The representation space of neural models for textual data emerges in an unsupervised manner during training. Understanding how those representations encode human-interpretable concepts is a fundamental problem. One prominent approach for the identification of concepts in neural representations is searching for a linear subspace whose erasure prevents the prediction of the concept from the representations. However, while many linear erasure algorithms are tractable and interpretable, neural networks do not necessarily represent concepts in a linear manner. To identify non-linearly encoded concepts, we propose a kernelization of a linear minimax game for concept erasure. We demonstrate that it is possible to prevent specific non-linear adversaries from predicting the concept. However, the protection does not transfer to different nonlinear adversaries. Therefore, exhaustively erasing a non-linearly encoded concept remains an open problem.

接受文本数据培训的现代神经模型取决于没有直接监督的预先训练的表示。由于这些表示越来越多地用于现实世界应用中，因此无法\ emph {Control}它们的内容成为一个越来越重要的问题。我们制定了与给定概念相对应的线性子空间的问题，以防止线性预测因子恢复概念。我们将此问题建模为受约束的线性最小游戏，并表明现有解决方案通常不是最佳的此任务。我们为某些目标提供了封闭式的解决方案，并提出了凸松弛的R-Lace，对他人效果很好。当在二元性别删除的背景下进行评估时，该方法恢复了一个低维子空间，其去除通过内在和外在评估会减轻偏见。我们表明，尽管是线性的，但该方法是高度表达性的，有效地减轻了深度非线性分类器中的偏见，同时保持拖延性和解释性。

Bias elimination and recent probing studies attempt to remove specific information from embedding spaces. Here it is important to remove as much of the target information as possible, while preserving any other information present. INLP is a popular recent method which removes specific information through iterative nullspace projections. Multiple iterations, however, increase the risk that information other than the target is negatively affected. We introduce two methods that find a single targeted projection: Mean Projection (MP, more efficient) and Tukey Median Projection (TMP, with theoretical guarantees). Our comparison between MP and INLP shows that (1) one MP projection removes linear separability based on the target and (2) MP has less impact on the overall space. Further analysis shows that applying random projections after MP leads to the same overall effects on the embedding space as the multiple projections of INLP. Applying one targeted (MP) projection hence is methodologically cleaner than applying multiple (INLP) projections that introduce random effects.

这篇综述的目的是将读者介绍到图表内，以将其应用于化学信息学中的分类问题。图内核是使我们能够推断分子的化学特性的功能，可以帮助您完成诸如寻找适合药物设计的化合物等任务。内核方法的使用只是一种特殊的两种方式量化了图之间的相似性。我们将讨论限制在这种方法上，尽管近年来已经出现了流行的替代方法，但最著名的是图形神经网络。

对于函数的矩阵或凸起的正半明确度（PSD）的形状约束在机器学习和科学的许多应用中起着核心作用，包括公制学习，最佳运输和经济学。然而，存在很少的功能模型，以良好的经验性能和理论担保来强制执行PSD-NESS或凸起。在本文中，我们介绍了用于在PSD锥中的值的函数的内核平方模型，其扩展了最近建议编码非负标量函数的内核平方型号。我们为这类PSD函数提供了一个代表性定理，表明它构成了PSD函数的普遍近似器，并在限定的平等约束的情况下导出特征值界限。然后，我们将结果应用于建模凸起函数，通过执行其Hessian的核心量子表示，并表明可以因此表示任何平滑且强凸的功能。最后，我们说明了我们在PSD矩阵值回归任务中的方法以及标准值凸起回归。

产品空间的嵌入方法是用于复杂数据结构的低失真和低维表示的强大技术。在这里，我们解决了Euclidean，球形和双曲线产品的产品空间形式的线性分类新问题。首先，我们描述了使用测地仪和黎曼·歧木的线性分类器的新型制剂，其使用大气和黎曼指标在向量空间中推广直线和内部产品。其次，我们证明了$ D $ -dimential空间形式的线性分类器的任何曲率具有相同的表现力，即，它们可以粉碎恰好$ d + 1 $积分。第三，我们在产品空间形式中正式化线性分类器，描述了第一个已知的Perceptron和支持这些空间的传染媒介机分类器，并为感知者建立严格的融合结果。此外，我们证明了vapnik-chervonenkis尺寸在尺寸的产品空间形式的线性分类器的维度为\ {至少} $ d + 1 $。我们支持我们的理论发现，在多个数据集上模拟，包括合成数据，图像数据和单细胞RNA测序（SCRNA-SEQ）数据。结果表明，与相同维度的欧几里德空间中的欧几里德空间中，SCRNA-SEQ数据的低维产品空间形式的分类为SCRNA-SEQ数据提供了$ \ SIM15 \％$的性能改进。

