用几何方法简化贝叶斯神经网络后验采样，提升效率与可扩展性。
Walking on the Fiber: A Simple Geometric Approximation for Bayesian Neural Networks
- 基于损失极小值的低维结构，设计简单几何近似采样策略。
- 在过参数化网络中实现快速后验采样，性能优于近期改进方法。
- 适合需要高效不确定性建模的深度学习应用，如医疗诊断、自动驾驶。
贝叶斯神经网络通过建模网络参数的后验分布，为不确定性量化提供了严谨框架。然而，精确的后验推断在计算上不可行，而常用的拉普拉斯近似在现代深度网络中面临可扩展性差和后验精度不足的问题。本文重新审视后验探索的采样技术，提出一种针对过参数化网络的简单变体，利用损失极小值的低维结构实现高效后验采样。在此基础上，我们引入一个模型，学习参数空间的形变，从而无需迭代即可快速采样。实验表明，该方法在后验逼近上表现优异，且相比近期精炼技术具有更好的可扩展性。这些贡献为深度学习中的贝叶斯推断提供了实用替代方案。
原文摘要 · Abstract (English)
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.
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