) has been shown to be an effective method for pre-training vision transformers, where ExFractalDB-21k was shown to exceed the pre-training effect of ImageNet-21k. These studies also indicate that contours mattered more than textures when pre-training vision transformers. However, the lack of a systematic investigation as to why these contour-oriented synthetic datasets can achieve the same accuracy as real datasets leaves much room for skepticism. In the present work, we develop a novel methodology based on circular harmonics for systematically investigating the design space of contour-oriented synthetic datasets. This allows us to efficiently search the optimal range of FDSL parameters and maximize the variety of synthetic images in the dataset, which we found to be a critical factor. When the resulting new dataset VisualAtom-21k is used for pre-training ViT-Base, the top-1 accuracy reached 83.7% when fine-tuning on ImageNet-1k. This is only 0.5% difference from the top-1 accuracy (84.2%) achieved by the JFT-300M pre-training, even though the scale of images is 1/14. Unlike JFT-300M which is a static dataset, the quality of synthetic datasets will continue to improve, and the current work is a testament to this possibility. FDSL is also free of the common issues associated with real images, e.g. privacy/copyright issues, labeling costs/errors, and ethical biases.

Formula-driven supervised learning (FDSL) is a pre-training method that relies on synthetic images generated from mathematical formulae such as fractals. Prior work on FDSL has shown that pre-training vision transformers on such synthetic datasets can yield competitive accuracy on a wide range of downstream tasks. These synthetic images are categorized according to the parameters in the mathematical formula that generate them. In the present work, we hypothesize that the process for generating different instances for the same category in FDSL, can be viewed as a form of data augmentation. We validate this hypothesis by replacing the instances with data augmentation, which means we only need a single image per category. Our experiments shows that this one-instance fractal database (OFDB) performs better than the original dataset where instances were explicitly generated. We further scale up OFDB to 21,000 categories and show that it matches, or even surpasses, the model pre-trained on ImageNet-21k in ImageNet-1k fine-tuning. The number of images in OFDB is 21k, whereas ImageNet-21k has 14M. This opens new possibilities for pre-training vision transformers with much smaller datasets.

In the present work, we show that the performance of formula-driven supervised learning (FDSL) can match or even exceed that of ImageNet-21k without the use of real images, human-, and self-supervision during the pre-training of Vision Transformers (ViTs). For example, ViT-Base pre-trained on ImageNet-21k shows 81.8% top-1 accuracy when fine-tuned on ImageNet-1k and FDSL shows 82.7% top-1 accuracy when pre-trained under the same conditions (number of images, hyperparameters, and number of epochs). Images generated by formulas avoid the privacy/copyright issues, labeling cost and errors, and biases that real images suffer from, and thus have tremendous potential for pre-training general models. To understand the performance of the synthetic images, we tested two hypotheses, namely (i) object contours are what matter in FDSL datasets and (ii) increased number of parameters to create labels affects performance improvement in FDSL pre-training. To test the former hypothesis, we constructed a dataset that consisted of simple object contour combinations. We found that this dataset can match the performance of fractals. For the latter hypothesis, we found that increasing the difficulty of the pre-training task generally leads to better fine-tuning accuracy.