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.

Deep neural networks (DNNs) have achieved great success, but the applications to mobile devices are limited due to their huge model size and low inference speed. Much effort thus has been devoted to pruning DNNs. Layer-wise neuron pruning methods have shown their effectiveness, which minimize the reconstruction error of linear response with a limited number of neurons in each single layer pruning. In this paper, we propose a new layer-wise neuron pruning approach by minimizing the reconstruction error of nonlinear units, which might be more reasonable since the error before and after activation can change significantly. An iterative optimization procedure combining greedy selection with gradient decent is proposed for single layer pruning. Experimental results on benchmark DNN models show the superiority of the proposed approach. Particularly, for VGGNet, the proposed approach can compress its disk space by 13.6× and bring a speedup of 3.7×; for AlexNet, it can achieve a compression rate of 4.1× and a speedup of 2.2×, respectively.

Layer-wise magnitude-based pruning (LMP) is a very popular method for deep neural network (DNN) compression. However, tuning the layer-specific thresholds is a difficult task, since the space of threshold candidates is exponentially large and the evaluation is very expensive. Previous methods are mainly by hand and require expertise. In this paper, we propose an automatic tuning approach based on optimization, named OLMP. The idea is to transform the threshold tuning problem into a constrained optimization problem (i.e., minimizing the size of the pruned model subject to a constraint on the accuracy loss), and then use powerful derivative-free optimization algorithms to solve it. To compress a trained DNN, OLMP is conducted within a new iterative pruning and adjusting pipeline. Empirical results show that OLMP can achieve the best pruning ratio on LeNet-style models (i.e., 114 times for LeNet-300-100 and 298 times for LeNet-5) compared with some state-of-the- art DNN pruning methods, and can reduce the size of an AlexNet-style network up to 82 times without accuracy loss.

The subset selection problem that selects a few items from a ground set arises in many applications such as maximum coverage, influence maximization, sparse regression, etc. The recently proposed POSS algorithm is a powerful approximation solver for this problem. However, POSS requires centralized access to the full ground set, and thus is impractical for large-scale real-world applications, where the ground set is too large to be stored on one single machine. In this paper, we propose a distributed version of POSS (DPOSS) with a bounded approximation guarantee. DPOSS can be easily implemented in the MapReduce framework. Our extensive experiments using Spark, on various real-world data sets with size ranging from thousands to millions, show that DPOSS can achieve competitive performance compared with the centralized POSS, and is almost always better than the state-of-the-art distributed greedy algorithm RANDGREEDI.

Purpose The purpose of this study is to develop a novel region-based convolutional neural networks (R-CNN) approach that is more efficient while at least as accurate as existing R-CNN methods. In this way, the proposed method, namely R2-CNN, provides a more powerful tool for pedestrian extraction for person re-identification, which involve a huge number of images and pedestrian needs to be extracted efficiently to meet the real-time requirement. Design/methodology/approach The proposed R2-CNN is tested on two types of data sets. The first one the USC Pedestrian Detection data set, which consists of three sub-sets USC-A, UCS-B and USC-C, with respect to their characteristics. This data set is used to test the performance of R2-CNN in the pedestrian extraction task. The speed and performance of the investigated algorithms were collected. The second data set is the PASCAL VOC 2007 data set, which is a common benchmark data set for object detection. This data set was used to analyze characteristics of R2-CNN in the case of general object detection task. Findings This study proposes a novel R-CNN method that is both more efficient and more accurate than existing methods. The method, when used as an object detector, would facilitate the data preprocessing stage of person re-identification. Originality/value The study proposes a novel approach for object detection, which shows advantages in both efficiency and accuracy for pedestrian detection task. It contributes to both data preprocessing for person re-identification and the research on deep learning.

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