We propose deeply-supervised nets (DSN), a method that simultaneously minimizes classification error and improves the directness and transparency of the hidden layer learning process. We focus our attention on three aspects of traditional convolutional-neuralnetwork-type (CNN-type) architectures: (1) transparency in the effect intermediate layers have on overall classification; (2) discriminativeness and robustness of learned features, especially in early layers; (3) training effectiveness in the face of "vanishing" gradients. To combat these issues, we introduce "companion" objective functions at each hidden layer, in addition to the overall objective function at the output layer (an integrated strategy distinct from layer-wise pretraining). We also analyze our algorithm using techniques extended from stochastic gradient methods. The advantages provided by our method are evident in our experimental results, showing state-of-the-art performance on MNIST, CIFAR-10, CIFAR-100, and SVHN.

Deep neural nets with a large number of parameters are very powerful machine learning systems. However, overfitting is a serious problem in such networks. Large networks are also slow to use, making it difficult to deal with overfitting by combining the predictions of many different large neural nets at test time. Dropout is a technique for addressing this problem. The key idea is to randomly drop units (along with their connections) from the neural network during training. This prevents units from co-adapting too much. During training, dropout samples from an exponential number of different "thinned" networks. At test time, it is easy to approximate the effect of averaging the predictions of all these thinned networks by simply using a single unthinned network that has smaller weights. This significantly reduces overfitting and gives major improvements over other regularization methods. We show that dropout improves the performance of neural networks on supervised learning tasks in vision, speech recognition, document classification and computational biology, obtaining state-of-the-art results on many benchmark data sets.

Recent work has shown that convolutional networks can be substantially deeper, more accurate, and efficient to train if they contain shorter connections between layers close to the input and those close to the output. In this paper, we embrace this observation and introduce the Dense Convolutional Network (DenseNet), which connects each layer to every other layer in a feed-forward fashion. Whereas traditional convolutional networks with L layers have L connections-one between each layer and its subsequent layer-our network has L(L+1) 2 direct connections. For each layer, the feature-maps of all preceding layers are used as inputs, and its own feature-maps are used as inputs into all subsequent layers. DenseNets have several compelling advantages: they alleviate the vanishing-gradient problem, strengthen feature propagation, encourage feature reuse, and substantially reduce the number of parameters. We evaluate our proposed architecture on four highly competitive object recognition benchmark tasks SVHN, and ImageNet). DenseNets obtain significant improvements over the state-of-the-art on most of them, whilst requiring less computation to achieve high performance. Code and pre-trained models are available at https://github.com/liuzhuang13/DenseNet.

Most modern convolutional neural networks (CNNs) used for object recognition are built using the same principles: Alternating convolution and max-pooling layers followed by a small number of fully connected layers. We re-evaluate the state of the art for object recognition from small images with convolutional networks, questioning the necessity of different components in the pipeline. We find that max-pooling can simply be replaced by a convolutional layer with increased stride without loss in accuracy on several image recognition benchmarks. Following this finding -and building on other recent work for finding simple network structures -we propose a new architecture that consists solely of convolutional layers and yields competitive or state of the art performance on several object recognition datasets (CIFAR-10, CIFAR-100, ImageNet). To analyze the network we introduce a new variant of the "deconvolution approach" for visualizing features learned by CNNs, which can be applied to a broader range of network structures than existing approaches.

Very deep convolutional networks with hundreds of layers have led to significant reductions in error on competitive benchmarks. Although the unmatched expressiveness of the many layers can be highly desirable at test time, training very deep networks comes with its own set of challenges. The gradients can vanish, the forward flow often diminishes, and the training time can be painfully slow. To address these problems, we propose stochastic depth, a training procedure that enables the seemingly contradictory setup to train short networks and use deep networks at test time. We start with very deep networks but during training, for each mini-batch, randomly drop a subset of layers and bypass them with the identity function. This simple approach complements the recent success of residual networks. It reduces training time substantially and improves the test error significantly on almost all data sets that we used for evaluation. With stochastic depth we can increase the depth of residual networks even beyond 1200 layers and still yield meaningful improvements in test error (4.91% on CIFAR-10).

