Given a symmetric matrix $M$ and a vector $\lambda$, we present new bounds on the Frobenius-distance utility of the Gaussian mechanism for approximating $M$ by a matrix whose spectrum is $\lambda$, under $(\varepsilon,\delta)$-differential privacy. Our bounds depend on both $\lambda$ and the gaps in the eigenvalues of $M$, and hold whenever the top $k+1$ eigenvalues of $M$ have sufficiently large gaps. When applied to the problems of private rank-$k$ covariance matrix approximation and subspace recovery, our bounds yield improvements over previous bounds. Our bounds are obtained by viewing the addition of Gaussian noise as a continuous-time matrix Brownian motion. This viewpoint allows us to track the evolution of eigenvalues and eigenvectors of the matrix, which are governed by stochastic differential equations discovered by Dyson. These equations allow us to bound the utility as the square-root of a sum-of-squares of perturbations to the eigenvectors, as opposed to a sum of perturbation bounds obtained via Davis-Kahan-type theorems.

考虑以下优化问题：给定$ n \ times n $矩阵$ a $和$ \ lambda $，最大化$ \ langle a，u \ lambda u^*\ rangle $，其中$ u $ $ u $在unital Group $ \ mathrm上变化{u}（n）$。这个问题试图通过矩阵大约$ a $，其频谱与$ \ lambda $相同，并且通过将$ \ lambda $设置为适当的对角矩阵，可以恢复矩阵近似问题，例如pca和等级$ k $近似。我们研究了在使用用户的私人数据构建矩阵$ a $的设置中，为这种优化问题设计差异化私有算法的问题。我们给出有效的私有算法，在近似误差上带有上和下限。我们的结果统一并改进了有关私人矩阵近似问题的几项先前的作品。他们依靠格拉斯曼尼亚人的包装/覆盖数量范围扩展到应该具有独立利益的单一轨道。

我们考虑从$ d $ d $二维log-concave分发进行抽样的问题。我们的主要结果是Dikin Walk Markov链的“软阈值”变体，最多需要$ o（（（md + d l^2 r^2）\ times md^{\ omega-1}）\ log（ \ frac {w} {\ delta}））$算术操作以从$ \ pi $中采样错误$ \ delta> 0 $在与$ w $ -warm启动的总变化距离中，其中$ l $是lipschitz - $ f $，$ k $包含在半径$ r $的球中，包含一个较小半径$ r $的球，而$ \ omega $是矩阵 - multiplication常数。当没有温暖的开始时，这意味着改进了$ \ tilde {o}（d^{3.5- \ omega}）$ arithmetic操作，以前从$ \ pi $采样中，在总变化错误$ \ delta $中采样，这是通过获得的在$ k $中，$ m = o（d）$不等式和$ lr = o（\ sqrt {d}）$。我们的算法在此环境中最佳以前的界限上提高了$ d^2 $算术操作，这是针对其他vers获得的Dikin Walk算法的离子。将我们的Dikin Walk Markov链插入Mangoubi和Vishnoi（2021）的后处理算法，我们在运行时间的依赖性方面取得了进一步的改进当$ k $是多层人士时。

对于$ d $ -dimensional log-tand distribus $ \ pi（\ theta）\ propto e ^ { - f（\ theta）} $ on polytope $ k $，我们考虑从分发$ \输出样本的问题nu $哪个是$ o（\ varepsilon）$ - 关闭无限距离$ \ sup _ {\ theta \在k} | \ log \ frac {\ nu（\ theta）} {\ pi（\ theta）} | $ $ \ pi $。具有无限远距离保证的这种采样器对于差异私密优化，特别是具有总变化距离或KL发散界限的传统采样算法不足以保证差别隐私。我们的主要结果是一种从分发$ o（\ varepsilon）$的点输出点 - 接近$ \ pi $ infifinity - 距离，需要$ o（（md + dl ^ 2r ^ 2）\ times（lr + d \ log（\ frac {rd + lrd} {\ varepsilon r}））\ times md ^ {\ omega-1}）$算术运算，其中$ f $ in $ l $ -lipschitz，$ k $由$ m $不平等，包含在半径$ r $的球中，并包含一个较小的半径$ $ $ $ r $，$ \ omega $是矩阵乘法常量。特别地，此运行时是在$ \ FRAC {1} {\ varepsilon} $中的对数，并显着提高了先前的作品。从技术上讲，我们从先前的作品离开，在$ \ frac {1} {\ varepsilon ^ 2} $ - 以$ k $的离散化，以获得$ o（\ varepsilon）$无限距离错误，并呈现一种方法将连续样本从$ k $转换为与具有无限界限的样本到样本。为了实现对$ D $的改进依赖，我们提出了一个“软阈值”版本的Dikin Walk，可能是独立的兴趣。将我们的算法插入指数机制的框架，在$ \ varepsilon $ -pure的运行时间内输出类似的改进，用于优化问题，例如Lipschitz-convex功能的经验风险和低秩近似，同时仍然实现最有名的已知效用范围。

