最近证明利用稀疏网络连接深神经网络中的连续层，可为大型最新模型提供好处。但是，网络连接性在浅网络的学习曲线中也起着重要作用，例如经典限制的玻尔兹曼机器（RBM）。一个基本问题是有效地找到了改善学习曲线的连接模式。最近的原则方法明确将网络连接作为参数，这些参数必须在模型中进行优化，但通常依靠连续功能来表示连接和明确的惩罚。这项工作提出了一种基于网络梯度的想法来找到RBM的最佳连接模式的方法：计算每个可能连接的梯度，给定特定的连接模式，并使用梯度驱动连续连接强度参数又使用确定连接模式。因此，学习RBM参数和学习网络连接是真正共同执行的，尽管学习率不同，并且没有改变目标函数。该方法应用于MNIST数据集，以显示针对样本生成和输入分类的基准任务找到更好的RBM模型。

最近，稀疏的培训方法已开始作为事实上的人工神经网络的培训和推理效率的方法。然而，这种效率只是理论上。在实践中，每个人都使用二进制掩码来模拟稀疏性，因为典型的深度学习软件和硬件已针对密集的矩阵操作进行了优化。在本文中，我们采用正交方法，我们表明我们可以训练真正稀疏的神经网络以收获其全部潜力。为了实现这一目标，我们介绍了三个新颖的贡献，这些贡献是专门为稀疏神经网络设计的：（1）平行训练算法及其相应的稀疏实现，（2）具有不可训练的参数的激活功能，以支持梯度流动，以支持梯度流量， （3）隐藏的神经元对消除冗余的重要性指标。总而言之，我们能够打破记录并训练有史以来最大的神经网络在代表力方面训练 - 达到蝙蝠大脑的大小。结果表明，我们的方法具有最先进的表现，同时为环保人工智能时代开辟了道路。

Many applications require sparse neural networks due to space or inference time restrictions. There is a large body of work on training dense networks to yield sparse networks for inference, but this limits the size of the largest trainable sparse model to that of the largest trainable dense model. In this paper we introduce a method to train sparse neural networks with a fixed parameter count and a fixed computational cost throughout training, without sacrificing accuracy relative to existing dense-tosparse training methods. Our method updates the topology of the sparse network during training by using parameter magnitudes and infrequent gradient calculations. We show that this approach requires fewer floating-point operations (FLOPs) to achieve a given level of accuracy compared to prior techniques. We demonstrate state-of-the-art sparse training results on a variety of networks and datasets, including ResNet-50, MobileNets on Imagenet-2012, and RNNs on WikiText-103. Finally, we provide some insights into why allowing the topology to change during the optimization can overcome local minima encountered when the topology remains static * .

Sparse neural networks attract increasing interest as they exhibit comparable performance to their dense counterparts while being computationally efficient. Pruning the dense neural networks is among the most widely used methods to obtain a sparse neural network. Driven by the high training cost of such methods that can be unaffordable for a low-resource device, training sparse neural networks sparsely from scratch has recently gained attention. However, existing sparse training algorithms suffer from various issues, including poor performance in high sparsity scenarios, computing dense gradient information during training, or pure random topology search. In this paper, inspired by the evolution of the biological brain and the Hebbian learning theory, we present a new sparse training approach that evolves sparse neural networks according to the behavior of neurons in the network. Concretely, by exploiting the cosine similarity metric to measure the importance of the connections, our proposed method, Cosine similarity-based and Random Topology Exploration (CTRE), evolves the topology of sparse neural networks by adding the most important connections to the network without calculating dense gradient in the backward. We carried out different experiments on eight datasets, including tabular, image, and text datasets, and demonstrate that our proposed method outperforms several state-of-the-art sparse training algorithms in extremely sparse neural networks by a large gap. The implementation code is available on https://github.com/zahraatashgahi/CTRE

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.

