This paper studies the infinite-width limit of deep linear neural networks initialized with random parameters. We obtain that, when the number of neurons diverges, the training dynamics converge (in a precise sense) to the dynamics obtained from a gradient descent on an infinitely wide deterministic linear neural network. Moreover, even if the weights remain random, we get their precise law along the training dynamics, and prove a quantitative convergence result of the linear predictor in terms of the number of neurons. We finally study the continuous-time limit obtained for infinitely wide linear neural networks and show that the linear predictors of the neural network converge at an exponential rate to the minimal $\ell_2$-norm minimizer of the risk.

制定关于涉及新数据的任务的训练模型的表现的陈述是机器学习的主要目标之一，即了解模型的泛化功率。各种能力措施试图捕捉这种能力，但通常在解释我们在实践中观察到的模型的重要特征。在这项研究中，我们将本地有效维度提出作为一种容量测量，似乎与标准数据集的泛化误差很好。重要的是，我们证明了本地有效维度界限泛化误差并讨论了机器学习模型的这种容量措施的适应性。

Real-world robotic grasping can be done robustly if a complete 3D Point Cloud Data (PCD) of an object is available. However, in practice, PCDs are often incomplete when objects are viewed from few and sparse viewpoints before the grasping action, leading to the generation of wrong or inaccurate grasp poses. We propose a novel grasping strategy, named 3DSGrasp, that predicts the missing geometry from the partial PCD to produce reliable grasp poses. Our proposed PCD completion network is a Transformer-based encoder-decoder network with an Offset-Attention layer. Our network is inherently invariant to the object pose and point's permutation, which generates PCDs that are geometrically consistent and completed properly. Experiments on a wide range of partial PCD show that 3DSGrasp outperforms the best state-of-the-art method on PCD completion tasks and largely improves the grasping success rate in real-world scenarios. The code and dataset will be made available upon acceptance.

Recent works have investigated the role of graph bottlenecks in preventing long-range information propagation in message-passing graph neural networks, causing the so-called `over-squashing' phenomenon. As a remedy, graph rewiring mechanisms have been proposed as preprocessing steps. Graph Echo State Networks (GESNs) are a reservoir computing model for graphs, where node embeddings are recursively computed by an untrained message-passing function. In this paper, we show that GESNs can achieve a significantly better accuracy on six heterophilic node classification tasks without altering the graph connectivity, thus suggesting a different route for addressing the over-squashing problem.

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.

Recent 3D-aware GANs rely on volumetric rendering techniques to disentangle the pose and appearance of objects, de facto generating entire 3D volumes rather than single-view 2D images from a latent code. Complex image editing tasks can be performed in standard 2D-based GANs (e.g., StyleGAN models) as manipulation of latent dimensions. However, to the best of our knowledge, similar properties have only been partially explored for 3D-aware GAN models. This work aims to fill this gap by showing the limitations of existing methods and proposing LatentSwap3D, a model-agnostic approach designed to enable attribute editing in the latent space of pre-trained 3D-aware GANs. We first identify the most relevant dimensions in the latent space of the model controlling the targeted attribute by relying on the feature importance ranking of a random forest classifier. Then, to apply the transformation, we swap the top-K most relevant latent dimensions of the image being edited with an image exhibiting the desired attribute. Despite its simplicity, LatentSwap3D provides remarkable semantic edits in a disentangled manner and outperforms alternative approaches both qualitatively and quantitatively. We demonstrate our semantic edit approach on various 3D-aware generative models such as pi-GAN, GIRAFFE, StyleSDF, MVCGAN, EG3D and VolumeGAN, and on diverse datasets, such as FFHQ, AFHQ, Cats, MetFaces, and CompCars. The project page can be found: \url{https://enisimsar.github.io/latentswap3d/}.

We investigate the sample complexity of learning the optimal arm for multi-task bandit problems. Arms consist of two components: one that is shared across tasks (that we call representation) and one that is task-specific (that we call predictor). The objective is to learn the optimal (representation, predictor)-pair for each task, under the assumption that the optimal representation is common to all tasks. Within this framework, efficient learning algorithms should transfer knowledge across tasks. We consider the best-arm identification problem for a fixed confidence, where, in each round, the learner actively selects both a task, and an arm, and observes the corresponding reward. We derive instance-specific sample complexity lower bounds satisfied by any $(\delta_G,\delta_H)$-PAC algorithm (such an algorithm identifies the best representation with probability at least $1-\delta_G$, and the best predictor for a task with probability at least $1-\delta_H$). We devise an algorithm OSRL-SC whose sample complexity approaches the lower bound, and scales at most as $H(G\log(1/\delta_G)+ X\log(1/\delta_H))$, with $X,G,H$ being, respectively, the number of tasks, representations and predictors. By comparison, this scaling is significantly better than the classical best-arm identification algorithm that scales as $HGX\log(1/\delta)$.

In recent years, there has been a growing interest in the effects of data poisoning attacks on data-driven control methods. Poisoning attacks are well-known to the Machine Learning community, which, however, make use of assumptions, such as cross-sample independence, that in general do not hold for linear dynamical systems. Consequently, these systems require different attack and detection methods than those developed for supervised learning problems in the i.i.d.\ setting. Since most data-driven control algorithms make use of the least-squares estimator, we study how poisoning impacts the least-squares estimate through the lens of statistical testing, and question in what way data poisoning attacks can be detected. We establish under which conditions the set of models compatible with the data includes the true model of the system, and we analyze different poisoning strategies for the attacker. On the basis of the arguments hereby presented, we propose a stealthy data poisoning attack on the least-squares estimator that can escape classical statistical tests, and conclude by showing the efficiency of the proposed attack.

Current methods for image-to-image translation produce compelling results, however, the applied transformation is difficult to control, since existing mechanisms are often limited and non-intuitive. We propose ParGAN, a generalization of the cycle-consistent GAN framework to learn image transformations with simple and intuitive controls. The proposed generator takes as input both an image and a parametrization of the transformation. We train this network to preserve the content of the input image while ensuring that the result is consistent with the given parametrization. Our approach does not require paired data and can learn transformations across several tasks and datasets. We show how, with disjoint image domains with no annotated parametrization, our framework can create smooth interpolations as well as learn multiple transformations simultaneously.

Federated Learning (FL) enables the training of Deep Learning models without centrally collecting possibly sensitive raw data. This paves the way for stronger privacy guarantees when building predictive models. The most used algorithms for FL are parameter-averaging based schemes (e.g., Federated Averaging) that, however, have well known limits: (i) Clients must implement the same model architecture; (ii) Transmitting model weights and model updates implies high communication cost, which scales up with the number of model parameters; (iii) In presence of non-IID data distributions, parameter-averaging aggregation schemes perform poorly due to client model drifts. Federated adaptations of regular Knowledge Distillation (KD) can solve and/or mitigate the weaknesses of parameter-averaging FL algorithms while possibly introducing other trade-offs. In this article, we provide a review of KD-based algorithms tailored for specific FL issues.