We show that parametric models trained by a stochastic gradient method (SGM) with few iterations have vanishing generalization error. We prove our results by arguing that SGM is algorithmically stable in the sense of Bousquet and Elisseeff. Our analysis only employs elementary tools from convex and continuous optimization. We derive stability bounds for both convex and non-convex optimization under standard Lipschitz and smoothness assumptions.Applying our results to the convex case, we provide new insights for why multiple epochs of stochastic gradient methods generalize well in practice. In the non-convex case, we give a new interpretation of common practices in neural networks, and formally show that popular techniques for training large deep models are indeed stability-promoting. Our findings conceptually underscore the importance of reducing training time beyond its obvious benefit.

We introduce DropConnect, a generalization of Dropout (Hinton et al., 2012), for regularizing large fully-connected layers within neural networks. When training with Dropout, a randomly selected subset of activations are set to zero within each layer. DropConnect instead sets a randomly selected subset of weights within the network to zero. Each unit thus receives input from a random subset of units in the previous layer. We derive a bound on the generalization performance of both Dropout and DropConnect. We then evaluate DropConnect on a range of datasets, comparing to Dropout, and show state-of-the-art results on several image recognition benchmarks by aggregating multiple DropConnect-trained models.

We introduce Parseval networks, a form of deep neural networks in which the Lipschitz constant of linear, convolutional and aggregation layers is constrained to be smaller than 1. Parseval networks are empirically and theoretically motivated by an analysis of the robustness of the predictions made by deep neural networks when their input is subject to an adversarial perturbation. The most important feature of Parseval networks is to maintain weight matrices of linear and convolutional layers to be (approximately) Parseval tight frames, which are extensions of orthogonal matrices to non-square matrices. We describe how these constraints can be maintained efficiently during SGD. We show that Parseval networks match the state-of-the-art in terms of accuracy on CIFAR-10/100 and Street View House Numbers (SVHN), while being more robust than their vanilla counterpart against adversarial examples. Incidentally, Parseval networks also tend to train faster and make a better usage of the full capacity of the networks.

We develop a new edge detection algorithm that addresses two important issues in this long-standing vision problem: (1) holistic image training and prediction; and (2) multi-scale and multi-level feature learning. Our proposed method, holistically-nested edge detection (HED), performs image-to-image prediction by means of a deep learning model that leverages fully convolutional neural networks and deeply-supervised nets. HED automatically learns rich hierarchical representations (guided by deep supervision on side responses) that are important in order to resolve the challenging ambiguity in edge and object boundary detection.We significantly advance the state-of-the-art on the BSD500 dataset (ODS F-score of .782) and the NYU Depth dataset (ODS F-score of .746), and do so with an improved speed (0.4s per image) that is orders of magnitude faster than some recent CNN-based edge detection algorithms.

使用卷积神经网络（CNN）已经显着改善了几种图像处理任务，例如图像分类和对象检测。与Reset和Abseralnet一样，许多架构在创建时至少在一个数据集中实现了出色的结果。培训的一个关键因素涉及网络的正规化，这可以防止结构过度装备。这项工作分析了在过去几年中开发的几种正规化方法，显示了不同CNN模型的显着改进。该作品分为三个主要区域：第一个称为“数据增强”，其中所有技术都侧重于执行输入数据的更改。第二个，命名为“内部更改”，旨在描述修改神经网络或内核生成的特征映射的过程。最后一个称为“标签”，涉及转换给定输入的标签。这项工作提出了与关于正则化的其他可用调查相比的两个主要差异：（i）第一个涉及在稿件中收集的论文并非超过五年，并第二个区别是关于可重复性，即所有作品此处推荐在公共存储库中可用的代码，或者它们已直接在某些框架中实现，例如Tensorflow或Torch。

While depth tends to improve network performances, it also makes gradient-based training more difficult since deeper networks tend to be more non-linear. The recently proposed knowledge distillation approach is aimed at obtaining small and fast-to-execute models, and it has shown that a student network could imitate the soft output of a larger teacher network or ensemble of networks. In this paper, we extend this idea to allow the training of a student that is deeper and thinner than the teacher, using not only the outputs but also the intermediate representations learned by the teacher as hints to improve the training process and final performance of the student. Because the student intermediate hidden layer will generally be smaller than the teacher's intermediate hidden layer, additional parameters are introduced to map the student hidden layer to the prediction of the teacher hidden layer. This allows one to train deeper students that can generalize better or run faster, a trade-off that is controlled by the chosen student capacity. For example, on CIFAR-10, a deep student network with almost 10.4 times less parameters outperforms a larger, state-of-the-art teacher network.

