# Deterministic Denominator Design for Localized Tamed Stochastic Gradient Langevin Dynamics

arXiv: https://arxiv.org/abs/2606.10559 · HTML: https://mlsanity.com/paper/2606.10559/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 14 of its 29 references that are in the map.
- First posted on arXiv 9 Jun 2026.

## Builds on (most cited first, 14 of 14)

- [Stochastic Gradient Hamiltonian Monte Carlo](https://mlsanity.com/paper/1402.4102/) (2014)
- [Non-convex learning via Stochastic Gradient Langevin Dynamics: a nonasymptotic analysis](https://mlsanity.com/paper/1702.03849/) (2017)
- [Theoretical guarantees for approximate sampling from smooth and log-concave densities](https://mlsanity.com/paper/1412.7392/) (2014)
- [Non-asymptotic convergence analysis for the Unadjusted Langevin Algorithm](https://mlsanity.com/paper/1507.05021/) (2015)
- [A Complete Recipe for Stochastic Gradient MCMC](https://mlsanity.com/paper/1506.04696/) (2015)
- [Preconditioned Stochastic Gradient Langevin Dynamics for Deep Neural Networks](https://mlsanity.com/paper/1512.07666/) (2015)
- [Revisiting Gradient Clipping: Stochastic bias and tight convergence guarantees](https://mlsanity.com/paper/2305.01588/) (2023)
- [The promises and pitfalls of Stochastic Gradient Langevin Dynamics](https://mlsanity.com/paper/1811.10072/) (2018)
- [Faster Convergence of Stochastic Gradient Langevin Dynamics for Non-Log-Concave Sampling](https://mlsanity.com/paper/2010.09597/) (2020)
- [The Tamed Unadjusted Langevin Algorithm](https://mlsanity.com/paper/1710.05559/) (2017)
- [Taming neural networks with TUSLA: Non-convex learning via adaptive stochastic gradient Langevin algorithms](https://mlsanity.com/paper/2006.14514/) (2020)
- [Perturbation theory for Markov chains via Wasserstein distance](https://mlsanity.com/paper/1503.04123/) (2015)
- [Tamed Langevin sampling under weaker conditions](https://mlsanity.com/paper/2405.17693/) (2024)
- [Deterministic Envelopes for Tamed SGLD: Decoupling Stochastic Gradient Noise and Localizing Taming](https://mlsanity.com/paper/2606.05242/) (2026)

## Built on by (most cited first, 1 of 1)

- [RELTA-SGLD: Relative-Growth Localized Taming for Nonconvex Stochastic-Gradient Langevin Learning](https://mlsanity.com/paper/2607.19544/) (2026)

## Abstract (arXiv)

If the denominator in a tamed stochastic gradient Langevin update uses the current stochastic-gradient draw, the conditional mean can be biased even when the stochastic-gradient oracle is unbiased. A state-dependent denominator fixed before that draw removes this coupling. We build practical deterministic denominators from a short pilot run. A log-scale proxy is fitted to the growth score G_star(x)=|b(x)|/(1+|x|), and empirical pilot quantiles set the activation thresholds of a local proxy-quantile envelope. The reported proxy-quantile experiments use this local denominator. Separately, we describe a final denominator with a norm-polynomial tail-floor correction that can be used when one wants to certify the global effective-linearity input required by the companion deterministic-envelope Lyapunov theory. We show how proxy and threshold errors enter denominator errors and the resulting stationary observable errors. In the reported experiments, the local proxy-quantile denominator improves over random-denominator tamed SGLD at comparable production cost. It also gives observable behavior close to the G_star-envelope benchmark, without the full-gradient growth-score evaluations required by that benchmark.