从物理的角度来看，深度神经网络是其“链接”和“顶点”迭代处理数据并以优选求解任务的图形。我们使用复杂的网络理论（CNT）作为定向的加权图代表深神网络（DNN）：在此框架内，我们引入指标将DNN作为动力学系统，其粒度从重量到包括神经元在内的层延伸到层。CNT区分参数和神经元数量不同的网络，隐藏层和激活的类型以及客观任务。我们进一步表明，我们的指标会区分低性能网络。CNT是一种理论DNN的综合方法，也是解释模型行为的互补方法，该方法实际上是基于网络理论的，并且超越了研究良好的输入输出关系。

Large language models (LLMs) have been reported to have strong performance on natural language processing tasks. However, performance metrics such as accuracy do not measure the quality of the model in terms of its ability to robustly represent complex linguistic structure. In this work, we propose a framework to evaluate the robustness of linguistic representations using probing tasks. We leverage recent advances in extracting emergent linguistic constructs from LLMs and apply syntax-preserving perturbations to test the stability of these constructs in order to better understand the representations learned by LLMs. Empirically, we study the performance of four LLMs across six different corpora on the proposed robustness measures. We provide evidence that context-free representation (e.g., GloVe) are in some cases competitive with context-dependent representations from modern LLMs (e.g., BERT), yet equally brittle to syntax-preserving manipulations. Emergent syntactic representations in neural networks are brittle, thus our work poses the attention on the risk of comparing such structures to those that are object of a long lasting debate in linguistics.

制定了具有机器学习模拟（骆驼）项目的宇宙学和天体物理学，通过数千名宇宙的流体动力模拟和机器学习将宇宙学与天体物理学结合起来。骆驼包含4,233个宇宙学仿真，2,049个n-body和2,184个最先进的流体动力模拟，在参数空间中采样巨大的体积。在本文中，我们介绍了骆驼公共数据发布，描述了骆驼模拟的特性和由它们产生的各种数据产品，包括光环，次麦，银河系和空隙目录，功率谱，Bispectra，Lyman - $ \ Alpha $光谱，概率分布函数，光环径向轮廓和X射线光子列表。我们还释放了超过骆驼 - 山姆的数十亿个星系的目录：与Santa Cruz半分析模型相结合的大量N身体模拟。我们释放包含350多个Terabytes的所有数据，并包含143,922个快照，数百万光环，星系和摘要统计数据。我们提供有关如何访问，下载，读取和处理数据AT \ URL {https://camels.readthedocs.io}的进一步技术详细信息。

日益增长的证据表明，由于NLP研究界的很大一部分，已经采用了最初被引入图像的对抗稳健性的经典概念。我们表明，在NLP的背景下，这一概念是有问题的，因为它考虑了一个狭隘的语言现象。在本文中，我们争论语义稳健性，与语言忠诚的人类概念更好。我们在偏差方面表征了语义稳健性，预计它将在模型中诱导。我们使用基于模板的生成试验台研究了一系列香草和强大的训练架构的语义稳健性。我们补充了经验证据的分析，尽管较难实施，语义稳健性可以提高性能％，为复杂语言现象提供保证，其中模型在经典感觉中的稳健失败。

Diffusion models have achieved justifiable popularity by attaining state-of-the-art performance in generating realistic objects from seemingly arbitrarily complex data distributions, including when conditioning generation on labels. Unfortunately, however, their iterative nature renders them very computationally inefficient during the sampling process. For the multi-class conditional generation problem, we propose a novel, structurally unique framework of diffusion models which are hierarchically branched according to the inherent relationships between classes. In this work, we demonstrate that branched diffusion models offer major improvements in efficiently generating samples from multiple classes. We also showcase several other advantages of branched diffusion models, including ease of extension to novel classes in a continual-learning setting, and a unique interpretability that offers insight into these generative models. Branched diffusion models represent an alternative paradigm to their traditional linear counterparts, and can have large impacts in how we use diffusion models for efficient generation, online learning, and scientific discovery.

