给定尺寸$ d $中的独立标准高斯点$ v_1，\ ldots，v_n $，对于$（n，d）$的值（n，d）$的值很高，概率很高，同时通过所有要点？将椭圆形拟合到随机点的基本问题与低级别矩阵分解，独立的组件分析和主成分分析有连接。基于有力的数值证据，桑德森，帕里洛和威尔斯基[Proc。关于决策和控制会议，第6031-6036页，2013年]猜想，椭圆形拟合问题的问题从可行的到不可行的$ n $增加，并在$ n \ sim d^2/4处急剧阈值$。我们通过为某些$ n = \ omega（\，d^2/\ log^5（d）\，）$构建合适的椭圆形来解决这个猜想，从而改善了Ghosh等人的先前工作。 [Proc。关于计算机科学基础的研讨会，第954-965、2020页]，需要$ n = o（d^{3/2}）$。我们的证明证明了Saunderson等人的最小二乘结构的可行性。使用对特定非标准随机矩阵的特征向量和特征值进行仔细的分析。

In the Earth's magnetosphere, there are fewer than a dozen dedicated probes beyond low-Earth orbit making in-situ observations at any given time. As a result, we poorly understand its global structure and evolution, the mechanisms of its main activity processes, magnetic storms, and substorms. New Artificial Intelligence (AI) methods, including machine learning, data mining, and data assimilation, as well as new AI-enabled missions will need to be developed to meet this Sparse Data challenge.

Microswimmers can acquire information on the surrounding fluid by sensing mechanical queues. They can then navigate in response to these signals. We analyse this navigation by combining deep reinforcement learning with direct numerical simulations to resolve the hydrodynamics. We study how local and non-local information can be used to train a swimmer to achieve particular swimming tasks in a non-uniform flow field, in particular a zig-zag shear flow. The swimming tasks are (1) learning how to swim in the vorticity direction, (2) the shear-gradient direction, and (3) the shear flow direction. We find that access to lab frame information on the swimmer's instantaneous orientation is all that is required in order to reach the optimal policy for (1,2). However, information on both the translational and rotational velocities seem to be required to achieve (3). Inspired by biological microorganisms we also consider the case where the swimmers sense local information, i.e. surface hydrodynamic forces, together with a signal direction. This might correspond to gravity or, for micro-organisms with light sensors, a light source. In this case, we show that the swimmer can reach a comparable level of performance as a swimmer with access to lab frame variables. We also analyse the role of different swimming modes, i.e. pusher, puller, and neutral swimmers.

Cutting planes are a crucial component of state-of-the-art mixed-integer programming solvers, with the choice of which subset of cuts to add being vital for solver performance. We propose new distance-based measures to qualify the value of a cut by quantifying the extent to which it separates relevant parts of the relaxed feasible set. For this purpose, we use the analytic centers of the relaxation polytope or of its optimal face, as well as alternative optimal solutions of the linear programming relaxation. We assess the impact of the choice of distance measure on root node performance and throughout the whole branch-and-bound tree, comparing our measures against those prevalent in the literature. Finally, by a multi-output regression, we predict the relative performance of each measure, using static features readily available before the separation process. Our results indicate that analytic center-based methods help to significantly reduce the number of branch-and-bound nodes needed to explore the search space and that our multiregression approach can further improve on any individual method.

In a recent paper Wunderlich and Pehle introduced the EventProp algorithm that enables training spiking neural networks by gradient descent on exact gradients. In this paper we present extensions of EventProp to support a wider class of loss functions and an implementation in the GPU enhanced neuronal networks framework which exploits sparsity. The GPU acceleration allows us to test EventProp extensively on more challenging learning benchmarks. We find that EventProp performs well on some tasks but for others there are issues where learning is slow or fails entirely. Here, we analyse these issues in detail and discover that they relate to the use of the exact gradient of the loss function, which by its nature does not provide information about loss changes due to spike creation or spike deletion. Depending on the details of the task and loss function, descending the exact gradient with EventProp can lead to the deletion of important spikes and so to an inadvertent increase of the loss and decrease of classification accuracy and hence a failure to learn. In other situations the lack of knowledge about the benefits of creating additional spikes can lead to a lack of gradient flow into earlier layers, slowing down learning. We eventually present a first glimpse of a solution to these problems in the form of `loss shaping', where we introduce a suitable weighting function into an integral loss to increase gradient flow from the output layer towards earlier layers.

