Robust Stochastic Gradient Posterior Sampling with Lattice Based Discretisation

2026-02-19 · Source: stat.ML updates on arXiv.org · Field: Technology & Digital — Artificial Intelligence & Machine Learning, Data Science & Analytics · Depth: Expert, extended

Summary

Stochastic Gradient Lattice Random Walk (SGLRW) is a novel Bayesian posterior sampling method designed to enhance the robustness of stochastic-gradient Markov chain Monte Carlo (SG-MCMC) techniques, particularly against minibatch size and gradient noise sensitivity. Unlike traditional Stochastic Gradient Langevin Dynamics (SGLD), SGLRW introduces stochastic noise exclusively through the off-diagonal elements of its update covariance, which significantly improves stability, especially with small minibatches or heavy-tailed gradient noise. The method replaces Gaussian increments with bounded binary or ternary updates on a lattice, maintaining asymptotic correctness while preventing large parameter jumps. Experimental validation across Bayesian regression, classification, and sentiment classification using LLM features demonstrates SGLRW's superior stability and predictive performance compared to SGLD and a Clipped-SGLD baseline, often achieving comparable accuracy with half the minibatch size and better calibration at larger learning rates.

Key takeaway

For research scientists developing scalable Bayesian inference methods, SGLRW offers a robust alternative to SGLD, particularly when dealing with small minibatch sizes or heavy-tailed gradient noise. You should consider integrating SGLRW into your workflow to achieve greater stability and potentially better predictive performance, especially in resource-constrained environments or when working with large models where minibatch size is a critical factor. Its compatibility with low-precision hardware also presents opportunities for more energy-efficient implementations.

Key insights

SGLRW improves SG-MCMC robustness by localizing stochastic noise to off-diagonal covariance elements via lattice-based updates.

Principles

• Bounded updates enhance stability against gradient noise.
• Off-diagonal noise confinement improves minibatch robustness.
• Lattice discretisation can enable low-precision hardware compatibility.

Method

SGLRW updates parameters using coordinate-wise bounded binary steps, where each direction's probability is state-dependent and derived from the stochastic gradient. This contrasts with SGLD's Gaussian increments, making SGLRW more stable under small minibatches and heavy-tailed noise.

In practice

• Use SGLRW for stable Bayesian sampling with small minibatches.
• Consider SGLRW for models with heavy-tailed gradient noise.
• Explore SGLRW for energy-efficient stochastic hardware implementations.

Topics

• Stochastic Gradient MCMC
• Lattice Random Walk
• Bayesian Posterior Sampling
• Gradient Noise Robustness
• Langevin Dynamics

Best for: Research Scientist, AI Researcher, AI Scientist, Machine Learning Engineer

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Editorial summary, takeaway, and curation by AIssential. Original article published by stat.ML updates on arXiv.org.