Tamed stochastic-gradient Langevin dynamics (SGLD) stabilizes large drifts by adding a denominator to the update. If this denominator uses the same stochastic-gradient sample as the update step, it can also change the conditional mean drift. We study deterministic denominators: the state-dependent envelope is fixed before the current oracle sample is drawn. The main question is how to design this envelope in practice. The design starts from an oracle score, builds a low-cost proxy score on pilot states, chooses activation thresholds by empirical quantiles, and then applies a small calibration layer. The analysis tracks three steps: proxy and threshold errors become envelope errors; envelope errors perturb one SGLD step; and the local residuals give stationary errors through a conditional perturbation bridge. Experiments show that the proxy-quantile denominators are close to oracle-score behavior, avoid the random-denominator mean-shift channel, and improve simple deterministic taming choices.

翻译：驯服随机梯度朗之万动力学（Tamed SGLD）通过向更新中添加分母来稳定较大漂移。若该分母与更新步使用相同的随机梯度样本，则可能改变条件均值漂移。本文研究确定性分母：当前查询样本生成前，状态依赖包络线已被固定。核心问题是如何在实际中设计该包络线。设计流程始于查询分数，在初始状态上构建低成本代理分数，通过经验分位数选取激活阈值，再应用小型校准层。分析过程追踪三个步骤：代理误差与阈值误差转化为包络线误差；包络线误差扰动单步SGLD；局部残差通过条件扰动桥接产生稳态误差。实验表明，代理-分位数分母逼近查询分数行为，避免随机分母的均值漂移通道，并改进了简单确定性驯服方案。