对称性一直是探索广泛复杂系统的基本工具。在机器学习中，在模型和数据中都探索了对称性。在本文中，我们试图将模型家族架构引起的对称性与该家族的内部数据表示的对称性联系起来。我们通过计算一组基本的对称组来做到这一点，我们称它们称为模型的\ emph {Intertwiner组}。这些中的每一个都来自模型的特定非线性层，不同的非线性导致不同的对称组。这些组以模型的权重更改模型的权重，使模型所代表的基础函数保持恒定，但模型内部数据的内部表示可能会改变。我们通过一系列实验将Intertwiner组连接到模型的数据内部表示，这些实验在具有相同体系结构的模型之间探测隐藏状态之间的相似性。我们的工作表明，网络的对称性在该网络的数据表示中传播到对称性中，从而使我们更好地了解架构如何影响学习和预测过程。最后，我们推测，对于Relu网络，交织组可能会为在隐藏层而不是任意线性组合的激活基础上集中模型可解释性探索的共同实践提供理由。

The basic idea of quantum computing is surprisingly similar to that of kernel methods in machine learning, namely to efficiently perform computations in an intractably large Hilbert space. In this paper we explore some theoretical foundations of this link and show how it opens up a new avenue for the design of quantum machine learning algorithms. We interpret the process of encoding inputs in a quantum state as a nonlinear feature map that maps data to quantum Hilbert space. A quantum computer can now analyse the input data in this feature space. Based on this link, we discuss two approaches for building a quantum model for classification. In the first approach, the quantum device estimates inner products of quantum states to compute a classically intractable kernel. This kernel can be fed into any classical kernel method such as a support vector machine. In the second approach, we can use a variational quantum circuit as a linear model that classifies data explicitly in Hilbert space. We illustrate these ideas with a feature map based on squeezing in a continuous-variable system, and visualise the working principle with 2-dimensional mini-benchmark datasets.

表明多语言语言模型允许跨脚本和语言进行非平凡的转移。在这项工作中，我们研究了能够转移的内部表示的结构。我们将重点放在性别区分作为实际案例研究的表示上，并研究在跨不同语言的共享子空间中编码性别概念的程度。我们的分析表明，性别表示由几个跨语言共享的重要组成部分以及特定于语言的组成部分组成。与语言无关和特定语言的组成部分的存在为我们做出的有趣的经验观察提供了解释：虽然性别分类跨语言良好地传递了跨语言，对性别删除的干预措施，对单一语言进行了培训，但不会轻易转移给其他人。

了解生物和人造网络的运作仍然是一个艰难而重要的挑战。为了确定一般原则，研究人员越来越有兴趣测量培训的大量网络，或者在培训或生物学地适应类似的任务。现在需要一种标准化的分析工具来确定网络级协变量 - 例如架构，解剖脑区和模型生物 - 影响神经表示（隐藏层激活）。在这里，我们通过定义量化代表性异化的广泛的公制空间，为这些分析提供严格的基础。使用本框架，我们根据规范相关分析修改现有的代表性相似度量，以满足三角形不等式，制定致扫描层中的感应偏差的新型度量，并识别使网络表示能够结合到基本上的近似的欧几里德嵌入物。货架机学习方法。我们展示了来自生物学（Allen Institute脑观测所）和深度学习（NAS-BENCH-101）的大规模数据集的这些方法。在这样做时，我们识别在解剖特征和模型性能方面可解释的神经表现之间的关系。

Adversarial examples have attracted significant attention in machine learning, but the reasons for their existence and pervasiveness remain unclear. We demonstrate that adversarial examples can be directly attributed to the presence of non-robust features: features (derived from patterns in the data distribution) that are highly predictive, yet brittle and (thus) incomprehensible to humans. After capturing these features within a theoretical framework, we establish their widespread existence in standard datasets. Finally, we present a simple setting where we can rigorously tie the phenomena we observe in practice to a misalignment between the (human-specified) notion of robustness and the inherent geometry of the data.

