Task Arithmetic has emerged as a simple yet effective method to merge models without additional training. However, by treating entire networks as flat parameter vectors, it overlooks key structural information and is susceptible to task interference. In this paper, we study task vectors at the layer level, focusing on task layer matrices and their singular value decomposition. In particular, we concentrate on the resulting singular vectors, which we refer to as Task Singular Vectors (TSV). Recognizing that layer task matrices are often low-rank, we propose TSV-Compress (TSV-C), a simple procedure that compresses them to 10% of their original size while retaining 99% of accuracy. We further leverage this low-rank space to define a new measure of task interference based on the interaction of singular vectors from different tasks. Building on these findings, we introduce TSV-Merge (TSV-M), a novel model merging approach that combines compression with interference reduction, significantly outperforming existing methods.

The message-passing mechanism underlying Graph Neural Networks (GNNs) is not naturally suited for heterophilic datasets, where adjacent nodes often have different labels. Most solutions to this problem remain confined to the task of node classification. In this article, we focus on the valuable task of link prediction under heterophily, an interesting problem for recommendation systems, social network analysis, and other applications. GNNs like GRAFF have improved node classification under heterophily by incorporating physics biases in the architecture. Similarly, we propose GRAFF-LP, an extension of GRAFF for link prediction. We show that GRAFF-LP effectively discriminates existing from non-existing edges by learning implicitly to separate the edge gradients. Based on this information, we propose a new readout function inspired by physics. Remarkably, this new function not only enhances the performance of GRAFF-LP but also improves that of other baseline models, leading us to reconsider how every link prediction experiment has been conducted so far. Finally, we provide evidence that even simple GNNs did not experience greater difficulty in predicting heterophilic links compared to homophilic ones. This leads us to believe in the necessity for heterophily measures specifically tailored for link prediction, distinct from those used in node classification. The code and appendix are available at https://github.com/difra100/Link_Prediction_with_PIGNN_IJCNN.

Handling noisy data is a longstanding challenge in machine learning, and the complexity increases when working with graph structured data. In domains such as social networks, biological networks, and financial systems, noisy labels can significantly impact model performance, leading to unreliable predictions. Despite its importance, graph classification under label noise remains a relatively underexplored problem. In this competition, Learning with Noisy Graph Labels, we invite researchers and practitioners to develop noise robust approaches for graph classification. By fostering the development of robust models, it enhances the reliability of graph based predictions in real world scenarios where obtaining clean labels is difficult. The competition also promotes broader adoption of graph learning in industry by providing more resilient decision making tools for noisy labeled data. In addition, it contributes to benchmarking and standardization, offering a baseline data set and evaluation protocol to drive future research in noise resistant graph classification.

We introduce a novel method for training machine learning models in the presence of noisy labels, which are prevalent in domains such as medical diagnosis and autonomous driving and have the potential to degrade a model’s generalization performance. Inspired by established literature that highlights how deep learning models are prone to overfitting to noisy samples in the later epochs of training, we propose a strategic approach. This strategy leverages the distance to class centroids in the latent space and incorporates a discounting mechanism, aiming to diminish the influence of samples that lie distant from all class centroids. By doing so, we effectively counteract the adverse effects of noisy labels. The foundational premise of our approach is the assumption that samples situated further from their respective class centroid in the initial stages of training are more likely to be associated with noise. Our methodology is grounded in robust theoretical principles and has been validated empirically through extensive experiments on several benchmark datasets. Our results show that our method consistently outperforms the existing state-of-the-art techniques, achieving significant improvements in classification accuracy in the presence of noisy labels. The code for our proposed loss function and supplementary materials is available at https://github.com/wanifarooq/NCOD

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.

In practical settings, classification datasets are obtained through a labelling process that is usually done by humans. Labels can be noisy as they are obtained by aggregating the different individual labels assigned to the same sample by multiple, and possibly disagreeing, annotators. The interrater agreement on these datasets can be measured while the underlying noise distribution to which the labels are subject is assumed to be unknown. In this work, we: (i) show how to leverage the inter-annotator statistics to estimate the noise distribution to which labels are subject; (ii) introduce methods that use the estimate of the noise distribution to learn from the noisy dataset; and (iii) establish generalization bounds in the empirical risk minimization framework that depend on the estimated quantities. We conclude the paper by providing experiments that illustrate our findings.

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, 1. 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. 2. For subspace clustering with $j$-dimensional subspaces, we show a convergence rate of $\tilde{O}\left(\sqrt{{(kj^2)}/{n}}\right)$. 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 converge rate of $\Omega\left(\sqrt{{(kj)}/{n}}\right)$ is necessary, thereby proving that the bounds from [Fefferman, Mitter, and Narayanan, Journal of the Mathematical Society 2016] are essentially optimal.

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 Newronallow the network to be interpretable without affecting their expressiveness. We can understand the rules governing the task by just inspecting the models produced by our Newnon-based networks. 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.