提出HiSS采样器，解决离散多模态分布采样难问题
Slithering Through Gaps: Capturing Discrete Isolated Modes via Logistic Bridging
- 用逻辑斯蒂卷积核连接离散与连续变量，实现跨模态跳跃
- 在伊辛模型等任务中，采样混合效率显著优于主流方法
- 适合高维离散多模态场景，如神经网络权重采样
高维复杂离散分布常因固有间断性呈现多模态特性，导致采样困难。基于梯度的离散采样器在崎岖或不连通的能量景观中易陷入局部模式，难以实现充分混合与收敛。为此，我们提出超双曲正割吉布斯采样（HiSS），一种新型采样算法，结合梅特罗波利斯-吉布斯框架提升混合效率。HiSS利用逻辑斯蒂卷积核将离散采样变量与连续辅助变量在联合分布中耦合，使辅助变量能捕获真实目标分布，并促进远距离、不连通模态间的便捷转移。我们提供了收敛性理论保证，并通过实验验证，HiSS在伊辛模型、二值神经网络及组合优化等多种任务上均优于众多主流方法。
原文摘要 · Abstract (English)
High-dimensional and complex discrete distributions often exhibit multimodal behavior due to inherent discontinuities, posing significant challenges for sampling. Gradient-based discrete samplers, while effective, frequently become trapped in local modes when confronted with rugged or disconnected energy landscapes. This limits their ability to achieve adequate mixing and convergence in high-dimensional multimodal discrete spaces. To address these challenges, we propose \emph{Hyperbolic Secant-squared Gibbs-Sampling (HiSS)}, a novel family of sampling algorithms that integrates a \emph{Metropolis-within-Gibbs} framework to enhance mixing efficiency. HiSS leverages a logistic convolution kernel to couple the discrete sampling variable with the continuous auxiliary variable in a joint distribution. This design allows the auxiliary variable to encapsulate the true target distribution while facilitating easy transitions between distant and disconnected modes. We provide theoretical guarantees of convergence and demonstrate empirically that HiSS outperforms many popular alternatives on a wide variety of tasks, including Ising models, binary neural networks, and combinatorial optimization.
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