任何相机的光学元件都会降低照片的清晰度，这是关键的视觉质量标准。该降解的特征是点传播函数（PSF），该函数取决于光的波长，并且在整个成像场中都是可变的。在本文中，我们提出了一个两步方案，以纠正单个RAW或JPEG图像中的光学畸变，即没有相机或镜头上任何事先信息。首先，我们估计当地的高斯模糊内核，以重叠斑块，并通过非盲脱毛技术锐化它们。基于数十个透镜的PSF的测量值，这些模糊内核被建模为由七个参数定义的RGB高斯人。其次，我们使用卷积神经网络去除其余的侧向色差（第一步中未考虑），该网络被训练，可将红色/绿色和蓝色/绿色残留图像最小化。关于合成图像和真实图像的实验表明，这两个阶段的组合产生了一种快速的最新盲目畸变补偿技术，该技术与商业非盲算法竞争。

神经辐射场（或NERF）代表了新的视图合成领域的突破和从多视图图像集合中对复杂场景进行的3D建模。最近的许多作品一直集中在通过正则化来使模型更加健壮，以便能够使用可能不一致和/或非常稀疏的数据进行训练。在这项工作中，我们刮擦了差异几何形状如何为稳健训练NERF样模型提供正则化工具的表面，这些工具经过修改，以表示连续和无限可区分的函数。特别是，我们展示了这些工具如何产生先前提出的NERF变体的直接数学形式主义，旨在改善具有挑战性的条件（即regnerf）。基于这一点，我们展示了如何使用相同的形式主义来培养表面的规律性（通过高斯和平均曲率），使得例如从非常有限的观点中学习表面。

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).

Searching for a path between two nodes in a graph is one of the most well-studied and fundamental problems in computer science. In numerous domains such as robotics, AI, or biology, practitioners develop search heuristics to accelerate their pathfinding algorithms. However, it is a laborious and complex process to hand-design heuristics based on the problem and the structure of a given use case. Here we present PHIL (Path Heuristic with Imitation Learning), a novel neural architecture and a training algorithm for discovering graph search and navigation heuristics from data by leveraging recent advances in imitation learning and graph representation learning. At training time, we aggregate datasets of search trajectories and ground-truth shortest path distances, which we use to train a specialized graph neural network-based heuristic function using backpropagation through steps of the pathfinding process. Our heuristic function learns graph embeddings useful for inferring node distances, runs in constant time independent of graph sizes, and can be easily incorporated in an algorithm such as A* at test time. Experiments show that PHIL reduces the number of explored nodes compared to state-of-the-art methods on benchmark datasets by 58.5\% on average, can be directly applied in diverse graphs ranging from biological networks to road networks, and allows for fast planning in time-critical robotics domains.

Pretrained language models that have been trained to predict the next word over billions of text documents have been shown to also significantly predict brain recordings of people comprehending language. Understanding the reasons behind the observed similarities between language in machines and language in the brain can lead to more insight into both systems. Recent works suggest that the prediction of the next word is a key mechanism that contributes to the alignment between the two. What is not yet understood is whether prediction of the next word is necessary for this observed alignment or simply sufficient, and whether there are other shared mechanisms or information that is similarly important. In this work, we take a first step towards a better understanding via two simple perturbations in a popular pretrained language model. The first perturbation is to improve the model's ability to predict the next word in the specific naturalistic stimulus text that the brain recordings correspond to. We show that this indeed improves the alignment with the brain recordings. However, this improved alignment may also be due to any improved word-level or multi-word level semantics for the specific world that is described by the stimulus narrative. We aim to disentangle the contribution of next word prediction and semantic knowledge via our second perturbation: scrambling the word order at inference time, which reduces the ability to predict the next word, but maintains any newly learned word-level semantics. By comparing the alignment with brain recordings of these differently perturbed models, we show that improvements in alignment with brain recordings are due to more than improvements in next word prediction and word-level semantics.