In deep learning and computer vision, data is often assumed to lie on a low-dimensional manifold, embedded within the potentially high-dimensional input space — as, for example, for images. However, the manifold is usually not known which hinders deeper understanding of many phenomena in deep learning, such as adversarial examples. Based on my recent CVPR’19 paper, I want to present FONTS, a MNIST-like, synthetically created dataset with known manifold to study adversarial example.
Many recent deep learning frameworks such as Tensorflow, PyTorch, Theano or Torch are based on dense tensors. However, deep learning on non-tensor data structures is also interesting – especially for sparse, three-dimensional data. This article summarizes some of my experiences regarding deep learning on custom data structures in the mentioned libraries.