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 propose an efficient method for approximating natural gradient descent in neural networks which we call Kronecker-factored Approximate Curvature (K-FAC). K-FAC is based on an efficiently invertible approximation of a neural network's Fisher information matrix which is neither diagonal nor low-rank, and in some cases is completely non-sparse. It is derived by approximating various large blocks of the Fisher (corresponding to entire layers) as being the Kronecker product of two much smaller matrices. While only several times more expensive to compute than the plain stochastic gradient, the updates produced by K-FAC make much more progress optimizing the objective, which results in an algorithm that can be much faster than stochastic gradient descent with momentum in practice. And unlike some previously proposed approximate natural-gradient/Newton methods which use high-quality non-diagonal curvature matrices (such as Hessian-free optimization), K-FAC works very well in highly stochastic optimization regimes. This is because the cost of storing and inverting K-FAC's approximation to the curvature matrix does not depend on the amount of data used to estimate it, which is a feature typically associated only with diagonal or low-rank approximations to the curvature matrix.

二阶优化器被认为具有加快神经网络训练的潜力，但是由于曲率矩阵的尺寸巨大，它们通常需要近似值才能计算。最成功的近似家庭是Kronecker因块状曲率估计值（KFAC）。在这里，我们结合了先前工作的工具，以评估确切的二阶更新和仔细消融以建立令人惊讶的结果：由于其近似值，KFAC与二阶更新无关，尤其是，它极大地胜过真实的第二阶段更新。订单更新。这一挑战广泛地相信，并立即提出了为什么KFAC表现如此出色的问题。为了回答这个问题，我们提出了强烈的证据，表明KFAC近似于一阶算法，该算法在神经元上执行梯度下降而不是权重。最后，我们表明，这种优化器通常会在计算成本和数据效率方面改善KFAC。

变异推理（VI）的核心原理是将计算复杂后概率密度计算的统计推断问题转换为可拖动的优化问题。该属性使VI比几种基于采样的技术更快。但是，传统的VI算法无法扩展到大型数据集，并且无法轻易推断出越野数据点，而无需重新运行优化过程。该领域的最新发展，例如随机，黑框和摊销VI，已帮助解决了这些问题。如今，生成的建模任务广泛利用摊销VI来实现其效率和可扩展性，因为它利用参数化函数来学习近似的后验密度参数。在本文中，我们回顾了各种VI技术的数学基础，以构成理解摊销VI的基础。此外，我们还概述了最近解决摊销VI问题的趋势，例如摊销差距，泛化问题，不一致的表示学习和后验崩溃。最后，我们分析了改善VI优化的替代差异度量。

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.

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。

统计模型是机器学习的核心，具有广泛适用性，跨各种下游任务。模型通常由通过最大似然估计从数据估计的自由参数控制。但是，当面对现实世界数据集时，许多模型运行到一个关键问题：它们是在完全观察到的数据方面配制的，而在实践中，数据集会困扰缺失数据。来自不完整数据的统计模型估计理论在概念上类似于潜在变量模型的估计，其中存在强大的工具，例如变分推理（VI）。然而，与标准潜在变量模型相比，具有不完整数据的参数估计通常需要估计缺失变量的指数 - 许多条件分布，因此使标准的VI方法是棘手的。通过引入变分Gibbs推理（VGI），是一种新的通用方法来解决这个差距，以估计来自不完整数据的统计模型参数。我们在一组合成和实际估算任务上验证VGI，从不完整的数据中估算重要的机器学习模型，VAE和标准化流程。拟议的方法，同时通用，实现比现有的特定模型特定估计方法竞争或更好的性能。

这项正在进行的工作旨在为统计学习提供统一的介绍，从诸如GMM和HMM等经典模型到现代神经网络（如VAE和扩散模型）缓慢地构建。如今，有许多互联网资源可以孤立地解释这一点或新的机器学习算法，但是它们并没有（也不能在如此简短的空间中）将这些算法彼此连接起来，或者与统计模型的经典文献相连现代算法出现了。同样明显缺乏的是一个单一的符号系统，尽管对那些已经熟悉材料的人（如这些帖子的作者）不满意，但对新手的入境造成了重大障碍。同样，我的目的是将各种模型（尽可能）吸收到一个用于推理和学习的框架上，表明（以及为什么）如何以最小的变化将一个模型更改为另一个模型（其中一些是新颖的，另一些是文献中的）。某些背景当然是必要的。我以为读者熟悉基本的多变量计算，概率和统计以及线性代数。这本书的目标当然不是​​完整性，而是从基本知识到过去十年中极强大的新模型的直线路径或多或少。然后，目标是补充而不是替换，诸如Bishop的\ emph {模式识别和机器学习}之类的综合文本，该文本现在已经15岁了。