我们研究了最近引入的最低最大优化框架的一种变体，其中最大玩具被限制以贪婪的方式更新其参数，直到达到一阶固定点为止。我们对此框架的平衡定义取决于最小玩家使用该方向来更新其参数的方向的提案分布。我们表明，鉴于一个平稳且有界的非Convex-Nonconcave目标函数，访问Min-player的更新的任何提案分布以及最大播放器的随机梯度甲骨文，我们的算法收敛于上述近似近似近似局部平衡，以众多的局部平衡。不取决于维度的迭代。我们的算法发现的平衡点取决于提议分布，在应用我们的算法来训练gans时，我们选择提案分布作为随机梯度的分布。我们从经验上评估了我们的算法，以挑战非凸孔测试功能和GAN培训中引起的损失功能。我们的算法在这些测试功能上收敛，并在用于训练gans时会在合成和现实世界中稳定训练，并避免模式崩溃

Key Point Analysis(KPA) is a relatively new task in NLP that combines summarization and classification by extracting argumentative key points (KPs) for a topic from a collection of texts and categorizing their closeness to the different arguments. In our work, we focus on the legal domain and develop methods that identify and extract KPs from premises derived from texts of judgments. The first method is an adaptation to an existing state-of-the-art method, and the two others are new methods that we developed from scratch. We present our methods and examples of their outputs, as well a comparison between them. The full evaluation of our results is done in the matching task -- match between the generated KPs to arguments (premises).

A gradual semantics takes a weighted argumentation framework as input and outputs a final acceptability degree for each argument, with different semantics performing the computation in different manners. In this work, we consider the problem of attack inference. That is, given a gradual semantics, a set of arguments with associated initial weights, and the final desirable acceptability degrees associated with each argument, we seek to determine whether there is a set of attacks on those arguments such that we can obtain these acceptability degrees. The main contribution of our work is to demonstrate that the associated decision problem, i.e., whether a set of attacks can exist which allows the final acceptability degrees to occur for given initial weights, is NP-complete for the weighted h-categoriser and cardinality-based semantics, and is polynomial for the weighted max-based semantics, even for the complete version of the problem (where all initial weights and final acceptability degrees are known). We then briefly discuss how this decision problem can be modified to find the attacks themselves and conclude by examining the partial problem where not all initial weights or final acceptability degrees may be known.

Offline reinforcement-learning (RL) algorithms learn to make decisions using a given, fixed training dataset without the possibility of additional online data collection. This problem setting is captivating because it holds the promise of utilizing previously collected datasets without any costly or risky interaction with the environment. However, this promise also bears the drawback of this setting. The restricted dataset induces subjective uncertainty because the agent can encounter unfamiliar sequences of states and actions that the training data did not cover. Moreover, inherent system stochasticity further increases uncertainty and aggravates the offline RL problem, preventing the agent from learning an optimal policy. To mitigate the destructive uncertainty effects, we need to balance the aspiration to take reward-maximizing actions with the incurred risk due to incorrect ones. In financial economics, modern portfolio theory (MPT) is a method that risk-averse investors can use to construct diversified portfolios that maximize their returns without unacceptable levels of risk. We integrate MPT into the agent's decision-making process to present a simple-yet-highly-effective risk-aware planning algorithm for offline RL. Our algorithm allows us to systematically account for the \emph{estimated quality} of specific actions and their \emph{estimated risk} due to the uncertainty. We show that our approach can be coupled with the Transformer architecture to yield a state-of-the-art planner for offline RL tasks, maximizing the return while significantly reducing the variance.

最近的几种方法，例如参数有效的微调（PEFT）和模式开发训练（PET），在标签筛选设置中取得了令人印象深刻的结果。但是，它们很难使用，因为它们会受到手动制作的提示的高度可变性，并且通常需要十亿参数语言模型才能达到高精度。为了解决这些缺点，我们提出了SETFIT（句子变压器微调），这是一个有效且迅速的框架，用于对句子变形金刚（ST）进行几次微调。 SetFit首先以对比的暹罗方式对少数文本对进行微调验证的st。然后将所得模型用于生成丰富的文本嵌入，这些嵌入方式用于训练分类头。这个简单的框架不需要任何提示或口头化，并且比现有技术少的参数较少，因此可以实现高精度。我们的实验表明，SetFit通过PEFT和PET技术获得了可比的结果，同时训练的速度更快。我们还表明，SETFIT可以通过简单地切换ST主体来应用于多语言设置。我们的代码可从https://github.com/huggingface/setFit以及我们的数据集获得，网址为https://huggingface.co/setfit。

我们建议第一个通过对弱的微型计算机进行深入学习的实时语义细分的系统，例如Raspberry Pi Zero Zero V2（其价格\ 15美元）附加到玩具无人机上。特别是，由于Raspberry Pi的重量不到$ 16 $，并且其大小是信用卡的一半，因此我们可以轻松地将其连接到普通的商业DJI Tello玩具器中（<\ $ 100，<90克，98 $ \ \时间$ 92.5 $ \ times $ 41毫米）。结果是可以从板载单眼RGB摄像头（无GPS或LIDAR传感器）实时检测和分类对象的自动无人机（无笔记本电脑或人类）。伴侣视频展示了这款Tello无人机如何扫描实验室的人（例如使用消防员或安全部队）以及在实验室外的空停车位。现有的深度学习解决方案要么在这种物联网设备上实时计算要么太慢，要么提供不切实际的质量结果。我们的主要挑战是设计一个系统，该系统在网络，深度学习平台/框架，压缩技术和压缩比的众多组合中占有最好的选择。为此，我们提供了一种有效的搜索算法，旨在找到最佳组合，从而导致网络运行时间与其准确性/性能之间的最佳权衡。