arXiv:2603. 10277v5 Announce Type: replace Abstract: In this paper, we propose a fast method for estimating the condition number of sparse matrices using graph neural networks (GNNs).
arXiv:2603. 10277v3 Announce Type: replace Abstract: In this paper, we propose a fast method for estimating the condition number of sparse matrices using graph neural networks (GNNs).
arXiv:2403. 10232v2 Announce Type: replace-cross Abstract: Conventional matrix completion methods approximate the missing values by assuming the matrix to be low-rank, which leads to a linear approximation of missing values.
arXiv:2601. 23207v2 Announce Type: replace-cross Abstract: Understanding what graph neural networks can learn, especially their ability to learn to execute algorithms, remains a central theoretical challenge.
arXiv:2607. 11938v1 Announce Type: cross Abstract: This book is about the mathematical foundations of data science.
arXiv:2602. 08785v2 Announce Type: replace Abstract: Generalization and approximation capabilities of message passing graph neural networks (MPNNs) are often studied by defining a compact metric on a space of input graphs under which MPNNs are equicontinuous.
arXiv:2603. 06952v2 Announce Type: replace Abstract: As graphs scale to billions of nodes and edges, graph Machine Learning workloads are constrained by the cost of multi-hop traversals over exponentially growing neighborhoods.
arXiv:2510. 10101v4 Announce Type: replace Abstract: Understanding the interplay between generalization, expressivity, and the geometry of the input space is a central challenge in graph learning.
arXiv:2607. 28456v1 Announce Type: cross Abstract: Solving large, sparse linear systems is a core task in scientific computing, and efficient iterative solvers rely critically on effective and robust preconditioning.
arXiv:2605. 09382v2 Announce Type: replace Abstract: The Linear Assignment Problem is a fundamental combinatorial optimization task where classical exact solvers ensure optimality but suffer from an $\mathcal{O}(N^{3})$ bottleneck, while recent neural approximations struggle with scalability and exactness.
arXiv:2410. 01669v3 Announce Type: replace Abstract: Covariance Neural Networks (VNNs) perform graph convolutions on the covariance matrix of input data to leverage correlation information as pairwise connections.
arXiv:2606. 26705v1 Announce Type: cross Abstract: Feedforward neural network (NN) expressivity is typically studied by emulating optimal basis-expansion schemes.
arXiv:2606. 02223v1 Announce Type: new Abstract: Estimating the generative mechanism of large-scale networks is a fundamental challenge in statistical machine learning.