$\nabla τ$: Gradient-based and Task-Agnostic machine Unlearning

Machine Unlearning, the process of selectively eliminating the influence of certain data examples used during a model's training, has gained significant attention as a means for practitioners to comply with recent data protection regulations. However, existing unlearning methods face critical drawbacks, including their prohibitively high cost, often associated with a large number of hyperparameters, and the limitation of forgetting only relatively small data portions. This often makes retraining the model from scratch a quicker and more effective solution. In this study, we introduce Gradient-based and Task-Agnostic machine Unlearning ($\nabla \tau$), an optimization framework designed to remove the influence of a subset of training data efficiently. It applies adaptive gradient ascent to the data to be forgotten while using standard gradient descent for the remaining data. $\nabla \tau$ offers multiple benefits over existing approaches. It enables the unlearning of large sections of the training dataset (up to 30%). It is versatile, supporting various unlearning tasks (such as subset forgetting or class removal) and applicable across different domains (images, text, etc.). Importantly, $\nabla \tau$ requires no hyperparameter adjustments, making it a more appealing option than retraining the model from scratch. We evaluate our framework's effectiveness using a set of well-established Membership Inference Attack metrics, demonstrating up to 10% enhancements in performance compared to state-of-the-art methods without compromising the original model's accuracy.

Link Prediction under Heterophily: A Physics-Inspired Graph Neural Network Approach

In the past years, Graph Neural Networks (GNNs) have become the `de facto' standard in various deep learning domains, thanks to their flexibility in modeling real-world phenomena represented as graphs. However, the message-passing mechanism of GNNs faces challenges in learnability and expressivity, hindering high performance on heterophilic graphs, where adjacent nodes frequently have different labels. Most existing solutions addressing these challenges are primarily confined to specific benchmarks focused on node classification tasks. This narrow focus restricts the potential impact that link prediction under heterophily could offer in several applications, including recommender systems. For example, in social networks, two users may be connected for some latent reason, making it challenging to predict such connections in advance. Physics-Inspired GNNs such as GRAFF provided a significant contribution to enhance node classification performance under heterophily, thanks to the adoption of physics biases in the message-passing. Drawing inspiration from these findings, we advocate that the methodology employed by GRAFF can improve link prediction performance as well. To further explore this hypothesis, we introduce GRAFF-LP, an extension of GRAFF to link prediction. We evaluate its efficacy within a recent collection of heterophilic graphs, establishing a new benchmark for link prediction under heterophily. Our approach surpasses previous methods, in most of the datasets, showcasing a strong flexibility in different contexts, and achieving relative AUROC improvements of up to 26.7%.

A topological description of loss surfaces based on Betti Numbers

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 to identify spurious minima and characterize gradient dynamics. Our work aims to contribute to this field by providing a topological measure to evaluate 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 on the complexity of their loss function 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 $\ell_2$ regularization term or implementing skip connections in a feedforward network, do not affect loss topology in specific cases.

On Generalization Bounds for Projective Clustering

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.

Hypergraph Neural Networks through the Lens of Message Passing: A Common Perspective to Homophily and Architecture Design

Most of the current hypergraph learning methodologies and benchmarking datasets in the hypergraph realm are obtained by lifting procedures from their graph analogs, simultaneously leading to overshadowing hypergraph network foundations. This paper attempts to confront some pending questions in that regard: Can the concept of homophily play a crucial role in Hypergraph Neural Networks (HGNNs), similar to its significance in graph-based research? Is there room for improving current hypergraph architectures and methodologies? (e.g. by carefully addressing the specific characteristics of higher-order networks) Do existing datasets provide a meaningful benchmark for HGNNs? Diving into the details, this paper proposes a novel conceptualization of homophily in higher-order networks based on a message passing scheme; this approach harmonizes the analytical frameworks of datasets and architectures, offering a unified perspective for exploring and interpreting complex, higher-order network structures and dynamics. Further, we propose MultiSet, a novel message passing framework that redefines HGNNs by allowing hyperedge-dependent node representations, as well as introduce a novel architecture MultiSetMixer that leverages a new hyperedge sampling strategy. Finally, we provide an extensive set of experiments that contextualize our proposals and lead to valuable insights in hypergraph representation learning.

Combining Distance to Class Centroids and Outlier Discounting for Improved Learning with Noisy Labels

In this paper, we propose a new approach for addressing the challenge of training machine learning models in the presence of noisy labels. By combining a clever usage of distance to class centroids in the items' latent space with a discounting strategy to reduce the importance of samples far away from all the class centroids (i.e., outliers), our method effectively addresses the issue of noisy labels. Our approach is based on the idea that samples farther away from their respective class centroid in the early stages of training are more likely to be noisy. We demonstrate the effectiveness of our method through extensive experiments on several popular benchmark datasets. Our results show that our approach outperforms the state-of-the-art in this area, achieving significant improvements in classification accuracy when the dataset contains noisy labels.

NEWRON: A New Generalization of the Artificial Neuron to Enhance the Interpretability of Neural Networks

In this work, we formulate NEWRON: a generalization of the McCulloch-Pitts neuron structure. This new framework aims to explore additional desirable properties of artificial neurons. We show that some specializations of NEWRON allow the network to be interpretable with no change in their expressiveness. By just inspecting the models produced by our NEWRON-based networks, we can understand the rules governing the task. Extensive experiments show that the quality of the generated models is better than traditional interpretable models and in line or better than standard neural networks.