Network pruning is a promising way to generate light but accurate models and enable their deployment on resource-limited edge devices. However, the current state-of-the-art assumes that the effective sub-network and the other superfluous parameters in the given network share the same distribution, where pruning inevitably involves a distribution truncation operation. They usually eliminate values near zero. While simple, it may not be the most appropriate method, as effective models may naturally have many small values associated with them. Removing near-zero values already embedded in model space may significantly reduce model accuracy. Another line of work has proposed to assign discrete prior over all possible sub-structures that still rely on human-crafted prior hypotheses. Worse still, existing methods use regularized point estimates, namely Hard Pruning, that can not provide error estimations and fail reliability justification for the pruned networks. In this paper, we propose a novel distribution-lossless pruning method, named DLLP, to theoretically find the pruned lottery within Bayesian treatment. Specifically, DLLP remodels the vanilla networks as discrete priors for the latent pruned model and the other redundancy. More importantly, DLLP uses Stein Variational Inference to approach the latent prior and effectively bypasses calculating KL divergence with unknown distribution. Extensive experiments based on small Cifar-10 and large-scaled ImageNet demonstrate that our method can obtain sparser networks with great generalization performance while providing quantified reliability for the pruned model.

在这项工作中，我们使用变分推论来量化无线电星系分类的深度学习模型预测的不确定性程度。我们表明，当标记无线电星系时，个体测试样本的模型后差水平与人类不确定性相关。我们探讨了各种不同重量前沿的模型性能和不确定性校准，并表明稀疏事先产生更良好的校准不确定性估计。使用单个重量的后部分布，我们表明我们可以通过从最低信噪比（SNR）中除去权重来修剪30％的完全连接的层权重，而无需显着损失性能。我们证明，可以使用基于Fisher信息的排名来实现更大程度的修剪，但我们注意到两种修剪方法都会影响Failaroff-Riley I型和II型无线电星系的不确定性校准。最后，我们表明，与此领域的其他工作相比，我们经历了冷的后效，因此后部必须缩小后加权以实现良好的预测性能。我们检查是否调整成本函数以适应模型拼盘可以弥补此效果，但发现它不会产生显着差异。我们还研究了原则数据增强的效果，并发现这改善了基线，而且还没有弥补观察到的效果。我们将其解释为寒冷的后效，因为我们的培训样本过于有效的策划导致可能性拼盘，并将其提高到未来无线电银行分类的潜在问题。

稀疏培训是一种自然的想法，可以加速深度神经网络的训练速度，并节省内存使用，特别是因为大型现代神经网络被显着过度参数化。然而，大多数现有方法在实践中无法实现这一目标，因为先前方法采用的基于链规则的梯度（W.R.T.结构参数）估计。至少在向后传播步骤中至少需要密集的计算。本文通过提出具有完全稀疏的前后通行证的有效稀疏训练方法来解决这个问题。我们首先在全球稀疏限制下将培训过程制定为连续最小化问题。然后，我们将优化过程分为两个步骤，对应于权重更新和结构参数更新。对于前一步，我们使用传统的链规则，这可以通过利用稀疏结构来稀疏。对于后一步，而不是使用基于链规则的梯度估计器，如现有方法中，我们提出了一个方差减少的策略梯度估计器，这只需要两个向前通过而不向后传播，从而实现完全稀疏的训练。我们证明了我们渐变估计器的差异是界定的。对现实世界数据集的广泛实验结果表明，与以前的方法相比，我们的算法在加速训练过程中更有效，速度快到速度更快。

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。

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.

事实证明，稀疏的深度神经网络在大规模研究中对于预测模型构建有效。尽管几项作品研究了稀疏神经体系结构的理论和数值特性，但它们主要集中在边缘选择上。通过优势选择的稀疏性可能具有直觉上的吸引力；但是，它不一定会降低网络的结构复杂性。相反，修剪过多的节点会导致一个结构稀疏的网络，并在推理过程中具有显着的计算加速。为此，我们建议使用Spike and-Slab Gaussian先验者提出贝叶斯稀疏溶液，以允许在训练过程中选择自动节点。使用Spike and-Slab先验减轻了对修剪的临时阈值规则的需求。此外，我们采用了一种差异贝叶斯方法来规避传统马尔可夫链蒙特卡洛（MCMC）实施的计算挑战。在节点选择的背景下，我们建立了变异后一致性的基本结果，以及先前参数的表征。与以前的作品相反，我们的理论发展放宽了所有网络权重的节点和均匀界限的假设，从而适应具有层依赖性节点结构或系数边界的稀疏网络。通过对先前纳入概率的层表表征，我们讨论了后部变异的最佳收缩率。我们从经验上证明，我们所提出的方法的表现优于计算复杂性的边缘选择方法，具有相似或更好的预测性能。我们的实验证据进一步证明了我们的理论工作有助于层面上的最佳节点恢复。

