History-dependent sampling can reduce long-run Monte Carlo variance by discouraging redundant revisits, but existing schemes typically encode history through empirical measure on finite state spaces, which is infeasible in high-dimensional discrete configuration spaces or ill-posed in continuous domains. We propose Score-Repellent Monte Carlo (SRMC) framework that summarizes trajectory history by a running average of score evaluations in $\mathbb{R}^d$, where $d$ is the dimension of the score and state representation. This history is converted into a surrogate target through an exponential score tilt, indexed with $α$ that represents the strength of repellence in controlling the magnitude of the history-based repulsion. The surrogate family is normalization-free in the standard MCMC sense, yielding a generic wrapper: at each iteration, any base kernel targeting $π$ can instead be run on the current surrogate $π_{θ_n}$ while the history is updated online. We analyze the coupled evolution of the history recursion and Monte Carlo estimators using stochastic approximation with controlled Markovian noise, establishing almost sure convergence and a joint central limit theorem. We further identify regimes in which the asymptotic covariance decreases as $α$ increases, with scaling $O(1/α)$, extending the near-zero-variance effect of finite-state history-dependent samplers to general state spaces with constant memory. Experiments on continuous targets and discrete energy-based models demonstrate improved estimator variance and mode coverage, while retaining $O(d)$ memory usage and modest per-iteration overhead.

翻译：[translated abstract in Chinese] 依赖历史的采样可以通过抑制冗余重访来降低长期蒙特卡洛方差，但现有方案通常通过有限状态空间上的经验测度编码历史，这在高维离散配置空间中不可行，在连续域中则可能不适定。我们提出分数排斥蒙特卡洛（SRMC）框架，通过 $\mathbb{R}^d$ 中分数评估的运行平均值来概括轨迹历史，其中 $d$ 是分数与状态表示的维度。该历史通过指数分数倾斜转换为替代目标，并用参数 $α$ 索引以表征排斥强度，从而控制基于历史的排斥幅度。在标准MCMC意义上，该替代函数族无需归一化，从而构成通用封装器：在每次迭代中，任何以 $π$ 为目标的基核可转而运行在当前替代函数 $π_{θ_n}$ 上，同时在线更新历史。我们利用带受控马尔可夫噪声的随机逼近方法，分析历史递归与蒙特卡洛估计器的耦合演化，建立了几乎必然收敛性与联合中心极限定理。我们进一步识别出渐近协方差随 $α$ 增大而按 $O(1/α)$ 标度减小的参数区域，将有限状态依赖历史采样器的近零方差效应推广至具有恒定内存的一般状态空间。在连续目标函数与离散能量模型上的实验表明，该方法在保持 $O(d)$ 内存使用与适度每迭代开销的同时，改善了估计器方差与模式覆盖。