Discrete distributions, particularly in high-dimensional deep models, are
often highly multimodal due to inherent discontinuities. While gradient-based
discrete sampling has proven effective, it is susceptible to becoming trapped
in local modes due to the gradient information. To tackle this challenge, we
propose an automatic cyclical scheduling, designed for efficient and accurate
sampling in multimodal discrete distributions. Our method contains three key
components: (1) a cyclical step size schedule where large steps discover new
modes and small steps exploit each mode; (2) a cyclical balancing schedule,
ensuring ``balanced" proposals for given step sizes and high efficiency of the
Markov chain; and (3) an automatic tuning scheme for adjusting the
hyperparameters in the cyclical schedules, allowing adaptability across diverse
datasets with minimal tuning. We prove the non-asymptotic convergence and
inference guarantee for our method in general discrete distributions. Extensive
experiments demonstrate the superiority of our method in sampling complex
multimodal discrete distributions.

多模离散分布的高效准确采样中，我们提出了一种自动循环调度方法，其中包括循环步长调度、循环平衡调度和自动调整超参数的方案，并证明了其在一般离散分布上的非渐近收敛性和推理保证。广泛实验证明了该方法在采样复杂多模离散分布方面的优势。