Deterministic Denominator Design for Tamed Stochastic-Gradient Langevin Dynamics
Researchers have proposed a deterministic denominator framework for tamed stochastic-gradient Langevin dynamics (SGLD) that avoids a mean-shift bias introduced by random denominators. The method constructs a state-dependent envelope from a low-cost proxy score and empirical quantile thresholds before drawing the current gradient sample, eliminating the random-denominator mean-shift channel. The work offers a principled, practical approach to stabilizing SGLD in high-noise or heavy-tailed settings while maintaining close-to-oracle performance.
Stochastic-gradient Langevin dynamics is a widely used sampling algorithm, but large gradient drifts can destabilize it; taming methods address this by dividing updates by a denominator that scales with gradient magnitude. This preprint, submitted to arXiv on June 9, 2026, identifies a subtle problem: when the denominator is computed from the same stochastic-gradient sample as the update, it inadvertently shifts the conditional mean drift, introducing a bias. The authors propose fixing the denominator deterministically before the current oracle sample is drawn, using a proxy score built on pilot states, with activation thresholds selected via empirical quantiles and a small calibration layer. Their theoretical analysis decomposes the error into three stages—proxy and threshold errors propagating into envelope errors, envelope errors perturbing a single SGLD step, and local residuals accumulating into stationary errors via a conditional perturbation bridge. Experiments reported in the 30-page paper demonstrate that the proxy-quantile denominators closely match oracle-score behavior and outperform simpler deterministic taming choices, suggesting practical utility for machine learning and Bayesian sampling applications.
What's missing
The paper is a preprint and has not yet undergone peer review. Key open questions include how the method scales to very high-dimensional problems and sensitivity of the empirical quantile threshold selection to pilot sample size.
What different sources said
- arXiv stat.MLCenter
Deterministic Denominator Design for Localized Tamed Stochastic-Gradient Langevin Dynamics
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