量化监督学习模型的不确定性在制定更可靠的预测方面发挥着重要作用。认知不确定性，通常是由于对模型的知识不足，可以通过收集更多数据或精炼学习模型来减少。在过去的几年里，学者提出了许多认识的不确定性处理技术，这些技术可以大致分为两类，即贝叶斯和集合。本文对过去五年来提供了对监督学习的认识性不确定性学习技术的全面综述。因此，我们首先，将认知不确定性分解为偏见和方差术语。然后，介绍了认知不确定性学习技术以及其代表模型的分层分类。此外，提出了几种应用，例如计算机视觉（CV）和自然语言处理（NLP），然后讨论研究差距和可能的未来研究方向。

通道修剪被广泛用于降低深网模型的复杂性。最近的修剪方法通常通过提出通道重要性标准来识别网络的哪些部分。但是，最近的研究表明，这些标准在所有情况下都不能很好地工作。在本文中，我们提出了一种新颖的功能最小化方法（FSM）方法来压缩CNN模型，该模型通过收敛功能和过滤器的信息来评估特征转移。具体而言，我们首先使用不同层深度的一些普遍方法研究压缩效率，然后提出特征转移概念。然后，我们引入了一种近似方法来估计特征移位的幅度，因为很难直接计算它。此外，我们提出了一种分布优化算法，以补偿准确性损失并提高网络压缩效率。该方法在各种基准网络和数据集上产生最先进的性能，并通过广泛的实验验证。这些代码可以在\ url {https://github.com/lscgx/fsm}上可用。

近似贝叶斯深度学习方法对于解决在智能系统中部署深度学习组件时，包括在智能系统中部署深度学习组件的几个问题，包括减轻过度自信的错误并提供增强的鲁棒性，从而超出分发示例。但是，现有近似贝叶斯推理方法的计算要求可以使它们不适合部署包括低功耗边缘设备的智能IOT系统。在本文中，我们为监督深度学习提供了一系列近似贝叶斯推理方法，并在应用这些方法对当前边缘硬件上的挑战和机遇。我们突出了几种潜在的解决方案来降低模型存储要求，提高计算可扩展性，包括模型修剪和蒸馏方法。

嵌套辍学是辍学操作的变体，能够根据训练期间的预定义重要性订购网络参数或功能。它已被探索：I。构造嵌套网络：嵌套网是神经网络，可以在测试时间（例如基于计算约束）中立即调整架构的架构。嵌套的辍学者隐含地对网络参数进行排名，生成一组子网络，从而使任何较小的子网络构成较大的子网络的基础。 ii。学习排序表示：应用于生成模型的潜在表示（例如自动编码器）对特征进行排名，从而在尺寸上执行密集表示的明确顺序。但是，在整个训练过程中，辍学率是固定为高参数的。对于嵌套网，当删除网络参数时，性能衰减在人类指定的轨迹中而不是从数据中学到的轨迹中。对于生成模型，特征的重要性被指定为恒定向量，从而限制了表示学习的灵活性。为了解决该问题，我们专注于嵌套辍学的概率对应物。我们提出了一个嵌套掉落（VND）操作，该操作以低成本绘制多维有序掩码的样品，为嵌套掉落的参数提供了有用的梯度。基于这种方法，我们设计了一个贝叶斯嵌套的神经网络，以了解参数分布的顺序知识。我们在不同的生成模型下进一步利用VND来学习有序的潜在分布。在实验中，我们表明所提出的方法在分类任务中的准确性，校准和室外检测方面优于嵌套网络。它还在数据生成任务上胜过相关的生成模型。

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.

