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.

Complexity theory of circuits strongly suggests that deep architectures can be much more efficient (sometimes exponentially) than shallow architectures, in terms of computational elements required to represent some functions. Deep multi-layer neural networks have many levels of non-linearities allowing them to compactly represent highly non-linear and highly-varying functions. However, until recently it was not clear how to train such deep networks, since gradient-based optimization starting from random initialization appears to often get stuck in poor solutions. Hinton et al. recently introduced a greedy layer-wise unsupervised learning algorithm for Deep Belief Networks (DBN), a generative model with many layers of hidden causal variables. In the context of the above optimization problem, we study this algorithm empirically and explore variants to better understand its success and extend it to cases where the inputs are continuous or where the structure of the input distribution is not revealing enough about the variable to be predicted in a supervised task. Our experiments also confirm the hypothesis that the greedy layer-wise unsupervised training strategy mostly helps the optimization, by initializing weights in a region near a good local minimum, giving rise to internal distributed representations that are high-level abstractions of the input, bringing better generalization.

Humans and animals learn much better when the examples are not randomly presented but organized in a meaningful order which illustrates gradually more concepts, and gradually more complex ones. Here, we formalize such training strategies in the context of machine learning, and call them "curriculum learning". In the context of recent research studying the difficulty of training in the presence of non-convex training criteria (for deep deterministic and stochastic neural networks), we explore curriculum learning in various set-ups. The experiments show that significant improvements in generalization can be achieved. We hypothesize that curriculum learning has both an effect on the speed of convergence of the training process to a minimum and, in the case of non-convex criteria, on the quality of the local minima obtained: curriculum learning can be seen as a particular form of continuation method (a general strategy for global optimization of non-convex functions).

We explore an original strategy for building deep networks, based on stacking layers of denoising autoencoders which are trained locally to denoise corrupted versions of their inputs. The resulting algorithm is a straightforward variation on the stacking of ordinary autoencoders. It is however shown on a benchmark of classification problems to yield significantly lower classification error, thus bridging the performance gap with deep belief networks (DBN), and in several cases surpassing it. Higher level representations learnt in this purely unsupervised fashion also help boost the performance of subsequent SVM classifiers. Qualitative experiments show that, contrary to ordinary autoencoders, denoising autoencoders are able to learn Gabor-like edge detectors from natural image patches and larger stroke detectors from digit images. This work clearly establishes the value of using a denoising criterion as a tractable unsupervised objective to guide the learning of useful higher level representations.

The success of machine learning algorithms generally depends on data representation, and we hypothesize that this is because different representations can entangle and hide more or less the different explanatory factors of variation behind the data. Although specific domain knowledge can be used to help design representations, learning with generic priors can also be used, and the quest for AI is motivating the design of more powerful representation-learning algorithms implementing such priors. This paper reviews recent work in the area of unsupervised feature learning and deep learning, covering advances in probabilistic models, auto-encoders, manifold learning, and deep networks. This motivates longer-term unanswered questions about the appropriate objectives for learning good representations, for computing representations (i.e., inference), and the geometrical connections between representation learning, density estimation and manifold learning.

Whereas before 2006 it appears that deep multilayer neural networks were not successfully trained, since then several algorithms have been shown to successfully train them, with experimental results showing the superiority of deeper vs less deep architectures. All these experimental results were obtained with new initialization or training mechanisms. Our objective here is to understand better why standard gradient descent from random initialization is doing so poorly with deep neural networks, to better understand these recent relative successes and help design better algorithms in the future. We first observe the influence of the non-linear activations functions. We find that the logistic sigmoid activation is unsuited for deep networks with random initialization because of its mean value, which can drive especially the top hidden layer into saturation. Surprisingly, we find that saturated units can move out of saturation by themselves, albeit slowly, and explaining the plateaus sometimes seen when training neural networks. We find that a new non-linearity that saturates less can often be beneficial. Finally, we study how activations and gradients vary across layers and during training, with the idea that training may be more difficult when the singular values of the Jacobian associated with each layer are far from 1. Based on these considerations, we propose a new initialization scheme that brings substantially faster convergence.

While logistic sigmoid neurons are more biologically plausible than hyperbolic tangent neurons, the latter work better for training multi-layer neural networks. This paper shows that rectifying neurons are an even better model of biological neurons and yield equal or better performance than hyperbolic tangent networks in spite of the hard non-linearity and non-differentiability at zero, creating sparse representations with true zeros, which seem remarkably suitable for naturally sparse data. Even though they can take advantage of semi-supervised setups with extra-unlabeled data, deep rectifier networks can reach their best performance without requiring any unsupervised pre-training on purely supervised tasks with large labeled datasets. Hence, these results can be seen as a new milestone in the attempts at understanding the difficulty in training deep but purely supervised neural networks, and closing the performance gap between neural networks learnt with and without unsupervised pre-training.