We reformulate unsupervised dimension reduction problem (UDR) in the language of tempered distributions, i.e. as a problem of approximating an empirical probability density function by another tempered distribution, supported in a $k$-dimensional subspace. We show that this task is connected with another classical problem of data science -- the sufficient dimension reduction problem (SDR). In fact, an algorithm for the first problem induces an algorithm for the second and vice versa. In order to reduce an optimization problem over distributions to an optimization problem over ordinary functions we introduce a nonnegative penalty function that ``forces'' the support of the model distribution to be $k$-dimensional. Then we present an algorithm for the minimization of the penalized objective, based on the infinite-dimensional low-rank optimization, which we call the alternating scheme. Also, we design an efficient approximate algorithm for a special case of the problem, where the distance between the empirical distribution and the model distribution is measured by Maximum Mean Discrepancy defined by a Mercer kernel of a certain type. We test our methods on four examples (three UDR and one SDR) using synthetic data and standard datasets.

在其表示中，已经发现接受过文本数据训练的神经网络模型编码不希望的语言或敏感属性。删除此类属性是不平凡的，因为属性，文本输入和学习的表示之间存在复杂的关系。最近的工作提出了事后和对抗方法，以从模型的表示中删除此类不需要的属性。通过广泛的理论和经验分析，我们表明这些方法可以适得其反：它们无法完全删除属性，在最坏的情况下，最终可能会破坏所有与任务相关的功能。原因是方法对探测分类器的依赖作为属性的代理。即使在最有利的条件下，当属性在表示空间中的特征可以提供100％的学习探测分类器时，我们证明事后或对抗方法将无法正确删除属性。这些理论含义通过经验实验在合成，多NLI和Twitter数据集的模型上证实。对于敏感的属性去除（例如公平性），我们建议您谨慎使用这些方法，并提出伪造度量，以评估最终分类器的质量。

We propose a framework for analyzing and comparing distributions, which we use to construct statistical tests to determine if two samples are drawn from different distributions. Our test statistic is the largest difference in expectations over functions in the unit ball of a reproducing kernel Hilbert space (RKHS), and is called the maximum mean discrepancy (MMD). We present two distributionfree tests based on large deviation bounds for the MMD, and a third test based on the asymptotic distribution of this statistic. The MMD can be computed in quadratic time, although efficient linear time approximations are available. Our statistic is an instance of an integral probability metric, and various classical metrics on distributions are obtained when alternative function classes are used in place of an RKHS. We apply our two-sample tests to a variety of problems, including attribute matching for databases using the Hungarian marriage method, where they perform strongly. Excellent performance is also obtained when comparing distributions over graphs, for which these are the first such tests.

已经假设量子计算机可以很好地为机器学习中的应用提供很好。在本作工作中，我们分析通过量子内核定义的函数类。量子计算机提供了有效地计算符合难以计算的指数大密度运算符的内部产品。然而，具有指数大的特征空间使得普遍化的问题造成泛化的问题。此外，能够有效地评估高尺寸空间中的内部产品本身不能保证量子优势，因为已经是经典的漫步核可以对应于高或无限的维度再现核Hilbert空间（RKHS）。我们分析量子内核的频谱属性，并发现我们可以期待优势如果其RKHS低维度，并且包含很难经典计算的功能。如果已知目标函数位于该类中，则这意味着量子优势，因为量子计算机可以编码这种电感偏压，而没有同样的方式对功能类进行经典有效的方式。但是，我们表明查找合适的量子内核并不容易，因为内核评估可能需要指数倍数的测量。总之，我们的信息是有点令人发声的：我们猜测量子机器学习模型只有在我们设法将关于传递到量子电路的问题的知识编码的情况下，才能提供加速，同时将相同的偏差置于经典模型。难的。然而，在学习由量子流程生成的数据时，这些情况可能会被典雅地发生，但对于古典数据集来说，它们似乎更难。

