Adam retains a moving average of past squared gradients in its denominator, but the optimization cost of this memory is not well understood. We show that second-moment memory can itself suppress progress toward the optimum even under finite-variance stochastic gradients. For a simple two-point oracle, the expected positive normalized update is $O(M_2^{-1/2})$ after an initialization transient, where $M_2=(1-β_2)^{-1}$ is the second-moment memory length. We convert this directional bound, under the stated memory and stepsize scaling, into an average-stationarity lower bound of the same order on a smooth convex problem with normalized gap, smoothness, and variance. Long second-moment memory can slow optimization even when the gradient noise has finite variance.
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.