现代的神经网络是著名的，但也高度多余和可压缩。在深度学习文献中存在许多修剪策略，这些策略产生了超过90％的稀疏子网，这些子网已全面训练，密集的体系结构，同时仍保持其原始精度。不过，在这些方法中，由于其概念上的简单性，易于实施和功效 - 迭代幅度修剪（IMP）在实践中占主导地位，并且实际上是在修剪社区中击败的基线。但是，关于为什么像IMP这样的简单方法完全有限的理论解释是很少且有限的。在这项工作中，我们利用持续的同源性的概念来了解IMP的运作，并表明它本质地鼓励保留那些保留受过训练的网络中拓扑信息的权重。随后，我们还提供有关在完美保留其零订单拓扑特征的同时可以修剪多少不同网络的界限，并为IMP的修改版本提供了相同的操作。

不服从统计学习理论的古典智慧，即使它们通常包含数百万参数，现代深度神经网络也概括了井。最近，已经表明迭代优化算法的轨迹可以具有分形结构，并且它们的泛化误差可以与这种分形的复杂性正式连接。这种复杂性由分形的内在尺寸测量，通常比网络中的参数数量小得多。尽管这种透视提供了对为什么跨分层化的网络不会过度装备的解释，但计算内在尺寸（例如，在训练期间进行监测泛化）是一种臭名昭着的困难任务，即使在中等环境维度中，现有方法也通常失败。在这项研究中，我们考虑了从拓扑数据分析（TDA）的镜头上的这个问题，并开发了一个基于严格的数学基础的通用计算工具。通过在学习理论和TDA之间进行新的联系，我们首先说明了泛化误差可以在称为“持久同源维度”（PHD）的概念中，与先前工作相比，我们的方法不需要关于培训动态的任何额外几何或统计假设。然后，通过利用最近建立的理论结果和TDA工具，我们开发了一种高效的算法来估计现代深度神经网络的规模中的博士，并进一步提供可视化工具，以帮助理解深度学习中的概括。我们的实验表明，所提出的方法可以有效地计算网络的内在尺寸，这些设置在各种设置中，这是预测泛化误差的。

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.

我们考虑了$ d $维图像的新拓扑效率化，该图像通过在计算持久性之前与各种过滤器进行卷积。将卷积滤波器视为图像中的图案，结果卷积的持久图描述了图案在整个图像中分布的方式。我们称之为卷积持久性的管道扩展了拓扑结合图像数据中模式的能力。的确，我们证明（通常说）对于任何两个图像，人们都可以找到某些过滤器，它们会为其产生不同的持久图，以便给定图像的所有可能的卷积持久性图的收集是一个不变的不变性。通过表现出卷积的持久性是另一种拓扑不变的持续性副学变换的特殊情况，这证明了这一点。卷积持久性的其他优势是提高噪声的稳定性和鲁棒性，对数据依赖性矢量化的更大灵活性以及对具有较大步幅向量的卷积的计算复杂性降低。此外，我们还有一套实验表明，即使人们使用随机过滤器并通过仅记录其总持久性，卷积大大提高了持久性的预测能力，即使一个人使用随机过滤器并将结果图进行量化。

In this paper, we investigate the impact of neural networks (NNs) topology on adversarial robustness. Specifically, we study the graph produced when an input traverses all the layers of a NN, and show that such graphs are different for clean and adversarial inputs. We find that graphs from clean inputs are more centralized around highway edges, whereas those from adversaries are more diffuse, leveraging under-optimized edges. Through experiments on a variety of datasets and architectures, we show that these under-optimized edges are a source of adversarial vulnerability and that they can be used to detect adversarial inputs.

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.

