Why and When Can Deep -- but Not Shallow -- Networks Avoid the Curse of Dimensionality: a Review

The paper characterizes classes of functions for which deep learning can be exponentially better than shallow learning. Deep convolutional networks are a special case of these conditions, though weight sharing is not the main reason for their exponential advantage

Image-based Relighting Using Implicit Neural Representation

Rendering a scene under novel lighting has been a problem in all fields that require computer graphics knowledge, and Image-based relighting is one of the best ways to reconstruct the scene correctly. Current research on Image-based relighting uses discrete convolutional neural networks, which tend to be less fit-able to different spatial resolutions and take up massive memory spaces. However, the implicit neural representation solves the problem by mapping the coordinates of the image directly to the value of the coordinate with a continuous function modeled through the neural network. In this way, despite the changing of the image resolution, the parameters taken in by the neural network stay the same, so the complexity stays the same. Also, the rectified linear activation unit (ReLU) based network used in current research lacks the representation of information of second and higher derivatives. On the other hand, the sinusoidal representation networks (SIREN) provide a new way to solve this problem by using periodic activation functions like the sin curve. Hence, my research intends to leverage implicit neural representation with periodic activation functions in image-based relighting. To tackle the research question, we proposed to base our image-relighting network on the SIREN network in the research by Sitzmann. Our method is to modify the SIREN network so that it takes in not only coordinates but also light positions. Then we train it with a set of input images depicting the same set of sparse objects in different lighting conditions and their corresponding light positions, as in previous image-based relighting research. We test our network by giving the network new lighting positions, and the result we aim for is to acquire a good representation of optimal sparse samples under novel lighting with high-frequency details. Eventually, we run the training and test with several different input sets and acquire their results. We also compare and evaluate the results, in order to find the advantage or limitation of the method