# Walking on the Fiber: A Simple Geometric Approximation for Bayesian Neural Networks

arXiv: https://arxiv.org/abs/2512.01500 · HTML: https://mlsanity.com/paper/2512.01500/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 18 of its 35 references that are in the map.
- First posted on arXiv 1 Dec 2025.

## Builds on (most cited first, 18 of 18)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Fashion-MNIST: a Novel Image Dataset for Benchmarking Machine Learning Algorithms](https://mlsanity.com/paper/1708.07747/) (2017)
- [Simple and Scalable Predictive Uncertainty Estimation using Deep Ensembles](https://mlsanity.com/paper/1612.01474/) (2016)
- [Benchmarking Neural Network Robustness to Common Corruptions and Perturbations](https://mlsanity.com/paper/1903.12261/) (2019)
- [Loss Surfaces, Mode Connectivity, and Fast Ensembling of DNNs](https://mlsanity.com/paper/1802.10026/) (2018)
- [A Simple Baseline for Bayesian Uncertainty in Deep Learning](https://mlsanity.com/paper/1902.02476/) (2019)
- [Bayesian Deep Learning and a Probabilistic Perspective of Generalization](https://mlsanity.com/paper/2002.08791/) (2020)
- [Laplace Redux -- Effortless Bayesian Deep Learning](https://mlsanity.com/paper/2106.14806/) (2021)
- [Advances in Variational Inference](https://mlsanity.com/paper/1711.05597/) (2017)
- [Bayesian Deep Learning via Subnetwork Inference](https://mlsanity.com/paper/2010.14689/) (2020)
- [Towards Safe Autonomous Driving: Capture Uncertainty in the Deep Neural Network For Lidar 3D Vehicle Detection](https://mlsanity.com/paper/1804.05132/) (2018)
- [Loss Surface Simplexes for Mode Connecting Volumes and Fast Ensembling](https://mlsanity.com/paper/2102.13042/) (2021)
- [Large Scale Structure of Neural Network Loss Landscapes](https://mlsanity.com/paper/1906.04724/) (2019)
- [Weight-space symmetry in deep networks gives rise to permutation saddles, connected by equal-loss valleys across the loss landscape](https://mlsanity.com/paper/1907.02911/) (2019)
- [Variational Boosting: Iteratively Refining Posterior Approximations](https://mlsanity.com/paper/1611.06585/) (2016)
- [Mixtures of Laplace Approximations for Improved Post-Hoc Uncertainty in Deep Learning](https://mlsanity.com/paper/2111.03577/) (2021)
- [Riemannian Laplace approximations for Bayesian neural networks](https://mlsanity.com/paper/2306.07158/) (2023)
- [Posterior Refinement Improves Sample Efficiency in Bayesian Neural Networks](https://mlsanity.com/paper/2205.10041/) (2022)

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

- [Don't Stop Me Yet: Sampling Loss Minima via Dissipative Riemannian Mechanics](https://mlsanity.com/paper/2605.15459/) (2026)

## Abstract (arXiv)

Bayesian Neural Networks provide a principled framework for uncertainty quantification by modeling the posterior distribution of network parameters. However, exact posterior inference is computationally intractable, and widely used approximations like the Laplace method struggle with scalability and posterior accuracy in modern deep networks. In this work, we revisit sampling techniques for posterior exploration, proposing a simple variation tailored to efficiently sample from the posterior in over-parameterized networks by leveraging the low-dimensional structure of loss minima. Building on this, we introduce a model that learns a deformation of the parameter space, enabling rapid posterior sampling without requiring iterative methods. Empirical results demonstrate that our approach achieves competitive posterior approximations with improved scalability compared to recent refinement techniques. These contributions provide a practical alternative for Bayesian inference in deep learning.