近年来，变压器模型的引入引发了自然语言处理（NLP）的革命。伯特（Bert）是仅使用注意机制的第一批文本编码者之一，没有任何复发部分来实现许多NLP任务的最新结果。本文使用拓扑数据分析介绍了文本分类器。我们将BERT的注意图转换为注意图作为该分类器的唯一输入。该模型可以解决诸如将垃圾邮件与HAM消息区分开的任务，认识到语法正确的句子，或将电影评论评估为负面还是正面。它与BERT基线相当表现，并在某些任务上表现优于它。此外，我们提出了一种新方法，以减少拓扑分类器考虑的BERT注意力头的数量，这使我们能够修剪从144个下降到只有10个，而不会降低性能。我们的工作还表明，拓扑模型比原始的BERT模型表现出对对抗性攻击的鲁棒性，该模型在修剪过程中维持。据我们所知，这项工作是第一个在NLP背景下以对抗性攻击的基于拓扑的模型。

As the accuracy of machine learning models increases at a fast rate, so does their demand for energy and compute resources. On a low level, the major part of these resources is consumed by data movement between different memory units. Modern hardware architectures contain a form of fast memory (e.g., cache, registers), which is small, and a slow memory (e.g., DRAM), which is larger but expensive to access. We can only process data that is stored in fast memory, which incurs data movement (input/output-operations, or I/Os) between the two units. In this paper, we provide a rigorous theoretical analysis of the I/Os needed in sparse feedforward neural network (FFNN) inference. We establish bounds that determine the optimal number of I/Os up to a factor of 2 and present a method that uses a number of I/Os within that range. Much of the I/O-complexity is determined by a few high-level properties of the FFNN (number of inputs, outputs, neurons, and connections), but if we want to get closer to the exact lower bound, the instance-specific sparsity patterns need to be considered. Departing from the 2-optimal computation strategy, we show how to reduce the number of I/Os further with simulated annealing. Complementing this result, we provide an algorithm that constructively generates networks with maximum I/O-efficiency for inference. We test the algorithms and empirically verify our theoretical and algorithmic contributions. In our experiments on real hardware we observe speedups of up to 45$\times$ relative to the standard way of performing inference.

经验结果表明神经网络的可读性与其大小直接相关。为了数学方式证明这一点，我们借用拓扑代数的工具：Betti号码来衡量输入数据和神经网络的拓扑几何复杂性。通过以拓扑复杂性为神经网络的表征能力，我们进行彻底的分析，并表明网络的表现能力受其层的规模受到限制。此外，我们从网络内的每个层上得出了贝蒂数的上限。结果，改变了神经网络的架构选择的问题，以确定可以表示输入数据复杂度的网络的比例。利用所提出的结果，完全连接的网络的架构选择逐渐归功于网络的合适尺寸，使得它能够提供不小于输入数据的贝蒂数的贝蒂数。我们在真实的数据集Mnist上执行实验，结果验证了我们的分析和结论。该代码可公开可用。

在本文中，我们研究了在深网（DNS）中修剪的重要性，以及（1）修剪高度参数的DNS之间的Yin＆Yang关系，这些DNS已从随机初始化训练，并且（2）培训“巧妙”的小型DNS，这些DNS已“巧妙”。初始化。在大多数情况下，从业者只能诉诸随机初始化，因此强烈需要对DN修剪建立扎实的理解。当前的文献在很大程度上仍然是经验的，缺乏对修剪如何影响DNS决策边界，如何解释修剪以及如何设计相应的原则修剪技术的理论理解。为了解决这些问题，我们建议在连续分段仿射（CPA）DNS的理论分析中采用最新进展。从这个角度来看，我们将能够检测到早期的鸟类（EB）票务现象，为当前的修剪技术提供可解释性，并制定有原则的修剪策略。在研究的每个步骤中，我们进行了广泛的实验，以支持我们的主张和结果；尽管我们的主要目标是增强对DN修剪的当前理解，而不是开发一种新的修剪方法，但我们的样条修剪标准在层和全球修剪方面与先进的修剪方法相当甚至超过了。

Neural network pruning-the task of reducing the size of a network by removing parameters-has been the subject of a great deal of work in recent years. We provide a meta-analysis of the literature, including an overview of approaches to pruning and consistent findings in the literature. After aggregating results across 81 papers and pruning hundreds of models in controlled conditions, our clearest finding is that the community suffers from a lack of standardized benchmarks and metrics. This deficiency is substantial enough that it is hard to compare pruning techniques to one another or determine how much progress the field has made over the past three decades. To address this situation, we identify issues with current practices, suggest concrete remedies, and introduce ShrinkBench, an open-source framework to facilitate standardized evaluations of pruning methods. We use ShrinkBench to compare various pruning techniques and show that its comprehensive evaluation can prevent common pitfalls when comparing pruning methods.