We propose a family of learning algorithms based on a new form of regularization that allows us to exploit the geometry of the marginal distribution. We focus on a semi-supervised framework that incorporates labeled and unlabeled data in a general-purpose learner. Some transductive graph learning algorithms and standard methods including support vector machines and regularized least squares can be obtained as special cases. We use properties of reproducing kernel Hilbert spaces to prove new Representer theorems that provide theoretical basis for the algorithms. As a result (in contrast to purely graph-based approaches) we obtain a natural out-of-sample extension to novel examples and so are able to handle both transductive and truly semi-supervised settings. We present experimental evidence suggesting that our semi-supervised algorithms are able to use unlabeled data effectively. Finally we have a brief discussion of unsupervised and fully supervised learning within our general framework.

We consider neural networks with a single hidden layer and non-decreasing positively homogeneous activation functions like the rectified linear units. By letting the number of hidden units grow unbounded and using classical non-Euclidean regularization tools on the output weights, they lead to a convex optimization problem and we provide a detailed theoretical analysis of their generalization performance, with a study of both the approximation and the estimation errors. We show in particular that they are adaptive to unknown underlying linear structures, such as the dependence on the projection of the input variables onto a low-dimensional subspace. Moreover, when using sparsity-inducing norms on the input weights, we show that high-dimensional non-linear variable selection may be achieved, without any strong assumption regarding the data and with a total number of variables potentially exponential in the number of observations. However, solving this convex optimization problem in infinite dimensions is only possible if the non-convex subproblem of addition of a new unit can be solved efficiently. We provide a simple geometric interpretation for our choice of activation functions and describe simple conditions for convex relaxations of the finite-dimensional non-convex subproblem to achieve the same generalization error bounds, even when constant-factor approximations cannot be found. We were not able to find strong enough convex relaxations to obtain provably polynomial-time algorithms and leave open the existence or non-existence of such tractable algorithms with non-exponential sample complexities.

Many applications of representation learning, such as privacy preservation, algorithmic fairness, and domain adaptation, desire explicit control over semantic information being discarded. This goal is formulated as satisfying two objectives: maximizing utility for predicting a target attribute while simultaneously being invariant (independent) to a known semantic attribute. Solutions to invariant representation learning (IRepL) problems lead to a trade-off between utility and invariance when they are competing. While existing works study bounds on this trade-off, two questions remain outstanding: 1) What is the exact trade-off between utility and invariance? and 2) What are the encoders (mapping the data to a representation) that achieve the trade-off, and how can we estimate it from training data? This paper addresses these questions for IRepLs in reproducing kernel Hilbert spaces (RKHS)s. Under the assumption that the distribution of a low-dimensional projection of high-dimensional data is approximately normal, we derive a closed-form solution for the global optima of the underlying optimization problem for encoders in RKHSs. This yields closed formulae for a near-optimal trade-off, corresponding optimal representation dimensionality, and the corresponding encoder(s). We also numerically quantify the trade-off on representative problems and compare them to those achieved by baseline IRepL algorithms.

已知量子计算机可以在某些专业设置中使用经典的最先进的机器学习方法提供加速。例如，已证明量子内核方法可以在离散对数问题的学习版本上提供指数加速。了解量子模型的概括对于实现实际利益问题的类似加速至关重要。最近的结果表明，量子特征空间的指数大小阻碍了概括。尽管这些结果表明，量子模型在量子数数量较大时无法概括，但在本文中，我们表明这些结果依赖于过度限制性的假设。我们通过改变称为量子内核带宽的超参数来考虑更广泛的模型。我们分析了大量限制，并为可以以封闭形式求解的量子模型的概括提供了明确的公式。具体而言，我们表明，更改带宽的值可以使模型从不能概括到任何目标函数到对准目标的良好概括。我们的分析表明，带宽如何控制内核积分操作员的光谱，从而如何控制模型的电感偏置。我们从经验上证明，我们的理论正确地预测带宽如何影响质量模型在具有挑战性的数据集上的概括，包括远远超出我们理论假设的数据集。我们讨论了结果对机器学习中量子优势的含义。

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。