深信仰网络（DBN）是随机神经网络，可以从感觉数据中提取丰富的环境内部表示。 DBN在触发深度学习革命方面具有催化作用，这是第一次证明在具有许多隐藏神经元层的网络中无监督学习的可行性。由于它们的生物学和认知合理性，这些等级架构也已成功利用，以在各种领域建立人类感知和认知的计算模型。但是，DBN的学习通常是以贪婪的，层次的方式进行的，这不允许模拟皮质回路的整体发展。在这里，我们提出IDBN，这是一种迭代学习算法，用于DBN，允许共同更新层次结构所有层的连接权重。我们在两组不同的视觉刺激上测试算法，我们表明网络开发也可以通过图理论属性来跟踪。使用我们的迭代方法训练的DBN实现了与贪婪对应物相当的最终性能，同时允许准确地分析生成模型中内部表示的逐步发展。我们的工作为使用IDBN进行建模神经认知发展铺平了道路。

由于稀疏神经网络通常包含许多零权重，因此可以在不降低网络性能的情况下潜在地消除这些不必要的网络连接。因此，设计良好的稀疏神经网络具有显着降低拖鞋和计算资源的潜力。在这项工作中，我们提出了一种新的自动修剪方法 - 稀疏连接学习（SCL）。具体地，重量被重新参数化为可培训权重变量和二进制掩模的元素方向乘法。因此，由二进制掩模完全描述网络连接，其由单位步进函数调制。理论上，从理论上证明了使用直通估计器（STE）进行网络修剪的基本原理。这一原则是STE的代理梯度应该是积极的，确保掩模变量在其最小值处收敛。在找到泄漏的Relu后，SoftPlus和Identity Stes可以满足这个原理，我们建议采用SCL的身份STE以进行离散面膜松弛。我们发现不同特征的面具梯度非常不平衡，因此，我们建议将每个特征的掩模梯度标准化以优化掩码变量训练。为了自动训练稀疏掩码，我们将网络连接总数作为我们的客观函数中的正则化术语。由于SCL不需要由网络层设计人员定义的修剪标准或超级参数，因此在更大的假设空间中探讨了网络，以实现最佳性能的优化稀疏连接。 SCL克服了现有自动修剪方法的局限性。实验结果表明，SCL可以自动学习并选择各种基线网络结构的重要网络连接。 SCL培训的深度学习模型以稀疏性，精度和减少脚波特的SOTA人类设计和自动修剪方法训练。

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.

深度学习文献通过新的架构和培训技术不断更新。然而，尽管有一些关于随机权重的发现，但最近的研究却忽略了重量初始化。另一方面，最近的作品一直在接近网络科学，以了解训练后人工神经网络（ANN）的结构和动态。因此，在这项工作中，我们分析了随机初始化网络中神经元的中心性。我们表明，较高的神经元强度方差可能会降低性能，而较低的神经元强度方差通常会改善它。然后，提出了一种新方法，根据其强度根据优先附着（PA）规则重新连接神经元连接，从而大大降低了通过常见方法初始化的层的强度方差。从这个意义上讲，重新布线仅重新组织连接，同时保留权重的大小和分布。我们通过对图像分类进行的广泛统计分析表明，在使用简单和复杂的体系结构和学习时间表时，在大多数情况下，在培训和测试过程中，性能都会提高。我们的结果表明，除了规模外，权重的组织也与更好的初始化初始化有关。

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。

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.

Helmholtz机器（HMS）是由两个Sigmoid信念网络（SBN）组成的一类生成模型，分别用作编码器和解码器。这些模型通常是使用称为唤醒 - 睡眠（WS）的两步优化算法对这些模型进行的，并且最近通过改进版本（例如重新恢复的尾流（RWS）和双向Helmholtz Machines（BIHM））进行了改进版本。 SBN中连接的局部性在与概率模型相关的Fisher信息矩阵中诱导稀疏性，并以细粒粒度的块状结构的形式引起。在本文中，我们利用自然梯度利用该特性来有效地训练SBN和HMS。我们提出了一种新颖的算法，称为“自然重新唤醒”（NRWS），该算法与其标准版本的几何适应相对应。以类似的方式，我们还引入了天然双向Helmholtz机器（NBIHM）。与以前的工作不同，我们将展示如何有效地计算自然梯度，而无需引入Fisher信息矩阵结构的任何近似值。在文献中进行的标准数据集进行的实验表明，NRW和NBIHM不仅在其非几何基准方面，而且在HMS的最先进培训算法方面都具有一致的改善。在训练后，汇聚速度以及对数可能达到的对数似然的值量化了改进。

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.