象征性的AI社区越来越多地试图在神经符号结构中接受机器学习，但由于文化障碍，仍在挣扎。为了打破障碍，这份相当有思想的个人备忘录试图解释和纠正统计，机器学习和深入学习的惯例，从局外人的角度进行深入学习。它提供了一个分步协议，用于设计一个机器学习系统，该系统满足符号AI社区认真对待所必需的最低理论保证，即，它讨论“在哪些条件下，我们可以停止担心和接受统计机器学习。 “一些亮点：大多数教科书都是为计划专门研究STAT/ML/DL的人编写的，应该接受术语。该备忘录适用于经验丰富的象征研究人员，他们听到了很多嗡嗡声，但仍然不确定和持怀疑态度。有关STAT/ML/DL的信息目前太分散或嘈杂而无法投资。此备忘录优先考虑紧凑性，并特别注意与象征性范式相互共鸣的概念。我希望这份备忘录能节省时间。它优先考虑一般数学建模，并且不讨论任何特定的函数近似器，例如神经网络（NNS），SVMS，决策树等。它可以对校正开放。将此备忘录视为与博客文章相似的内容，采用有关Arxiv的论文的形式。

现有的可区分通道修剪方法通常将缩放因子或掩模在通道后面的掩盖范围内，以减少重要性的修剪过滤器，并假设输入样品统一贡献以过滤重要性。具体而言，实例复杂性对修剪性能的影响尚未得到充分研究。在本文中，我们提出了一个基于实例复杂性滤波器的重要性得分的简单而有效的可区分网络修剪方法上限。我们通过给硬样品给出更高的权重来定义每个样品的实例复杂性与重量相关的重量，并测量样品特异性软膜的加权总和，以模拟不同输入的非均匀贡献，这鼓励硬样品主导修剪过程和模型性能保存完好。此外，我们还引入了一个新的正规器，以鼓励面具两极分化，以便很容易找到甜蜜的位置以识别要修剪的过滤器。各种网络体系结构和数据集的性能评估表明，CAP在修剪大型网络方面具有优势。例如，CAP在删除65.64％的拖鞋后，CAP在CIFAR-10数据集上的RESNET56的准确性提高了0.33％，而Prunes在ImagEnet数据集上的RESNET50的PRUNES 87.75％，只有0.89％的TOP-1精度损失。

The mainstream approach for filter pruning is usually either to force a hard-coded importance estimation upon a computation-heavy pretrained model to select "important" filters, or to impose a hyperparameter-sensitive sparse constraint on the loss objective to regularize the network training. In this paper, we present a novel filter pruning method, dubbed dynamic-coded filter fusion (DCFF), to derive compact CNNs in a computation-economical and regularization-free manner for efficient image classification. Each filter in our DCFF is firstly given an inter-similarity distribution with a temperature parameter as a filter proxy, on top of which, a fresh Kullback-Leibler divergence based dynamic-coded criterion is proposed to evaluate the filter importance. In contrast to simply keeping high-score filters in other methods, we propose the concept of filter fusion, i.e., the weighted averages using the assigned proxies, as our preserved filters. We obtain a one-hot inter-similarity distribution as the temperature parameter approaches infinity. Thus, the relative importance of each filter can vary along with the training of the compact CNN, leading to dynamically changeable fused filters without both the dependency on the pretrained model and the introduction of sparse constraints. Extensive experiments on classification benchmarks demonstrate the superiority of our DCFF over the compared counterparts. For example, our DCFF derives a compact VGGNet-16 with only 72.77M FLOPs and 1.06M parameters while reaching top-1 accuracy of 93.47% on CIFAR-10. A compact ResNet-50 is obtained with 63.8% FLOPs and 58.6% parameter reductions, retaining 75.60% top-1 accuracy on ILSVRC-2012. Our code, narrower models and training logs are available at https://github.com/lmbxmu/DCFF.