Pruning large neural networks while maintaining their performance is often desirable due to the reduced space and time complexity. In existing methods, pruning is done within an iterative optimization procedure with either heuristically designed pruning schedules or additional hyperparameters, undermining their utility. In this work, we present a new approach that prunes a given network once at initialization prior to training. To achieve this, we introduce a saliency criterion based on connection sensitivity that identifies structurally important connections in the network for the given task. This eliminates the need for both pretraining and the complex pruning schedule while making it robust to architecture variations. After pruning, the sparse network is trained in the standard way. Our method obtains extremely sparse networks with virtually the same accuracy as the reference network on the MNIST, CIFAR-10, and Tiny-ImageNet classification tasks and is broadly applicable to various architectures including convolutional, residual and recurrent networks. Unlike existing methods, our approach enables us to demonstrate that the retained connections are indeed relevant to the given task.

我们为神经网络提出了一种新颖，结构化修剪算法 - 迭代，稀疏结构修剪算法，称为I-Spasp。从稀疏信号恢复的思想启发，I-Spasp通过迭代地识别网络内的较大的重要参数组（例如，滤波器或神经元），这些参数组大多数对修剪和密集网络输出之间的残差贡献，然后基于这些组阈值以较小的预定定义修剪比率。对于具有Relu激活的双层和多层网络架构，我们展示了通过多项式修剪修剪诱导的错误，该衰减是基于密集网络隐藏表示的稀疏性任意大的。在我们的实验中，I-Spasp在各种数据集（即MNIST和ImageNet）和架构（即馈送前向网络，Resnet34和MobileNetv2）中进行评估，其中显示用于发现高性能的子网和改进经过几种数量级的可提供基线方法的修剪效率。简而言之，I-Spasp很容易通过自动分化实现，实现强大的经验结果，具有理论收敛保证，并且是高效的，因此将自己区分开作为少数几个计算有效，实用，实用，实用，实用，实用，实用，实用，实用和可提供的修剪算法之一。

识别各个网络单元的状态对于了解卷积神经网络（CNNS）的机制至关重要。但是，它仍然有挑战性，可以可靠地指示单位状态，特别是对于不同网络模型中的单位。为此，我们提出了一种使用代数拓扑工具定量阐明CNN中单位状态的新方法。单位状态通过计算定义的拓扑熵来指示称为特征熵，该特征熵，测量隐藏在单位的全局空间模式的混沌程度。通过这种方式，特征熵可以提供不同网络中单位的准确指示，具有不同的情况，如权重操作。此外，我们表明特征熵随着层次更深，并且在训练期间几乎同时同时趋于趋势而分享。我们表明，通过调查仅在培训数据上的单位的特征熵，它可以从特征表示的有效性看出具有不同泛化能力的网络之间的歧视。

持续的同源性（PH）是拓扑数据分析中最流行的方法之一。尽管PH已用于许多不同类型的应用程序中，但其成功背后的原因仍然难以捉摸。特别是，尚不知道哪种类别的问题最有效，或者在多大程度上可以检测几何或拓扑特征。这项工作的目的是确定pH在数据分析中比其他方法更好甚至更好的问题。我们考虑三个基本形状分析任务：从形状采样的2D和3D点云中检测孔数，曲率和凸度。实验表明，pH在这些任务中取得了成功，超过了几个基线，包括PointNet，这是一个精确地受到点云的属性启发的体系结构。此外，我们观察到，pH对于有限的计算资源和有限的培训数据以及分布外测试数据，包括各种数据转换和噪声，仍然有效。

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 * .

