Several Fundamental Problems in Deep Learning and Meta-Learning

The main purpose of this research project is to study several fundamental problems in deep learning and meta-Learning. The first topic is on the expressive power of deep neural networks. One fundamental problem in deep learning is understanding the outstanding performance of deep neural networks in practice. One explanation for the superiority of deep neural networks is that they can realize a large class of complicated functions, i.e., they have powerful expressivity. There are several measures for the expressivity of neural networks, such as the maximal number of linear regions a neural network can realize. Our aim is to have a better understanding of these measures, which could be useful in the selection of neural network architectures in practice and thus lead to better performance on practical problems.

The second topic is on the meta-learning for domain generalization. Domain shift has been extensively researched in domain generalization, mostly by learning feature representations that are invariant across domains. The general challenge of domain generalization in image classification is to exploit the data variations of seen image domains with the aim to generalize well to unseen image domains. Our aim is to develop meta-learning methods to deal with the prediction uncertainty on unseen domains.