# Guiding Posterior Exploration with Optimizer-Derived Geometry

arXiv: https://arxiv.org/abs/2607.25312 · HTML: https://mlsanity.com/paper/2607.25312/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 14 of its 17 references that are in the map.
- First posted on arXiv 28 Jul 2026.

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

- [Simple and Scalable Predictive Uncertainty Estimation using Deep Ensembles](https://mlsanity.com/paper/1612.01474/) (2016)
- [Stochastic Gradient Hamiltonian Monte Carlo](https://mlsanity.com/paper/1402.4102/) (2014)
- [What Are Bayesian Neural Network Posteriors Really Like?](https://mlsanity.com/paper/2104.14421/) (2021)
- [Sophia: A Scalable Stochastic Second-order Optimizer for Language Model Pre-training](https://mlsanity.com/paper/2305.14342/) (2023)
- [Cyclical Stochastic Gradient MCMC for Bayesian Deep Learning](https://mlsanity.com/paper/1902.03932/) (2019)
- [ADAHESSIAN: An Adaptive Second Order Optimizer for Machine Learning](https://mlsanity.com/paper/2006.00719/) (2020)
- [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)
- [Filter Response Normalization Layer: Eliminating Batch Dependence in the Training of Deep Neural Networks](https://mlsanity.com/paper/1911.09737/) (2019)
- [BlackJAX: Composable Bayesian inference in JAX](https://mlsanity.com/paper/2402.10797/) (2024)
- [Fishers for Free? Approximating the Fisher Information Matrix by Recycling the Squared Gradient Accumulator](https://mlsanity.com/paper/2507.18807/) (2025)
- [Scalable Bayesian Learning with posteriors](https://mlsanity.com/paper/2406.00104/) (2024)
- [Can Microcanonical Langevin Dynamics Leverage Mini-Batch Gradient Noise?](https://mlsanity.com/paper/2602.06500/) (2026)
- [Approximate blocked Gibbs sampling for Bayesian neural networks](https://mlsanity.com/paper/2208.11389/) (2022)

## Abstract (arXiv)

Sampling-based methods offer a principled approach to uncertainty quantification in Bayesian neural networks. Their practical use, however, is often challenged by the computational cost of exploring high-dimensional and multimodal posterior distributions. To overcome these difficulties, Bayesian Deep Ensembles, i.e., warmstarting the sampling from several optimized solutions, have proven to be an effective strategy. In this paper, we demonstrate that curvature estimates computed during the warmstart as a byproduct in adaptive optimizers such as AdamW can inform the sampling phase at negligible additional cost. Specifically, our proposed preconditioned sampling strategy based on optimizer-derived geometries can substantially reduce or even eliminate the need for a lengthy sampling burn-in phase and leads to greater numerical stability. This approach consistently maintains or improves predictive performance and uncertainty quantification without any additional computational costs. We confirm the consistency of our findings across various datasets and network architectures.