We marry ideas from deep neural networks and approximate Bayesian inference to derive a generalised class of deep, directed generative models, endowed with a new algorithm for scalable inference and learning. Our algorithm introduces a recognition model to represent an approximate posterior distribution and uses this for optimisation of a variational lower bound. We develop stochastic backpropagation -rules for gradient backpropagation through stochastic variables -and derive an algorithm that allows for joint optimisation of the parameters of both the generative and recognition models. We demonstrate on several real-world data sets that by using stochastic backpropagation and variational inference, we obtain models that are able to generate realistic samples of data, allow for accurate imputations of missing data, and provide a useful tool for high-dimensional data visualisation.

A large amount of recent research has the far-reaching goal of finding training methods for deep neural networks that can serve as alternatives to backpropagation (BP). A prominent example is predictive coding (PC), which is a neuroscience-inspired method that performs inference on hierarchical Gaussian generative models. These methods, however, fail to keep up with modern neural networks, as they are unable to replicate the dynamics of complex layers and activation functions. In this work, we solve this problem by generalizing PC to arbitrary probability distributions, enabling the training of architectures, such as transformers, that are hard to approximate with only Gaussian assumptions. We perform three experimental analyses. First, we study the gap between our method and the standard formulation of PC on multiple toy examples. Second, we test the reconstruction quality on variational autoencoders, where our method reaches the same reconstruction quality as BP. Third, we show that our method allows us to train transformer networks and achieve a performance comparable with BP on conditional language models. More broadly, this method allows neuroscience-inspired learning to be applied to multiple domains, since the internal distributions can be flexibly adapted to the data, tasks, and architectures used.

深度学习在广泛的AI应用方面取得了有希望的结果。较大的数据集和模型一致地产生更好的性能。但是，我们一般花费更长的培训时间，以更多的计算和沟通。在本调查中，我们的目标是在模型精度和模型效率方面提供关于大规模深度学习优化的清晰草图。我们调查最常用于优化的算法，详细阐述了大批量培训中出现的泛化差距的可辩论主题，并审查了解决通信开销并减少内存足迹的SOTA策略。

随机梯度马尔可夫链蒙特卡洛（SGMCMC）被认为是大型模型（例如贝叶斯神经网络）中贝叶斯推断的金标准。由于从业人员在这些模型中面临速度与准确性权衡，因此变异推理（VI）通常是可取的选择。不幸的是，VI对后部的分解和功能形式做出了有力的假设。在这项工作中，我们提出了一个新的非参数变分近似，该近似没有对后验功能形式进行假设，并允许从业者指定算法应尊重或断裂的确切依赖性。该方法依赖于在修改的能量函数上运行的新的langevin型算法，其中潜在变量的一部分是在马尔可夫链的早期迭代中平均的。这样，统计依赖性可以以受控的方式破裂，从而使链条混合更快。可以以“辍学”方式进一步修改该方案，从而导致更大的可扩展性。我们在CIFAR-10，SVHN和FMNIST上测试RESNET-20的计划。在所有情况下，与SG-MCMC和VI相比，我们都会发现收敛速度和/或最终精度的提高。

This paper proposes a new optimization algorithm called Entropy-SGD for training deep neural networks that is motivated by the local geometry of the energy landscape. Local extrema with low generalization error have a large proportion of almost-zero eigenvalues in the Hessian with very few positive or negative eigenvalues. We leverage upon this observation to construct a local-entropy-based objective function that favors well-generalizable solutions lying in large flat regions of the energy landscape, while avoiding poorly-generalizable solutions located in the sharp valleys. Conceptually, our algorithm resembles two nested loops of SGD where we use Langevin dynamics in the inner loop to compute the gradient of the local entropy before each update of the weights. We show that the new objective has a smoother energy landscape and show improved generalization over SGD using uniform stability, under certain assumptions. Our experiments on convolutional and recurrent networks demonstrate that Entropy-SGD compares favorably to state-of-the-art techniques in terms of generalization error and training time.

