Score-Repellent Monte Carlo: Toward Efficient Non-Markovian Sampler with Constant Memory in General State Spaces
arXiv:2604.22948v2 Announce Type: replace Abstract: 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 $\alpha$ 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 $\pi$ can instead be run on the current surrogate $\pi_{\theta_n}$ wh