Robots operating in human environments must be able to rearrange objects into semantically-meaningful configurations, even if these objects are previously unseen. In this work, we focus on the problem of building physically-valid structures without step-by-step instructions. We propose StructDiffusion, which combines a diffusion model and an object-centric transformer to construct structures out of a single RGB-D image based on high-level language goals, such as "set the table." Our method shows how diffusion models can be used for complex multi-step 3D planning tasks. StructDiffusion improves success rate on assembling physically-valid structures out of unseen objects by on average 16% over an existing multi-modal transformer model, while allowing us to use one multi-task model to produce a wider range of different structures. We show experiments on held-out objects in both simulation and on real-world rearrangement tasks. For videos and additional results, check out our website: http://weiyuliu.com/StructDiffusion/.

We present the Habitat-Matterport 3D Semantics (HM3DSEM) dataset. HM3DSEM is the largest dataset of 3D real-world spaces with densely annotated semantics that is currently available to the academic community. It consists of 142,646 object instance annotations across 216 3D spaces and 3,100 rooms within those spaces. The scale, quality, and diversity of object annotations far exceed those of prior datasets. A key difference setting apart HM3DSEM from other datasets is the use of texture information to annotate pixel-accurate object boundaries. We demonstrate the effectiveness of HM3DSEM dataset for the Object Goal Navigation task using different methods. Policies trained using HM3DSEM perform outperform those trained on prior datasets. Introduction of HM3DSEM in the Habitat ObjectNav Challenge lead to an increase in participation from 400 submissions in 2021 to 1022 submissions in 2022.

从分布式敏感数据中学习隐私的模型是一个越来越重要的问题，通常在联邦学习环境中提出。最近通过分区的变异推理算法扩展到了非私有联盟学习设置。为了保护隐私，当前的黄金标准称为差异隐私。差异隐私在强大的数学上明确定义的意义上保证了隐私。在本文中，我们介绍了差异化的分区变异推断，这是学习与联合学习环境中贝叶斯后分布的差异近似的第一个通用框架，同时最大程度地减少了通信弹的数量并为数据主体提供差异隐私保证。我们在通用框架中提出了三个替代实现，一个基于单个方面的本地优化，而两个基于扰动全局更新（一种使用联合平均版本，一个将虚拟方添加到协议中），并比较其属性，并比较其属性理论上和经验。我们表明，只要各方都有足够的本地数据，扰动本地优化与简单且复杂的模型效果很好。但是，每个方始终独立保证隐私。相比之下，扰动全局更新与相对简单的模型最有效。鉴于可以访问合适的安全原始词，例如安全聚合或安全的改组，所有各方都可以共同保证隐私。

上印度河盆地喜马拉雅山为2.7亿人和无数的生态系统提供水。然而，在这一领域，降水是水文建模的关键组成部分。围绕这种不确定性的关键挑战来自整个盆地降水的复杂时空分布。在这项工作中，我们提出了具有结构化非平稳核的高斯过程，以模拟UIB中的降水模式。先前试图在印度库什karakoram喜马拉雅地区量化或建模降水的尝试通常是定性的，或者包括在较低分辨率下无法解决的粗略假设和简化。这项研究也几乎没有错误传播。我们用非平稳的Gibbs内核参数为输入依赖性长度尺度来解释降水的空间变化。这允许后函数样品适应印度河地区不同基础地形所固有的不同降水模式。输入依赖的长度尺寸由带有固定平方 - 指数内核的潜在高斯过程控制，以使功能级别的超参数平稳变化。在消融实验中，我们通过证明其对空间协方差，时间结构和关节时空重建的能力来激励所提出的内核的每个组成部分。我们通过固定的高斯工艺和深度高斯工艺进行基准测试模型。

模拟和混合信号（AMS）电路设计仍然依赖于人类设计专业知识。机器学习一直通过用人工智能代替人类的体验来协助电路设计自动化。本文介绍了标签，这是一种从利用文本，自我注意力和图形的布局中学习电路表示的新范式。嵌入网络模型在无手动标签的情况下学习空间信息。我们向AMS电路学习介绍文本嵌入和自我注意的机制。实验结果表明，具有工业罚款技术基准的实例之间的布局距离的能力。通过在案例研究中显示有限数据的其他三个学习任务的转移性，可以验证电路表示的有效性：布局匹配预测，线长度估计和净寄生电容预测。