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.

量子哈密顿学习和量子吉布斯采样的双重任务与物理和化学中的许多重要问题有关。在低温方案中，这些任务的算法通常会遭受施状能力，例如因样本或时间复杂性差而遭受。为了解决此类韧性，我们将量子自然梯度下降的概括引入了参数化的混合状态，并提供了稳健的一阶近似算法，即量子 - 固定镜下降。我们使用信息几何学和量子计量学的工具证明了双重任务的数据样本效率，因此首次将经典Fisher效率的开创性结果推广到变异量子算法。我们的方法扩展了以前样品有效的技术，以允许模型选择的灵活性，包括基于量子汉密尔顿的量子模型，包括基于量子的模型，这些模型可能会规避棘手的时间复杂性。我们的一阶算法是使用经典镜下降二元性的新型量子概括得出的。两种结果都需要特殊的度量选择，即Bogoliubov-Kubo-Mori度量。为了从数值上测试我们提出的算法，我们将它们的性能与现有基准进行了关于横向场ISING模型的量子Gibbs采样任务的现有基准。最后，我们提出了一种初始化策略，利用几何局部性来建模状态的序列（例如量子 - 故事过程）的序列。我们从经验上证明了它在实际和想象的时间演化的经验上，同时定义了更广泛的潜在应用。

We develop an optimization algorithm suitable for Bayesian learning in complex models. Our approach relies on natural gradient updates within a general black-box framework for efficient training with limited model-specific derivations. It applies within the class of exponential-family variational posterior distributions, for which we extensively discuss the Gaussian case for which the updates have a rather simple form. Our Quasi Black-box Variational Inference (QBVI) framework is readily applicable to a wide class of Bayesian inference problems and is of simple implementation as the updates of the variational posterior do not involve gradients with respect to the model parameters, nor the prescription of the Fisher information matrix. We develop QBVI under different hypotheses for the posterior covariance matrix, discuss details about its robust and feasible implementation, and provide a number of real-world applications to demonstrate its effectiveness.

How can we perform efficient inference and learning in directed probabilistic models, in the presence of continuous latent variables with intractable posterior distributions, and large datasets? We introduce a stochastic variational inference and learning algorithm that scales to large datasets and, under some mild differentiability conditions, even works in the intractable case. Our contributions is two-fold. First, we show that a reparameterization of the variational lower bound yields a lower bound estimator that can be straightforwardly optimized using standard stochastic gradient methods. Second, we show that for i.i.d. datasets with continuous latent variables per datapoint, posterior inference can be made especially efficient by fitting an approximate inference model (also called a recognition model) to the intractable posterior using the proposed lower bound estimator. Theoretical advantages are reflected in experimental results.

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。

This paper presents a tutorial introduction to the use of variational methods for inference and learning in graphical models (Bayesian networks and Markov random fields). We present a number of examples of graphical models, including the QMR-DT database, the sigmoid belief network, the Boltzmann machine, and several variants of hidden Markov models, in which it is infeasible to run exact inference algorithms. We then introduce variational methods, which exploit laws of large numbers to transform the original graphical model into a simplified graphical model in which inference is efficient. Inference in the simpified model provides bounds on probabilities of interest in the original model. We describe a general framework for generating variational transformations based on convex duality. Finally we return to the examples and demonstrate how variational algorithms can be formulated in each case.

当前独立于域的经典计划者需要问题域和实例作为输入的符号模型，从而导致知识采集瓶颈。同时，尽管深度学习在许多领域都取得了重大成功，但知识是在与符号系统（例如计划者）不兼容的亚符号表示中编码的。我们提出了Latplan，这是一种无监督的建筑，结合了深度学习和经典计划。只有一组未标记的图像对，显示了环境中允许的过渡子集（训练输入），Latplan学习了环境的完整命题PDDL动作模型。稍后，当给出代表初始状态和目标状态（计划输入）的一对图像时，Latplan在符号潜在空间中找到了目标状态的计划，并返回可视化的计划执行。我们使用6个计划域的基于图像的版本来评估LATPLAN：8个插头，15个式嘴，Blockworld，Sokoban和两个LightsOut的变体。