While machine learning is traditionally a resource intensive task, embedded systems, autonomous navigation, and the vision of the Internet of Things fuel the interest in resource-efficient approaches. These approaches aim for a carefully chosen trade-off between performance and resource consumption in terms of computation and energy. The development of such approaches is among the major challenges in current machine learning research and key to ensure a smooth transition of machine learning technology from a scientific environment with virtually unlimited computing resources into everyday's applications. In this article, we provide an overview of the current state of the art of machine learning techniques facilitating these real-world requirements. In particular, we focus on deep neural networks (DNNs), the predominant machine learning models of the past decade. We give a comprehensive overview of the vast literature that can be mainly split into three non-mutually exclusive categories: (i) quantized neural networks, (ii) network pruning, and (iii) structural efficiency. These techniques can be applied during training or as post-processing, and they are widely used to reduce the computational demands in terms of memory footprint, inference speed, and energy efficiency. We also briefly discuss different concepts of embedded hardware for DNNs and their compatibility with machine learning techniques as well as potential for energy and latency reduction. We substantiate our discussion with experiments on well-known benchmark datasets using compression techniques (quantization, pruning) for a set of resource-constrained embedded systems, such as CPUs, GPUs and FPGAs. The obtained results highlight the difficulty of finding good trade-offs between resource efficiency and predictive performance.

结构化修剪是一种常用的技术，用于将深神经网络（DNN）部署到资源受限的设备上。但是，现有的修剪方法通常是启发式，任务指定的，并且需要额外的微调过程。为了克服这些限制，我们提出了一个框架，将DNN压缩成纤薄的架构，具有竞争性表现，并且仅通过列车 - 一次（OTO）减少重大拖车。 OTO包含两个键：（i）我们将DNN的参数分区为零不变组，使我们能够修剪零组而不影响输出; （ii）促进零群，我们制定了结构性稀疏优化问题，提出了一种新颖的优化算法，半空间随机投影梯度（HSPG），以解决它，这优于组稀疏性探索的标准近端方法和保持可比的收敛性。为了展示OTO的有效性，我们从划痕上同时培训和压缩全模型，而无需微调推理加速和参数减少，并且在CIFAR10的VGG16实现最先进的结果，为CIFAR10和Squad的BERT为BERT竞争结果在resnet50上为想象成。源代码可在https://github.com/tianyic/only_train_once上获得。

Pruning refers to the elimination of trivial weights from neural networks. The sub-networks within an overparameterized model produced after pruning are often called Lottery tickets. This research aims to generate winning lottery tickets from a set of lottery tickets that can achieve similar accuracy to the original unpruned network. We introduce a novel winning ticket called Cyclic Overlapping Lottery Ticket (COLT) by data splitting and cyclic retraining of the pruned network from scratch. We apply a cyclic pruning algorithm that keeps only the overlapping weights of different pruned models trained on different data segments. Our results demonstrate that COLT can achieve similar accuracies (obtained by the unpruned model) while maintaining high sparsities. We show that the accuracy of COLT is on par with the winning tickets of Lottery Ticket Hypothesis (LTH) and, at times, is better. Moreover, COLTs can be generated using fewer iterations than tickets generated by the popular Iterative Magnitude Pruning (IMP) method. In addition, we also notice COLTs generated on large datasets can be transferred to small ones without compromising performance, demonstrating its generalizing capability. We conduct all our experiments on Cifar-10, Cifar-100 & TinyImageNet datasets and report superior performance than the state-of-the-art methods.

彩票假设猜测稀疏子网的存在大型随机初始化的深神经网络，可以在隔离中成功培训。最近的工作已经通过实验观察到这些门票中的一些可以在各种任务中实际重复使用，以某种形式的普遍性暗示。我们正规化这一概念，理论上证明不仅存在此类环球票，而且还不需要进一步培训。我们的证据介绍了一些与强化强烈彩票票据相关的技术创新，包括延长子集合结果的扩展和利用更高量的深度的策略。我们的明确稀疏建设普遍函数家庭可能具有独立的兴趣，因为它们突出了单变量卷积架构引起的代表效益。