We propose a simultaneous learning and pruning algorithm capable of identifying and eliminating irrelevant structures in a neural network during the early stages of training. Thus, the computational cost of subsequent training iterations, besides that of inference, is considerably reduced. Our method, based on variational inference principles using Gaussian scale mixture priors on neural network weights, learns the variational posterior distribution of Bernoulli random variables multiplying the units/filters similarly to adaptive dropout. Our algorithm, ensures that the Bernoulli parameters practically converge to either 0 or 1, establishing a deterministic final network. We analytically derive a novel hyper-prior distribution over the prior parameters that is crucial for their optimal selection and leads to consistent pruning levels and prediction accuracy regardless of weight initialization or the size of the starting network. We prove the convergence properties of our algorithm establishing theoretical and practical pruning conditions. We evaluate the proposed algorithm on the MNIST and CIFAR-10 data sets and the commonly used fully connected and convolutional LeNet and VGG16 architectures. The simulations show that our method achieves pruning levels on par with state-of the-art methods for structured pruning, while maintaining better test-accuracy and more importantly in a manner robust with respect to network initialization and initial size.

最近对反向传播的近似（BP）减轻了BP的许多计算效率低下和与生物学的不兼容性，但仍然存在重要的局限性。此外，近似值显着降低了基准的准确性，这表明完全不同的方法可能更富有成果。在这里，基于在软冠军全网络中Hebbian学习的最新理论基础上，我们介绍了多层softhebb，即一种训练深神经网络的算法，没有任何反馈，目标或错误信号。结果，它通过避免重量传输，非本地可塑性，层更新的时间锁定，迭代平衡以及（自我）监督或其他反馈信号来实现效率，这在其他方法中是必不可少的。与最先进的生物学知识学习相比，它提高的效率和生物兼容性不能取得准确性的折衷，而是改善了准确性。 MNIST，CIFAR-10，STL-10和IMAGENET上最多五个隐藏层和添加的线性分类器，分别达到99.4％，80.3％，76.2％和27.3％。总之，SOFTHEBB显示出与BP的截然不同的方法，即对几层的深度学习在大脑中可能是合理的，并提高了生物学上的机器学习的准确性。

We propose a novel deep network structure called "Network In Network"(NIN) to enhance model discriminability for local patches within the receptive field. The conventional convolutional layer uses linear filters followed by a nonlinear activation function to scan the input. Instead, we build micro neural networks with more complex structures to abstract the data within the receptive field. We instantiate the micro neural network with a multilayer perceptron, which is a potent function approximator. The feature maps are obtained by sliding the micro networks over the input in a similar manner as CNN; they are then fed into the next layer. Deep NIN can be implemented by stacking mutiple of the above described structure. With enhanced local modeling via the micro network, we are able to utilize global average pooling over feature maps in the classification layer, which is easier to interpret and less prone to overfitting than traditional fully connected layers. We demonstrated the state-of-the-art classification performances with NIN on CIFAR-10 and CIFAR-100, and reasonable performances on SVHN and MNIST datasets.

We introduce a method to train Quantized Neural Networks (QNNs) -neural networks with extremely low precision (e.g., 1-bit) weights and activations, at run-time. At traintime the quantized weights and activations are used for computing the parameter gradients. During the forward pass, QNNs drastically reduce memory size and accesses, and replace most arithmetic operations with bit-wise operations. As a result, power consumption is expected to be drastically reduced. We trained QNNs over the MNIST, CIFAR-10, SVHN and ImageNet datasets. The resulting QNNs achieve prediction accuracy comparable to their 32-bit counterparts. For example, our quantized version of AlexNet with 1-bit weights and 2-bit activations achieves 51% top-1 accuracy. Moreover, we quantize the parameter gradients to 6-bits as well which enables gradients computation using only bit-wise operation. Quantized recurrent neural networks were tested over the Penn Treebank dataset, and achieved comparable accuracy as their 32-bit counterparts using only 4-bits. Last but not least, we programmed a binary matrix multiplication GPU kernel with which it is possible to run our MNIST QNN 7 times faster than with an unoptimized GPU kernel, without suffering any loss in classification accuracy. The QNN code is available online.

