To address this issue, we propose using probabilistic reparameterization ( PR).

Graph Neural Networks (GNNs) have been widely used for graph analysis. Federated Graph Learning (FGL) is an emerging learning framework to collaboratively train graph data from various clients. Although FGL allows client data to remain localized, a malicious server can still steal client private data information through uploaded gradient. In this paper, we for the first time propose label distribution attacks (LDAs) on FGL that aim to infer the label distributions of the client-side data. Firstly, we observe that the effectiveness of LDA is closely related to the variance of node embeddings in GNNs. Next, we analyze the relation between them and propose a new attack named EC-LDA, which significantly improves the attack effectiveness by compressing node embeddings. Then, extensive experiments on node classification and link prediction tasks across six widely used graph datasets show that EC-LDA outperforms the SOTA LDAs. Specifically, EC-LDA can achieve the Cos-sim as high as 1.0 under almost all cases. Finally, we explore the robustness of EC-LDA under differential privacy protection and discuss the potential effective defense methods to EC-LDA. Our code is available at https://github.com/cheng-t/EC-LDA.

This paper investigates theoretical and methodological foundations for stochastic optimal control (SOC) in discrete time. We start formulating the control problem in a general dynamic programming framework, introducing the mathematical structure needed for a detailed convergence analysis. The associate value function is estimated through a sequence of approximations combining nonparametric regression methods and Monte Carlo subsampling. The regression step is performed within reproducing kernel Hilbert spaces (RKHSs), exploiting the classical KRR algorithm, while Monte Carlo sampling methods are introduced to estimate the continuation value. To assess the accuracy of our value function estimator, we propose a natural error decomposition and rigorously control the resulting error terms at each time step. We then analyze how this error propagates backward in time-from maturity to the initial stage-a relatively underexplored aspect of the SOC literature. Finally, we illustrate how our analysis naturally applies to a key financial application: the pricing of American options.

Discrete diffusion models (DDMs) have shown powerful generation ability for discrete data modalities like text and molecules. However, their practical application is hindered by inefficient sampling, requiring a large number of sampling steps. Accelerating DDMs by using larger step sizes typically introduces significant problems in generation quality, as it amplifies the impact of both the compounding decoding error due to factorized predictions and discretization error from numerical approximations, leading to a significant decrease in sampling quality. To address these challenges, we propose learnable sampler distillation (LSD), a novel approach to train fast and high-fidelity samplers for DDMs. LSD employs a distillation approach where a student sampler with a few steps learns to align its intermediate score trajectory with that of a high-quality teacher sampler with numerous steps. This alignment is achieved by optimizing learnable sampler coefficients that adaptively adjust sampling dynamics. Additionally, we further propose LSD+, which also learns time schedules that allocate steps non-uniformly. Experiments across text generation, image generation, and synthetic tasks demonstrate that our proposed approaches outperform existing samplers for DDMs, achieving substantially higher sampling quality with significantly fewer sampling steps. Our code is available at \href{https://github.com/feiyangfu/LSD}{https://github.com/feiyangfu/LSD}.