训练有素的神经网络的性能至关重要。加上深度学习模型的不断增长的规模，这种观察激发了对学习稀疏模型的广泛研究。在这项工作中，我们专注于控制稀疏学习时的稀疏水平的任务。基于稀疏性惩罚的现有方法涉及对罚款因素的昂贵反复试验调整，因此缺乏直接控制所得模型的稀疏性。作为响应，我们采用了一个约束的公式：使用Louizos等人提出的栅极机制。 （2018年），我们制定了一个受约束的优化问题，其中稀疏以训练目标和所需的稀疏目标以端到端的方式指导。使用WIDERESNET和RESNET {18，50}模型进行了CIFAR-10/100，Tinyimagenet和ImageNet的实验验证了我们的提案的有效性，并证明我们可以可靠地实现预定的稀疏目标，而不会损害预测性能。

受限的玻尔兹曼机器（RBMS）提供了一种用于无监督的机器学习的多功能体系结构，原则上可以以任意准确性近似任何目标概率分布。但是，RBM模型通常由于其计算复杂性而无法直接访问，并调用了Markov-Chain采样以分析学习概率分布。因此，对于培训和最终应用，希望拥有既准确又有效的采样器。我们强调，这两个目标通常相互竞争，无法同时实现。更具体地说，我们确定并定量地表征了RBM学习的三个制度：独立学习，精度提高而不会失去效率；相关学习，较高的精度需要较低的效率；和退化，精度和效率都不再改善甚至恶化。这些发现基于数值实验和启发式论点。

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.

Large multilayer neural networks trained with backpropagation have recently achieved state-ofthe-art results in a wide range of problems. However, using backprop for neural net learning still has some disadvantages, e.g., having to tune a large number of hyperparameters to the data, lack of calibrated probabilistic predictions, and a tendency to overfit the training data. In principle, the Bayesian approach to learning neural networks does not have these problems. However, existing Bayesian techniques lack scalability to large dataset and network sizes. In this work we present a novel scalable method for learning Bayesian neural networks, called probabilistic backpropagation (PBP). Similar to classical backpropagation, PBP works by computing a forward propagation of probabilities through the network and then doing a backward computation of gradients. A series of experiments on ten real-world datasets show that PBP is significantly faster than other techniques, while offering competitive predictive abilities. Our experiments also show that PBP provides accurate estimates of the posterior variance on the network weights.

持续学习的目标（CL）是随着时间的推移学习不同的任务。与CL相关的主要Desiderata是在旧任务上保持绩效，利用后者来改善未来任务的学习，并在培训过程中引入最小的开销（例如，不需要增长的模型或再培训）。我们建议通过固定密度的稀疏神经网络来解决这些避难所的神经启发性塑性适应（NISPA）体系结构。 NISPA形成了稳定的途径，可以从较旧的任务中保存知识。此外，NISPA使用连接重新设计来创建新的塑料路径，以重用有关新任务的现有知识。我们对EMNIST，FashionMnist，CIFAR10和CIFAR100数据集的广泛评估表明，NISPA的表现明显胜过代表性的最先进的持续学习基线，并且与盆地相比，它的可学习参数最多少了十倍。我们还认为稀疏是持续学习的重要组成部分。 NISPA代码可在https://github.com/burakgurbuz97/nispa上获得。

We show how to use "complementary priors" to eliminate the explainingaway effects that make inference difficult in densely connected belief nets that have many hidden layers. Using complementary priors, we derive a fast, greedy algorithm that can learn deep, directed belief networks one layer at a time, provided the top two layers form an undirected associative memory. The fast, greedy algorithm is used to initialize a slower learning procedure that fine-tunes the weights using a contrastive version of the wake-sleep algorithm. After fine-tuning, a network with three hidden layers forms a very good generative model of the joint distribution of handwritten digit images and their labels. This generative model gives better digit classification than the best discriminative learning algorithms. The low-dimensional manifolds on which the digits lie are modeled by long ravines in the free-energy landscape of the top-level associative memory, and it is easy to explore these ravines by using the directed connections to display what the associative memory has in mind.

在神经网络的经验风险景观中扁平最小值的性质已经讨论了一段时间。越来越多的证据表明他们对尖锐物质具有更好的泛化能力。首先，我们讨论高斯混合分类模型，并分析显示存在贝叶斯最佳点估算器，其对应于属于宽平区域的最小值。可以通过直接在分类器（通常是独立的）或学习中使用的可分解损耗函数上应用最大平坦度算法来找到这些估计器。接下来，我们通过广泛的数值验证将分析扩展到深度学习场景。使用两种算法，熵-SGD和复制-SGD，明确地包括在优化目标中，所谓的非局部平整度措施称为本地熵，我们一直提高常见架构的泛化误差（例如Resnet，CeffectnNet）。易于计算的平坦度测量显示与测试精度明确的相关性。