过滤器修剪的目标是搜索不重要的过滤器以删除以便使卷积神经网络（CNNS）有效而不牺牲过程中的性能。挑战在于找到可以帮助确定每个过滤器关于神经网络的最终输出的重要或相关的信息的信息。在这项工作中，我们分享了我们的观察说，预先训练的CNN的批量标准化（BN）参数可用于估计激活输出的特征分布，而无需处理训练数据。在观察时，我们通过基于预先训练的CNN的BN参数评估每个滤波器的重要性来提出简单而有效的滤波修剪方法。 CiFar-10和Imagenet的实验结果表明，该方法可以在准确性下降和计算复杂性的计算复杂性和降低的折衷方面具有和不进行微调的卓越性能。

We investigate a local reparameterizaton technique for greatly reducing the variance of stochastic gradients for variational Bayesian inference (SGVB) of a posterior over model parameters, while retaining parallelizability. This local reparameterization translates uncertainty about global parameters into local noise that is independent across datapoints in the minibatch. Such parameterizations can be trivially parallelized and have variance that is inversely proportional to the minibatch size, generally leading to much faster convergence. Additionally, we explore a connection with dropout: Gaussian dropout objectives correspond to SGVB with local reparameterization, a scale-invariant prior and proportionally fixed posterior variance. Our method allows inference of more flexibly parameterized posteriors; specifically, we propose variational dropout, a generalization of Gaussian dropout where the dropout rates are learned, often leading to better models. The method is demonstrated through several experiments.

We propose SWA-Gaussian (SWAG), a simple, scalable, and general purpose approach for uncertainty representation and calibration in deep learning. Stochastic Weight Averaging (SWA), which computes the first moment of stochastic gradient descent (SGD) iterates with a modified learning rate schedule, has recently been shown to improve generalization in deep learning. With SWAG, we fit a Gaussian using the SWA solution as the first moment and a low rank plus diagonal covariance also derived from the SGD iterates, forming an approximate posterior distribution over neural network weights; we then sample from this Gaussian distribution to perform Bayesian model averaging. We empirically find that SWAG approximates the shape of the true posterior, in accordance with results describing the stationary distribution of SGD iterates. Moreover, we demonstrate that SWAG performs well on a wide variety of tasks, including out of sample detection, calibration, and transfer learning, in comparison to many popular alternatives including MC dropout, KFAC Laplace, SGLD, and temperature scaling.

Kullback-Leibler（KL）差异广泛用于贝叶斯神经网络（BNNS）的变异推理。然而，KL差异具有无限性和不对称性等局限性。我们检查了更通用，有限和对称的詹森 - 香农（JS）差异。我们根据几何JS差异为BNN制定新的损失函数，并表明基于KL差异的常规损失函数是其特殊情况。我们以封闭形式的高斯先验评估拟议损失函数的差异部分。对于任何其他一般的先验，都可以使用蒙特卡洛近似值。我们提供了实施这两种情况的算法。我们证明所提出的损失函数提供了一个可以调整的附加参数，以控制正则化程度。我们得出了所提出的损失函数在高斯先验和后代的基于KL差异的损失函数更好的条件。我们证明了基于嘈杂的CIFAR数据集和有偏见的组织病理学数据集的最新基于KL差异的BNN的性能提高。

现代深度学习方法构成了令人难以置信的强大工具，以解决无数的挑战问题。然而，由于深度学习方法作为黑匣子运作，因此与其预测相关的不确定性往往是挑战量化。贝叶斯统计数据提供了一种形式主义来理解和量化与深度神经网络预测相关的不确定性。本教程概述了相关文献和完整的工具集，用于设计，实施，列车，使用和评估贝叶斯神经网络，即使用贝叶斯方法培训的随机人工神经网络。

Previous works utilized "smaller-norm-less-important" criterion to prune filters with smaller norm values in a convolutional neural network. In this paper, we analyze this norm-based criterion and point out that its effectiveness depends on two requirements that are not always met: (1) the norm deviation of the filters should be large; (2) the minimum norm of the filters should be small. To solve this problem, we propose a novel filter pruning method, namely Filter Pruning via Geometric Median (FPGM), to compress the model regardless of those two requirements. Unlike previous methods, FPGM compresses CNN models by pruning filters with redundancy, rather than those with "relatively less" importance. When applied to two image classification benchmarks, our method validates its usefulness and strengths. Notably, on CIFAR-10, FPGM reduces more than 52% FLOPs on ResNet-110 with even 2.69% relative accuracy improvement. Moreover, on ILSVRC-2012, FPGM reduces more than 42% FLOPs on ResNet-101 without top-5 accuracy drop, which has advanced the state-of-the-art. Code is publicly available on GitHub: https://github.com/he-y/filter-pruning-geometric-median * Corresponding Author. Part of this work was done when Yi Yang was visiting Baidu Research during his Professional Experience Program.