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.

本文探讨了深度学习在计算机视觉领域的成功是否源于自然图像数据低维结构的存在，研究表明自然图像数据集确实具有很低的内在维度，并且低维度数据集更容易被神经网络学习和泛化。同时提出了一种可以在生成对抗网络（GAN）生成的合成数据上验证维度估计工具的技术。

图像的内在维度及其对学习的影响