Gang Xu

Fengpei Li, Haoxian Chen, Jiahe Lin et al.

For many complex simulation tasks spanning areas such as healthcare, engineering, and finance, Monte Carlo (MC) methods are invaluable due to their unbiased estimates and precise error quantification. Nevertheless, Monte Carlo simulations often become computationally prohibitive, especially for nested, multi-level, or path-dependent evaluations lacking effective variance reduction techniques. While machine learning (ML) surrogates appear as natural alternatives, naive replacements typically introduce unquantifiable biases. We address this challenge by introducing Prediction-Enhanced Monte Carlo (PEMC), a framework that leverages modern ML models as learned predictors, using cheap and parallelizable simulation as features, to output unbiased evaluation with reduced variance and runtime. PEMC can also be viewed as a "modernized" view of control variates, where we consider the overall computation-cost-aware variance reduction instead of per-replication reduction, while bypassing the closed-form mean function requirement and maintaining the advantageous unbiasedness and uncertainty quantifiability of Monte Carlo. We illustrate PEMC's broader efficacy and versatility through three examples: first, equity derivatives such as variance swaps under stochastic local volatility models; second, interest rate derivatives such as swaption pricing under the Heath-Jarrow-Morton (HJM) interest-rate model. Finally, we showcase PEMC in a socially significant context - ambulance dispatch and hospital load balancing - where accurate mortality rate estimates are key for ethically sensitive decision-making. Across these diverse scenarios, PEMC consistently reduces variance while preserving unbiasedness, highlighting its potential as a powerful enhancement to standard Monte Carlo baselines.

Ziyi Wang, Songbai Tan, Gang Xu et al.

With the success of autoregressive learning in large language models, it has become a dominant approach for text-to-image generation, offering high efficiency and visual quality. However, invisible watermarking for visual autoregressive (VAR) models remains underexplored, despite its importance in misuse prevention. Existing watermarking methods, designed for diffusion models, often struggle to adapt to the sequential nature of VAR models. To bridge this gap, we propose Safe-VAR, the first watermarking framework specifically designed for autoregressive text-to-image generation. Our study reveals that the timing of watermark injection significantly impacts generation quality, and watermarks of different complexities exhibit varying optimal injection times. Motivated by this observation, we propose an Adaptive Scale Interaction Module, which dynamically determines the optimal watermark embedding strategy based on the watermark information and the visual characteristics of the generated image. This ensures watermark robustness while minimizing its impact on image quality. Furthermore, we introduce a Cross-Scale Fusion mechanism, which integrates mixture of both heads and experts to effectively fuse multi-resolution features and handle complex interactions between image content and watermark patterns. Experimental results demonstrate that Safe-VAR achieves state-of-the-art performance, significantly surpassing existing counterparts regarding image quality, watermarking fidelity, and robustness against perturbations. Moreover, our method exhibits strong generalization to an out-of-domain watermark dataset QR Codes.