与2D栅格图像不同，没有用于3D视觉数据处理的单个主导表示。点云，网格或隐式功能等不同格式都具有其优点和劣势。尽管如此，诸如签名距离函数之类的网格表示在3D中也具有吸引人的属性。特别是，它们提供恒定的随机访问，并且非常适合现代机器学习。不幸的是，网格的存储大小随其尺寸而呈指数增长。因此，即使在中等分辨率下，它们也经常超过内存限制。这项工作探讨了各种低量张量格式，包括Tucker，Tensor Train和Wartenics Tensor tensor tensor tensor tensor分解，以压缩时间变化的3D数据。我们的方法迭代地计算，体素化和压缩每个帧的截断符号距离函数，并将张量式截断施加到代表整个4D场景的单个压缩张量中，将所有框架凝结到一个单个压缩张量中。我们表明，低级张量压缩对于存储和查询时间变化的签名距离功能非常紧凑。它大大降低了4D场景的内存足迹，同时令人惊讶地保留了它们的几何质量。与现有的基于迭代学习的方法（如DEEPSDF和NERF）不同，我们的方法使用具有理论保证的封闭式算法。

我们提出了Tntorch，这是一个张量学习框架，该框架支持统一界面下的多个分解（包括CandeComp/Parafac，Tucker和Tensor Train）。借助我们的库，用户可以通过自动差异，无缝的GPU支持以及Pytorch的API的便利性学习和处理低排名的张量。除分解算法外，TNTORCH还实施可区分的张量代数，等级截断，交叉透视，批处理处理，全面的张量算术等。

我们提出了一个端到端的可训练框架，通过仅通过查看其条目的一小部分来处理大规模的视觉数据张量。我们的方法将神经网络编码器与张振火车分解组合以学习低级潜在编码，耦合与交叉近似（CA）耦合，以通过原始样本的子集学习表示。 CA是一种自适应采样算法，它是原产的张量分解，并避免明确地使用全高分辨率数据。相反，它主动选择我们获取核心和按需获取的本地代表性样本。所需数量的样本仅使用输入的大小对数进行对数。我们网络中的张量的隐式表示，可以处理在其未压缩形式中不能以其他方式丢失的大网格。所提出的方法对于大规模的多维网格数据（例如，3D断层扫描）以及需要在大型接收领域（例如，预测整个器官的医学条件）的任务，特别适用于需要上下文的任务。代码可在https://github.com/aelphy/c-pic中获得。

Neural networks have achieved impressive results on many technological and scientific tasks. Yet, their empirical successes have outpaced our fundamental understanding of their structure and function. By identifying mechanisms driving the successes of neural networks, we can provide principled approaches for improving neural network performance and develop simple and effective alternatives. In this work, we isolate the key mechanism driving feature learning in fully connected neural networks by connecting neural feature learning to the average gradient outer product. We subsequently leverage this mechanism to design \textit{Recursive Feature Machines} (RFMs), which are kernel machines that learn features. We show that RFMs (1) accurately capture features learned by deep fully connected neural networks, (2) close the gap between kernel machines and fully connected networks, and (3) surpass a broad spectrum of models including neural networks on tabular data. Furthermore, we demonstrate that RFMs shed light on recently observed deep learning phenomena such as grokking, lottery tickets, simplicity biases, and spurious features. We provide a Python implementation to make our method broadly accessible [\href{https://github.com/aradha/recursive_feature_machines}{GitHub}].

Deep neural networks (DNNs) are often used for text classification tasks as they usually achieve high levels of accuracy. However, DNNs can be computationally intensive with billions of parameters and large amounts of labeled data, which can make them expensive to use, to optimize and to transfer to out-of-distribution (OOD) cases in practice. In this paper, we propose a non-parametric alternative to DNNs that's easy, light-weight and universal in text classification: a combination of a simple compressor like gzip with a $k$-nearest-neighbor classifier. Without any training, pre-training or fine-tuning, our method achieves results that are competitive with non-pretrained deep learning methods on six in-distributed datasets. It even outperforms BERT on all five OOD datasets, including four low-resource languages. Our method also performs particularly well in few-shot settings where labeled data are too scarce for DNNs to achieve a satisfying accuracy.

