The increasing penetration of distributed generation (DG) across power distribution networks (DNs) is forcing distribution system operators (DSOs) to improve the voltage regulation capabilities of the system. The increase in power flows due to the installation of renewable plants in unexpected zones of the distribution grid can affect the voltage profile, even causing interruptions at the secondary substations (SSs) with the voltage limit violation. At the same time, widespread cyberattacks across critical infrastructure raise new challenges in security and reliability for DSOs. This paper analyzes the impact of false data injection related to residential and non-residential customers on a centralized voltage regulation system, in which the DG is required to adapt the reactive power exchange with the grid according to the voltage profile. The centralized system estimates the distribution grid state according to the field data and provides the DG plants with a reactive power request to avoid voltage violations. A preliminary false data analysis in the context of the energy sector is carried out to build up a false data generator algorithm. Afterward, a configurable false data generator is developed and exploited. The false data injection is tested in the IEEE 118-bus system with an increasing DG penetration. The false data injection impact analysis highlights the need to increase the security framework of DSOs to avoid facing a relevant number of electricity interruptions.

In the context of deep learning models, attention has recently been paid to studying the surface of the loss function in order to better understand training with methods based on gradient descent. This search for an appropriate description, both analytical and topological, has led to numerous efforts in identifying spurious minima and characterize gradient dynamics. Our work aims to contribute to this field by providing a topological measure for evaluating loss complexity in the case of multilayer neural networks. We compare deep and shallow architectures with common sigmoidal activation functions by deriving upper and lower bounds for the complexity of their respective loss functions and revealing how that complexity is influenced by the number of hidden units, training models, and the activation function used. Additionally, we found that certain variations in the loss function or model architecture, such as adding an ℓ₂ regularization term or implementing skip connections in a feedforward network, do not affect loss topology in specific cases.

Given a set of points, clustering consists of finding a partition of a point set into $k$ clusters such that the center to which a point is assigned is as close as possible. Most commonly, centers are points themselves, which leads to the famous $k$-median and $k$-means objectives. One may also choose centers to be $j$ dimensional subspaces, which gives rise to subspace clustering. In this paper, we consider learning bounds for these problems. That is, given a set of $n$ samples $P$ drawn independently from some unknown, but fixed distribution $\mathcal{D}$, how quickly does a solution computed on $P$ converge to the optimal clustering of $\mathcal{D}$? We give several near optimal results. In particular, For center-based objectives, we show a convergence rate of $\tilde{O}\left(\sqrt{{k}/{n}}\right)$. This matches the known optimal bounds of [Fefferman, Mitter, and Narayanan, Journal of the Mathematical Society 2016] and [Bartlett, Linder, and Lugosi, IEEE Trans. Inf. Theory 1998] for $k$-means and extends it to other important objectives such as $k$-median. For subspace clustering with $j$-dimensional subspaces, we show a convergence rate of $\tilde{O}\left(\sqrt{\frac{kj^2}{n}}\right)$. These are the first provable bounds for most of these problems. For the specific case of projective clustering, which generalizes $k$-means, we show a convergence rate of $\Omega\left(\sqrt{\frac{kj}{n}}\right)$ is necessary, thereby proving that the bounds from [Fefferman, Mitter, and Narayanan, Journal of the Mathematical Society 2016] are essentially optimal.

Corrupted training data are ubiquitous. Corrective Machine Unlearning (CMU) seeks to remove the influence of such corruption post-training. Prior CMU typically assumes access to identified corrupted training samples (a "forget set"). However, in many real-world scenarios the training data are no longer accessible. We formalize source-free CMU, where the original training data are unavailable and, consequently, no forget set of identified corrupted training samples can be specified. Instead, we assume a small proxy (surrogate) set of corrupted samples that reflect the suspected corruption type without needing to be the original training samples. In this stricter setting, methods relying on forget set are ineffective or narrow in scope. We introduce Corrective Unlearning in Task Space (CUTS), a lightweight weight space correction method guided by the proxy set using task arithmetic principles. CUTS treats the clean and the corruption signal as distinct tasks. Specifically, we briefly fine-tune the corrupted model on the proxy to amplify the corruption mechanism in the weight space, compute the difference between the corrupted and fine-tuned weights as a proxy task vector, and subtract a calibrated multiple of this vector to cancel the corruption. Without access to clean data or a forget set, CUTS recovers a large fraction of the lost utility under label noise and, for backdoor triggers, nearly eliminates the attack with minimal damage to utility, outperforming state-of-the-art specialized CMU methods in source-free setting.

In practical settings, classification datasets are often labeled by humans, leading to potential noise due to varying annotations from different individuals. The exact noise distribution impacting these labels is typically unknown; however, one quantity we can measure and attempt to exploit is inter-rater agreement. Building on this, our work makes key contributions: we (i) demonstrate how inter-annotator statistics can be used to estimate the label noise distribution; (ii) propose methods that leverage these estimates to train models on noisy data; and (iii) derive generalization bounds within the empirical risk minimization framework that depend on the estimated noise characteristics. Finally, we present experiments that support our findings. Our code can be found at https://github.com/amazon-science/learning under noisy labels.