arXiv:2508. 02158v2 Announce Type: replace-cross Abstract: Detection of planted subgraphs in Erd\"os-R\'enyi random graphs has been extensively studied, leading to a rich body of results characterizing both statistical and computational thresholds.
arXiv:2511.22435v2 Announce Type: replace Abstract: Invariant learning on graphs aims to build predictors that rely on causal substructures rather than on environment-specific shortcuts. Current meth...
arXiv:2601. 03946v3 Announce Type: replace-cross Abstract: We consider the densest submatrix problem, which seeks the submatrix of fixed size of a given binary matrix that contains the most nonzero entries.
arXiv:2606. 05266v1 Announce Type: new Abstract: We establish the first sharp thresholds for low-degree polynomial tests in planted-vs-planted settings, where the goal is to determine with vanishing error which of two structured planted mechanisms generated the observed data.
arXiv:2608. 16315v1 Announce Type: cross Abstract: Correlation clustering is a fundamental unsupervised learning problem.
arXiv:2609.26199v1 Announce Type: new Abstract: A large graph is often available only in part: a crawl stopped by its budget, a panel, a partial dump. When the sampled fraction $s$ is known by design...
The paper introduces MS‑WDRO, a multi‑source Wasserstein distributionally robust optimization framework for reconstructing complex network topologies from scarce target‑domain data and abundant heterogeneous source data. It fuses sources via a weighted Wasserstein barycenter, builds an ambiguity set around it, and solves a regularized Laplacian estimator using a provably convergent ADMM scheme. The authors provide finite‑sample guarantees, demonstrate that naive aggregation is suboptimal, and show through experiments on synthetic data and the ABIDE I neuroimaging dataset that MS‑WDRO outperforms seven baselines in graph recovery, sample efficiency, and diagnostic utility, especially when target samples are limited.
arXiv:2606. 14335v1 Announce Type: cross Abstract: Recovering structural information from noisy high-dimensional data is a fundamental task in statistical inference.
arXiv:2601. 17130v2 Announce Type: replace Abstract: Graph neural networks (GNNs) are widely used for tasks such as node classification and link prediction, but their use in sensitive settings raises concerns about training-data leakage.
arXiv:2608. 19914v1 Announce Type: new Abstract: Network topology inference from graph signals is central to graph signal processing with applications in neuroscience, sensor, and social networks.
arXiv:2503. 22998v2 Announce Type: replace-cross Abstract: Despite advancements in Graph Neural Networks (GNNs), adaptive attacks continue to challenge their robustness.
The paper tackles selecting a cost‑constrained set of experiments that most effectively tighten bounds on a partially identifiable causal query. It formalizes this as the NP‑hard max‑potency problem, introduces efficient graphical pruning rules to reduce the search space, and demonstrates the approach on synthetic graphs and real NHANES data to estimate the effect of physical activity on diabetes.
AutoGraphForge is a computational pipeline designed to automate the discovery, refutation, formalization, and proving of graph-theoretic conjectures. It generates conjectures using a Graffiti3 generator, filters out known results with a novelty filter, tests candidates against a large dataset of graphs, and refines surviving conjectures through counterexample search. The pipeline then translates each conjecture into Lean 4, verifies proofs with neural provers, and integrates the results into a formal library.