In this paper, we propose training very deep neural networks (DNNs) for supervised learning of hash codes. Existing methods in this context train relatively "shallow" networks limited by the issues arising in back propagation (e.e. vanishing gradients) as well as computational efficiency. We propose a novel and efficient training algorithm inspired by alternating direction method of multipliers (ADMM) that overcomes some of these limitations. Our method decomposes the training process into independent layer-wise local updates through auxiliary variables. Empirically we observe that our training algorithm always converges and its computational complexity is linearly proportional to the number of edges in the networks. Empirically we manage to train DNNs with 64 hidden layers and 1024 nodes per layer for supervised hashing in about 3 hours using a single GPU. Our proposed very deep supervised hashing (VDSH) method significantly outperforms the state-of-the-art on several benchmark datasets.
( 2 ) DNNs: In the literature, many different DNN architectures ( LeNet @cite_9 , AlexNet @cite_0 , GoogLeNet @cite_46 and VGG-VD @cite_18 ) and weighting structures ( sparse network @cite_21 , circulant structure @cite_32 , low-rank approximation @cite_11 ) have been proposed. Several techniques have been proposed to improve the generalization of networks such as dropout @cite_45 and dropconnet @cite_15 , which can be viewed as better regularization. Some techniques for speeding-up the training have been proposed as well such as distributed training @cite_13 and batch normalization @cite_48 . These architectures and methods, however, are trained using backprop, suffering from the same issues such as vanishing gradients.
@cite_18 @cite_15 @cite_48 @cite_9 @cite_21 @cite_32 @cite_0 @cite_45 @cite_46 @cite_13 @cite_11
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Optimizing deep neural networks (DNNs) often suffers from the ill-conditioned problem. We observe that the scaling-based weight space symmetry property in rectified nonlinear network will cause this negative effect. Therefore, we propose to constrain the incoming weights of each neuron to be unit-norm, which is formulated as an optimization problem over Oblique manifold. A simple yet efficient method referred to as projection based weight normalization (PBWN) is also developed to solve this problem. PBWN executes standard gradient updates, followed by projecting the updated weight back to Oblique manifold. This proposed method has the property of regularization and collaborates well with the commonly used batch normalization technique. We conduct comprehensive experiments on several widely-used image datasets including CIFAR-10, CIFAR-100, SVHN and ImageNet for supervised learning over the state-of-the-art convolutional neural networks, such as Inception, VGG and residual networks. The results show that our method is able to improve the performance of DNNs with different architectures consistently. We also apply our method to Ladder network for semi-supervised learning on permutation invariant MNIST dataset, and our method outperforms the state-of-the-art methods: we obtain test errors as 2.52 , 1.06 , and 0.91 with only 20, 50, and 100 labeled samples, respectively. Recently, DNN model compression based on network architecture design, e.g., SqueezeNet, attracted a lot attention. No accuracy drop on image classification is observed on these extremely compact networks, compared to well-known models. An emerging question, however, is whether these model compression techniques hurt DNNs learning ability other than classifying images on a single dataset. Our preliminary experiment shows that these compression methods could degrade domain adaptation (DA) ability, though the classification performance is preserved. Therefore, we propose a new compact network architecture and unsupervised DA method in this paper. The DNN is built on a new basic module Conv-M which provides more diverse feature extractors without significantly increasing parameters. The unified framework of our DA method will simultaneously learn invariance across domains, reduce divergence of feature representations, and adapt label prediction. Our DNN has 4.1M parameters, which is only 6.7 of AlexNet or 59 of GoogLeNet. Experiments show that our DNN obtains GoogLeNet-level accuracy both on classification and DA, and our DA method slightly outperforms previous competitive ones. Put all together, our DA strategy based on our DNN achieves state-of-the-art on sixteen of total eighteen DA tasks on popular Office-31 and Office-Caltech datasets. Deep neural networks (DNNs) have begun to have a pervasive impact on various applications of machine learning. However, the problem of finding an optimal DNN architecture for large applications is challenging. Common approaches go for deeper and larger DNN architectures but may incur substantial redundancy. To address these problems, we introduce a network growth algorithm that complements network pruning to learn both weights and compact DNN architectures during training. We propose a DNN synthesis tool (NeST) that combines both methods to automate the generation of compact and accurate DNNs. NeST starts with a randomly initialized sparse network called the seed architecture. It iteratively tunes the architecture with gradient-based growth and magnitude-based pruning of neurons and connections. Our experimental results show that NeST yields accurate, yet very compact DNNs, with a wide range of seed architecture selection. For the LeNet-300-100 (LeNet-5) architecture, we reduce network parameters by 70.2x (74.3x) and floating-point operations (FLOPs) by 79.4x (43.7x). For the AlexNet and VGG-16 architectures, we reduce network parameters (FLOPs) by 15.7x (4.6x) and 30.2x (8.6x), respectively. NeST's grow-and-prune paradigm delivers significant additional parameter and FLOPs reduction relative to pruning-only methods. Deep neural networks (DNNs) have begun to have a pervasive impact on various applications of machine learning. However, the problem of finding an optimal DNN architecture for large applications is challenging. Common approaches go for deeper and larger DNN architectures but may incur substantial redundancy. To address these problems, we introduce a network growth algorithm that complements network pruning to learn both weights and compact DNN architectures during training. We propose a DNN synthesis tool (NeST) that combines both methods to automate the generation of compact and accurate DNNs. NeST starts with a randomly initialized sparse network called the seed architecture. It iteratively tunes the architecture with gradient-based growth and magnitude-based pruning of neurons and connections. Our experimental results show that NeST yields accurate, yet very compact DNNs, with a wide range of seed architecture selection. For the LeNet-300-100 (LeNet-5) architecture, we reduce network parameters by @math 70.2× ( @math 74.3×) and floating-point operations (FLOPs) by @math 79.4× ( @math 43.7×). For the AlexNet, VGG-16, and ResNet-50 architectures, we reduce network parameters (FLOPs) by @math 15.7× ( @math 4.6×), @math 33.2× ( @math 8.9×), and @math 4.1× ( @math 2.1×) respectively. NeST's grow-and-prune paradigm delivers significant additional parameter and FLOPs reduction relative to pruning-only methods.