深度神经网络（DNN）的计算要求增加导致获得稀疏，且准确的DNN模型的兴趣。最近的工作已经调查了稀疏训练的更加困难的情况，其中DNN重量尽可能稀少，以减少训练期间的计算成本。现有的稀疏训练方法通常是经验的，并且可以具有相对于致密基线的准确性较低。在本文中，我们介绍了一种称为交替压缩/解压缩（AC / DC）训练DNN的一般方法，证明了算法变体的收敛，并表明AC / DC在类似的计算预算中准确地表现出现有的稀疏训练方法;在高稀疏水平下，AC / DC甚至优于现有的现有方法，依赖于准确的预训练密集模型。 AC / DC的一个重要属性是它允许联合培训密集和稀疏的型号，在训练过程结束时产生精确的稀疏密集模型对。这在实践中是有用的，其中压缩变体可能是为了在资源受限的设置中进行部署而不重新执行整个训练流，并且还为我们提供了深入和压缩模型之间的精度差距的见解。代码可在：https://github.com/ist-daslab/acdc。

Much recent research has been devoted to learning algorithms for deep architectures such as Deep Belief Networks and stacks of autoencoder variants with impressive results being obtained in several areas, mostly on vision and language datasets. The best results obtained on supervised learning tasks often involve an unsupervised learning component, usually in an unsupervised pre-training phase. The main question investigated here is the following: why does unsupervised pre-training work so well? Through extensive experimentation, we explore several possible explanations discussed in the literature including its action as a regularizer (Erhan et al., 2009b) and as an aid to optimization . Our results build on the work of Erhan et al. (2009b), showing that unsupervised pre-training appears to play predominantly a regularization role in subsequent supervised training. However our results in an online setting, with a virtually unlimited data stream, point to a somewhat more nuanced interpretation of the roles of optimization and regularization in the unsupervised pre-training effect.

Training a very deep neural network is a challenging task, as the deeper a neural network is, the more non-linear it is. We compare the performances of various preconditioned Langevin algorithms with their non-Langevin counterparts for the training of neural networks of increasing depth. For shallow neural networks, Langevin algorithms do not lead to any improvement, however the deeper the network is and the greater are the gains provided by Langevin algorithms. Adding noise to the gradient descent allows to escape from local traps, which are more frequent for very deep neural networks. Following this heuristic we introduce a new Langevin algorithm called Layer Langevin, which consists in adding Langevin noise only to the weights associated to the deepest layers. We then prove the benefits of Langevin and Layer Langevin algorithms for the training of popular deep residual architectures for image classification.

Deep convolutional networks have proven to be very successful in learning task specific features that allow for unprecedented performance on various computer vision tasks. Training of such networks follows mostly the supervised learning paradigm, where sufficiently many input-output pairs are required for training. Acquisition of large training sets is one of the key challenges, when approaching a new task. In this paper, we aim for generic feature learning and present an approach for training a convolutional network using only unlabeled data. To this end, we train the network to discriminate between a set of surrogate classes. Each surrogate class is formed by applying a variety of transformations to a randomly sampled 'seed' image patch. In contrast to supervised network training, the resulting feature representation is not class specific. It rather provides robustness to the transformations that have been applied during training. This generic feature representation allows for classification results that outperform the state of the art for unsupervised learning on several popular datasets . While such generic features cannot compete with class specific features from supervised training on a classification task, we show that they are advantageous on geometric matching problems, where they also outperform the SIFT descriptor.

We trained a large, deep convolutional neural network to classify the 1.2 million high-resolution images in the ImageNet LSVRC-2010 contest into the 1000 different classes. On the test data, we achieved top-1 and top-5 error rates of 37.5% and 17.0% which is considerably better than the previous state-of-the-art. The neural network, which has 60 million parameters and 650,000 neurons, consists of five convolutional layers, some of which are followed by max-pooling layers, and three fully-connected layers with a final 1000-way softmax. To make training faster, we used non-saturating neurons and a very efficient GPU implementation of the convolution operation. To reduce overfitting in the fully-connected layers we employed a recently-developed regularization method called "dropout" that proved to be very effective. We also entered a variant of this model in the ILSVRC-2012 competition and achieved a winning top-5 test error rate of 15.3%, compared to 26.2% achieved by the second-best entry.