Neural network pruning techniques can reduce the parameter counts of trained networks by over 90%, decreasing storage requirements and improving computational performance of inference without compromising accuracy. However, contemporary experience is that the sparse architectures produced by pruning are difficult to train from the start, which would similarly improve training performance.We find that a standard pruning technique naturally uncovers subnetworks whose initializations made them capable of training effectively. Based on these results, we articulate the lottery ticket hypothesis: dense, randomly-initialized, feed-forward networks contain subnetworks (winning tickets) that-when trained in isolationreach test accuracy comparable to the original network in a similar number of iterations. The winning tickets we find have won the initialization lottery: their connections have initial weights that make training particularly effective.We present an algorithm to identify winning tickets and a series of experiments that support the lottery ticket hypothesis and the importance of these fortuitous initializations. We consistently find winning tickets that are less than 10-20% of the size of several fully-connected and convolutional feed-forward architectures for MNIST and CIFAR10. Above this size, the winning tickets that we find learn faster than the original network and reach higher test accuracy.

Very large deep learning models trained using gradient descent are remarkably resistant to memorization given their huge capacity, but are at the same time capable of fitting large datasets of pure noise. Here methods are introduced by which models may be trained to memorize datasets that normally are generalized. We find that memorization is difficult relative to generalization, but that adding noise makes memorization easier. Increasing the dataset size exaggerates the characteristics of that dataset: model access to more training samples makes overfitting easier for random data, but somewhat harder for natural images. The bias of deep learning towards generalization is explored theoretically, and we show that generalization results from a model's parameters being attracted to points of maximal stability with respect to that model's inputs during gradient descent.

我们介绍了SubGD，这是一种新颖的几声学习方法，基于最近的发现，即随机梯度下降更新往往生活在低维参数子空间中。在实验和理论分析中，我们表明模型局限于合适的预定义子空间，可以很好地推广用于几次学习。合适的子空间符合给定任务的三个标准：IT（a）允许通过梯度流量减少训练误差，（b）导致模型良好的模型，并且（c）可以通过随机梯度下降来识别。 SUBGD从不同任务的更新说明的自动相关矩阵的特征组合中标识了这些子空间。明确的是，我们可以识别出低维合适的子空间，用于对动态系统的几次学习，而动态系统具有不同的属性，这些属性由分析系统描述的一个或几个参数描述。这种系统在科学和工程领域的现实应用程序中无处不在。我们在实验中证实了SubGD在三个不同的动态系统问题设置上的优势，在样本效率和性能方面，均超过了流行的几次学习方法。

Despite the widespread practical success of deep learning methods, our theoretical understanding of the dynamics of learning in deep neural networks remains quite sparse. We attempt to bridge the gap between the theory and practice of deep learning by systematically analyzing learning dynamics for the restricted case of deep linear neural networks. Despite the linearity of their input-output map, such networks have nonlinear gradient descent dynamics on weights that change with the addition of each new hidden layer. We

Grid search and manual search are the most widely used strategies for hyper-parameter optimization. This paper shows empirically and theoretically that randomly chosen trials are more efficient for hyper-parameter optimization than trials on a grid. Empirical evidence comes from a comparison with a large previous study that used grid search and manual search to configure neural networks and deep belief networks. Compared with neural networks configured by a pure grid search, we find that random search over the same domain is able to find models that are as good or better within a small fraction of the computation time. Granting random search the same computational budget, random search finds better models by effectively searching a larger, less promising configuration space. Compared with deep belief networks configured by a thoughtful combination of manual search and grid search, purely random search over the same 32-dimensional configuration space found statistically equal performance on four of seven data sets, and superior performance on one of seven. A Gaussian process analysis of the function from hyper-parameters to validation set performance reveals that for most data sets only a few of the hyper-parameters really matter, but that different hyper-parameters are important on different data sets. This phenomenon makes grid search a poor choice for configuring algorithms for new data sets. Our analysis casts some light on why recent "High Throughput" methods achieve surprising success-they appear to search through a large number of hyper-parameters because most hyper-parameters do not matter much. We anticipate that growing interest in large hierarchical models will place an increasing burden on techniques for hyper-parameter optimization; this work shows that random search is a natural baseline against which to judge progress in the development of adaptive (sequential) hyper-parameter optimization algorithms.

