We study the problem of sampling from a distribution under local differential privacy (LDP). Given a private distribution P P, the goal is to generate a single sample from a distribution that remains close to P in f-divergence while satisfying the constraints of LDP.

A full understanding of the behavior of a large language model (LLM) requires our grasp of its input token space. If this space differs from our assumptions, our comprehension of and conclusions about the LLM will likely be flawed.

Graph Neural Networks (GNNs) are widely used to compute representations of node pairs for downstream tasks such as link prediction. Yet, theoretical understanding of their expressive power has focused almost entirely on graph-level representations. In this work, we shift the focus to links and provide the first comprehensive study of GNN expressiveness in link representation. We introduce a unifying framework, the kϕ-kρ-mframework, that subsumes existing messagepassing link models and enables formal expressiveness comparisons. Using this framework, we derive a hierarchy of state-of-the-art methods and offer theoretical tools to analyze future architectures. To complement our analysis, we propose a synthetic evaluation protocol comprising the first benchmark specifically designed to assess link-level expressiveness. Finally, we ask: does expressiveness matter in practice? We use a graph symmetry metric that quantifies the difficulty of distinguishing links and show that while expressive models may underperform on standard benchmarks, they significantly outperform simpler ones as symmetry increases, highlighting the need for dataset-aware model selection.

Membership inference tests aim to determine whether a particular data point was included in a language model's training set. However, recent works have shown that such tests often fail under the strict definition of membership based on exact matching, and have suggested relaxing this definition to include semantic neighbors as members as well. In this work, we show that membership inference tests are still unreliable under this relaxation -- it is possible to poison the training dataset in a way that causes the test to produce incorrect predictions for a target point. We theoretically reveal a trade-off between a test's accuracy and its robustness to poisoning. We also present a concrete instantiation of this poisoning attack and empirically validate its effectiveness. Our results show that it can degrade the performance of existing tests to well below random.

The rise of smart manufacturing under Industry 4.0 introduces mass customization and dynamic production, demanding more advanced and flexible scheduling techniques. The flexible job-shop scheduling problem (FJSP) has attracted significant attention due to its complex constraints and strong alignment with real-world production scenarios. Current deep reinforcement learning (DRL)-based approaches to FJSP predominantly employ constructive methods. While effective, they often fall short of reaching (near-)optimal solutions. In contrast, improvement-based methods iteratively explore the neighborhood of initial solutions and are more effective in approaching optimality.

We study the fundamental problem of estimating an unknown discrete distribution p over d symbols, given n i.i.d.

The VC-dimension is a well-studied and fundamental complexity measure of a set system (or hypergraph) that is central to many areas of machine learning. We establish several new results on the complexity of computing the VC-dimension. In particular, given a hypergraph H = (V,E), we prove that the naive 2O(|V|)-time algorithm is asymptotically tight under the Exponential Time Hypothesis (ETH). We then prove that the problem admits a 1-additive fixed-parameter approximation algorithm when parameterized by the maximum degree of Hand a fixed-parameter algorithm when parameterized by its dimension, and that these are essentially the only such exploitable structural parameters.

Graph anomaly detection (GAD) is widely prevalent in scenarios such as financial fraud detection, anti-money laundering and social bot detecion. However, structural distribution shifts are commonly observed in real-world GAD data due to selection bias, resulting in reduced homophily. Existing GAD methods tend to rely on homophilic shortcuts when trained on high-homophily structures, limiting their ability to generalize well to data with low homophily under structural distribution shifts. In this study, we propose to handle structural distribution shifts by generating novel environments characterized by diverse homophilic structures and utilizing invariant patterns, i.e., features and structures with the capability of stable prediction across structural distribution shifts, which face two challenges: (1) How to discover invariant patterns from entangled features and structures, as structures are sensitive to varying homophilic distributions.

Graph Neural Networks (GNNs) excel in graph mining tasks thanks to their message-passing mechanism, which aligns with the homophily assumption. However, connected nodes can also exhibit inconsistent behaviors, termed heterophilic patterns, sparking interest in heterophilic GNNs (HTGNNs). Although the messagepassing mechanism seems unsuitable for heterophilic graphs owing to the propagation of dissimilar messages, it is still popular in HTGNNs and consistently achieves notable success. Some efforts have investigated such an interesting phenomenon, but are limited in the data perspective. The model-perspective understanding remains largely unexplored, which is conducive to guiding the designs of HTGNNs.

Graph Neural Networks (GNNs) have achieved great success but are often considered to be challenged by varying levels of homophily in graphs. Recent empirical studies have surprisingly shown that homophilic GNNs can perform well across datasets of different homophily levels with proper hyperparameter tuning, but the underlying theory and effective architectures remain unclear. To advance GNN universality across varying homophily, we theoretically revisit GNN message passing and uncover a novel smoothness-generalization dilemma, where increasing hops inevitably enhances smoothness at the cost of generalization. This dilemma hinders learning in high-order homophilic neighborhoods and all heterophilic ones, where generalization is critical due to complex neighborhood class distributions that are sensitive to shifts induced by noise or sparsity. To address this, we introduce the Inceptive Graph Neural Network (IGNN) built on three simple yet effective design principles, which alleviate the dilemma by enabling distinct hop-wise generalization alongside improved overall generalization with adaptive smoothness. Benchmarking against 30 baselines demonstrates IGNN's superiority and reveals notable universality in certain homophilic GNN variants. Our code and datasets are available at https://github.com/galogm/IGNN.