Hyperparameter tuning is critical to the success of federated learning applications. Unfortunately, appropriately selecting hyperparameters is challenging in federated networks. Issues of scale, privacy, and heterogeneity introduce noise in the tuning process and make it difficult to evaluate the performance of various hyperparameters. In this work, we perform the first systematic study on the effect of noisy evaluation in federated hyperparameter tuning. We first identify and rigorously explore key sources of noise, including client subsampling, data and systems heterogeneity, and data privacy. Surprisingly, our results indicate that even small amounts of noise can significantly impact tuning methods-reducing the performance of state-of-the-art approaches to that of naive baselines. To address noisy evaluation in such scenarios, we propose a simple and effective approach that leverages public proxy data to boost the evaluation signal. Our work establishes general challenges, baselines, and best practices for future work in federated hyperparameter tuning.

Deep Learning (DL) models tend to perform poorly when the data comes from a distribution different from the training one. In critical applications such as medical imaging, out-of-distribution (OOD) detection helps to identify such data samples, increasing the model's reliability. Recent works have developed DL-based OOD detection that achieves promising results on 2D medical images. However, scaling most of these approaches on 3D images is computationally intractable. Furthermore, the current 3D solutions struggle to achieve acceptable results in detecting even synthetic OOD samples. Such limited performance might indicate that DL often inefficiently embeds large volumetric images. We argue that using the intensity histogram of the original CT or MRI scan as embedding is descriptive enough to run OOD detection. Therefore, we propose a histogram-based method that requires no DL and achieves almost perfect results in this domain. Our proposal is supported two-fold. We evaluate the performance on the publicly available datasets, where our method scores 1.0 AUROC in most setups. And we score second in the Medical Out-of-Distribution challenge without fine-tuning and exploiting task-specific knowledge. Carefully discussing the limitations, we conclude that our method solves the sample-level OOD detection on 3D medical images in the current setting.

Efficient characterization of highly entangled multi-particle systems is an outstanding challenge in quantum science. Recent developments have shown that a modest number of randomized measurements suffices to learn many properties of a quantum many-body system. However, implementing such measurements requires complete control over individual particles, which is unavailable in many experimental platforms. In this work, we present rigorous and efficient algorithms for learning quantum many-body states in systems with any degree of control over individual particles, including when every particle is subject to the same global field and no additional ancilla particles are available. We numerically demonstrate the effectiveness of our algorithms for estimating energy densities in a U(1) lattice gauge theory and classifying topological order using very limited measurement capabilities.

In 2016-2017, TUS, the world's first experiment for testing the possibility of registering ultra-high energy cosmic rays (UHECRs) by their fluorescent radiation in the night atmosphere of Earth was carried out. Since 2019, the Russian-Italian fluorescence telescope (FT) Mini-EUSO ("UV Atmosphere") has been operating on the ISS. The stratospheric experiment EUSO-SPB2, which will employ an FT for registering UHECRs, is planned for 2023. We show how a simple convolutional neural network can be effectively used to find track-like events in the variety of data obtained with such instruments.

Knowledge graphs, modeling multi-relational data, improve numerous applications such as question answering or graph logical reasoning. Many graph neural networks for such data emerged recently, often outperforming shallow architectures. However, the design of such multi-relational graph neural networks is ad-hoc, driven mainly by intuition and empirical insights. Up to now, their expressivity, their relation to each other, and their (practical) learning performance is poorly understood. Here, we initiate the study of deriving a more principled understanding of multi-relational graph neural networks. Namely, we investigate the limitations in the expressive power of the well-known Relational GCN and Compositional GCN architectures and shed some light on their practical learning performance. By aligning both architectures with a suitable version of the Weisfeiler-Leman test, we establish under which conditions both models have the same expressive power in distinguishing non-isomorphic (multi-relational) graphs or vertices with different structural roles. Further, by leveraging recent progress in designing expressive graph neural networks, we introduce the $k$-RN architecture that provably overcomes the expressiveness limitations of the above two architectures. Empirically, we confirm our theoretical findings in a vertex classification setting over small and large multi-relational graphs.