  It is widely believed that natural image data exhibits low-dimensional
structure despite the high dimensionality of conventional pixel
representations. This idea underlies a common intuition for the remarkable
success of deep learning in computer vision. In this work, we apply dimension
estimation tools to popular datasets and investigate the role of
low-dimensional structure in deep learning. We find that common natural image
datasets indeed have very low intrinsic dimension relative to the high number
of pixels in the images. Additionally, we find that low dimensional datasets
are easier for neural networks to learn, and models solving these tasks
generalize better from training to test data. Along the way, we develop a
technique for validating our dimension estimation tools on synthetic data
generated by GANs allowing us to actively manipulate the intrinsic dimension by
controlling the image generation process. Code for our experiments may be found
here https://github.com/ppope/dimensions.
