Guiying Li

Yunwen Lei, Ting Hu, Guiying Li et al.

Stochastic gradient descent (SGD) is a popular and efficient method with wide applications in training deep neural nets and other nonconvex models. While the behavior of SGD is well understood in the convex learning setting, the existing theoretical results for SGD applied to nonconvex objective functions are far from mature. For example, existing results require to impose a nontrivial assumption on the uniform boundedness of gradients for all iterates encountered in the learning process, which is hard to verify in practical implementations. In this paper, we establish a rigorous theoretical foundation for SGD in nonconvex learning by showing that this boundedness assumption can be removed without affecting convergence rates. In particular, we establish sufficient conditions for almost sure convergence as well as optimal convergence rates for SGD applied to both general nonconvex objective functions and gradient-dominated objective functions. A linear convergence is further derived in the case with zero variances.

Guiying Li, Junlong Liu, Chunhui Jiang et al.

R-CNN style methods are sorts of the state-of-the-art object detection methods, which consist of region proposal generation and deep CNN classification. However, the proposal generation phase in this paradigm is usually time consuming, which would slow down the whole detection time in testing. This paper suggests that the value discrepancies among features in deep convolutional feature maps contain plenty of useful spatial information, and proposes a simple approach to extract the information for fast region proposal generation in testing. The proposed method, namely Relief R-CNN (R2-CNN), adopts a novel region proposal generator in a trained R-CNN style model. The new generator directly generates proposals from convolutional features by some simple rules, thus resulting in a much faster proposal generation speed and a lower demand of computation resources. Empirical studies show that R2-CNN could achieve the fastest detection speed with comparable accuracy among all the compared algorithms in testing.