The polynomial kernels are widely used in machine learning and they are one of the default choices to develop kernel-based classification and regression models. However, they are rarely used and considered in numerical analysis due to their lack of strict positive definiteness. In particular they do not enjoy the usual property of unisolvency for arbitrary point sets, which is one of the key properties used to build kernel-based interpolation methods. This paper is devoted to establish some initial results for the study of these kernels, and their related interpolation algorithms, in the context of approximation theory. We will first prove necessary and sufficient conditions on point sets which guarantee the existence and uniqueness of an interpolant. We will then study the Reproducing Kernel Hilbert Spaces (or native spaces) of these kernels and their norms, and provide inclusion relations between spaces corresponding to different kernel parameters. With these spaces at hand, it will be further possible to derive generic error estimates which apply to sufficiently smooth functions, thus escaping the native space. Finally, we will show how to employ an efficient stable algorithm to these kernels to obtain accurate interpolants, and we will test them in some numerical experiment. After this analysis several computational and theoretical aspects remain open, and we will outline possible further research directions in a concluding section. This work builds some bridges between kernel and polynomial interpolation, two topics to which the authors, to different extents, have been introduced under the supervision or through the work of Stefano De Marchi. For this reason, they wish to dedicate this work to him in the occasion of his 60th birthday.

This paper presents the development of a system able to estimate the 2D relative position of nodes in a wireless network, based on distance measurements between the nodes. The system uses ultra wide band ranging technology and the Bluetooth Low Energy protocol to acquire data. Furthermore, a nonlinear least squares problem is formulated and solved numerically for estimating the relative positions of the nodes. The localization performance of the system is validated by experimental tests, demonstrating the capability of measuring the relative position of a network comprised of 4 nodes with an accuracy of the order of 3 cm and an update rate of 10 Hz. This shows the feasibility of applying the proposed system for multi-robot cooperative localization and formation control scenarios.

Steerable convolutional neural networks (CNNs) provide a general framework for building neural networks equivariant to translations and other transformations belonging to an origin-preserving group $G$, such as reflections and rotations. They rely on standard convolutions with $G$-steerable kernels obtained by analytically solving the group-specific equivariance constraint imposed onto the kernel space. As the solution is tailored to a particular group $G$, the implementation of a kernel basis does not generalize to other symmetry transformations, which complicates the development of group equivariant models. We propose using implicit neural representation via multi-layer perceptrons (MLPs) to parameterize $G$-steerable kernels. The resulting framework offers a simple and flexible way to implement Steerable CNNs and generalizes to any group $G$ for which a $G$-equivariant MLP can be built. We apply our method to point cloud (ModelNet-40) and molecular data (QM9) and demonstrate a significant improvement in performance compared to standard Steerable CNNs.

The development and adoption of artificial intelligence (AI) technologies in space applications is growing quickly as the consensus increases on the potential benefits introduced. As more and more aerospace engineers are becoming aware of new trends in AI, traditional approaches are revisited to consider the applications of emerging AI technologies. Already at the time of writing, the scope of AI-related activities across academia, the aerospace industry and space agencies is so wide that an in-depth review would not fit in these pages. In this chapter we focus instead on two main emerging trends we believe capture the most relevant and exciting activities in the field: differentiable intelligence and on-board machine learning. Differentiable intelligence, in a nutshell, refers to works making extensive use of automatic differentiation frameworks to learn the parameters of machine learning or related models. Onboard machine learning considers the problem of moving inference, as well as learning, onboard. Within these fields, we discuss a few selected projects originating from the European Space Agency's (ESA) Advanced Concepts Team (ACT), giving priority to advanced topics going beyond the transposition of established AI techniques and practices to the space domain.

The term ``neuromorphic'' refers to systems that are closely resembling the architecture and/or the dynamics of biological neural networks. Typical examples are novel computer chips designed to mimic the architecture of a biological brain, or sensors that get inspiration from, e.g., the visual or olfactory systems in insects and mammals to acquire information about the environment. This approach is not without ambition as it promises to enable engineered devices able to reproduce the level of performance observed in biological organisms -- the main immediate advantage being the efficient use of scarce resources, which translates into low power requirements. The emphasis on low power and energy efficiency of neuromorphic devices is a perfect match for space applications. Spacecraft -- especially miniaturized ones -- have strict energy constraints as they need to operate in an environment which is scarce with resources and extremely hostile. In this work we present an overview of early attempts made to study a neuromorphic approach in a space context at the European Space Agency's (ESA) Advanced Concepts Team (ACT).