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.

Several machine learning models, including neural networks, consistently misclassify adversarial examples-inputs formed by applying small but intentionally worst-case perturbations to examples from the dataset, such that the perturbed input results in the model outputting an incorrect answer with high confidence. Early attempts at explaining this phenomenon focused on nonlinearity and overfitting. We argue instead that the primary cause of neural networks' vulnerability to adversarial perturbation is their linear nature. This explanation is supported by new quantitative results while giving the first explanation of the most intriguing fact about them: their generalization across architectures and training sets. Moreover, this view yields a simple and fast method of generating adversarial examples. Using this approach to provide examples for adversarial training, we reduce the test set error of a maxout network on the MNIST dataset.

培训深度神经网络是一项非常苛刻的任务，尤其是具有挑战性的是如何适应体系结构以提高训练有素的模型的性能。我们可以发现，有时，浅网络比深网概括得更好，并且增加更多层会导致更高的培训和测试错误。深层残留学习框架通过将跳过连接添加到几个神经网络层来解决此降解问题。最初，需要这种跳过连接才能成功地训练深层网络，因为网络的表达性会随着深度的指数增长而成功。在本文中，我们首先通过神经网络分析信息流。我们介绍和评估批处理循环，该批处理通过神经网络的每一层量化信息流。我们从经验和理论上证明，基于梯度下降的训练方法需要正面批处理融合，以成功地优化给定的损失功能。基于这些见解，我们引入了批处理凝聚正则化，以使基于梯度下降的训练算法能够单独通过每个隐藏层来优化信息流。借助批处理正则化，梯度下降优化器可以将不可吸引的网络转换为可训练的网络。我们从经验上表明，因此我们可以训练“香草”完全连接的网络和卷积神经网络 - 没有跳过连接，批处理标准化，辍学或任何其他建筑调整 - 只需将批处理 - 凝集正则术语添加到500层中损失功能。批处理 - 注入正则化的效果不仅在香草神经网络上评估，还评估了在各种计算机视觉以及自然语言处理任务上的剩余网络，自动编码器以及变压器模型上。

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.

We examine the role of memorization in deep learning, drawing connections to capacity, generalization, and adversarial robustness. While deep networks are capable of memorizing noise data, our results suggest that they tend to prioritize learning simple patterns first. In our experiments, we expose qualitative differences in gradient-based optimization of deep neural networks (DNNs) on noise vs. real data. We also demonstrate that for appropriately tuned explicit regularization (e.g., dropout) we can degrade DNN training performance on noise datasets without compromising generalization on real data. Our analysis suggests that the notions of effective capacity which are dataset independent are unlikely to explain the generalization performance of deep networks when trained with gradient based methods because training data itself plays an important role in determining the degree of memorization.

梯度下降可能令人惊讶地擅长优化深层神经网络，而不会过度拟合并且没有明确的正则化。我们发现，梯度下降的离散步骤通过惩罚具有较大损耗梯度的梯度下降轨迹来隐式化模型。我们称之为隐式梯度正则化（IGR），并使用向后错误分析来计算此正则化的大小。我们从经验上确认，隐式梯度正则化偏向梯度下降到平面最小值，在该较小情况下，测试误差很小，溶液对嘈杂的参数扰动是可靠的。此外，我们证明了隐式梯度正规化项可以用作显式正常化程序，从而使我们能够直接控制此梯度正则化。从更广泛的角度来看，我们的工作表明，向后错误分析是一种有用的理论方法，即对学习率，模型大小和参数正则化如何相互作用以确定用梯度下降优化的过度参数化模型的属性。

这是一门专门针对STEM学生开发的介绍性机器学习课程。我们的目标是为有兴趣的读者提供基础知识，以在自己的项目中使用机器学习，并将自己熟悉术语作为进一步阅读相关文献的基础。在这些讲义中，我们讨论受监督，无监督和强化学习。注释从没有神经网络的机器学习方法的说明开始，例如原理分析，T-SNE，聚类以及线性回归和线性分类器。我们继续介绍基本和先进的神经网络结构，例如密集的进料和常规神经网络，经常性的神经网络，受限的玻尔兹曼机器，（变性）自动编码器，生成的对抗性网络。讨论了潜在空间表示的解释性问题，并使用梦和对抗性攻击的例子。最后一部分致力于加强学习，我们在其中介绍了价值功能和政策学习的基本概念。

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.