# Condensed Stein Variational Gradient Descent for Uncertainty Quantification of Neural Networks

arXiv: https://arxiv.org/abs/2412.16462 · HTML: https://mlsanity.com/paper/2412.16462/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 2 of its 36 references that are in the map.
- First posted on arXiv 21 Dec 2024.

## Builds on (most cited first, 2 of 2)

- [Learning Sparse Neural Networks through L0 Regularization](https://mlsanity.com/paper/1712.01312/) (2017)
- [A stochastic Stein Variational Newton method](https://mlsanity.com/paper/2204.09039/) (2022)

## Built on by (most cited first, 3 of 3)

- [Physics Augmented Machine Learning Discovery of Composition-Dependent Constitutive Laws for 3D Printed Digital Materials](https://mlsanity.com/paper/2507.02991/) (2025)
- [Uncertainty quantification of neural network models of evolving processes via Langevin sampling](https://mlsanity.com/paper/2504.14854/) (2025)
- [Interval and fuzzy physics-augmented neural networks (iPANN and fPANN) for uncertainty quantification and propagation in constitutive modeling](https://mlsanity.com/paper/2607.20339/) (2026)

## Abstract (arXiv)

We propose a Stein variational gradient descent method to concurrently sparsify, train, and provide uncertainty quantification of a complexly parameterized model such as a neural network. It employs a graph reconciliation and condensation process to reduce complexity and increase similarity in the Stein ensemble of parameterizations. Therefore, the proposed condensed Stein variational gradient (cSVGD) method provides uncertainty quantification on parameters, not just outputs. Furthermore, the parameter reduction speeds up the convergence of the Stein gradient descent as it reduces the combinatorial complexity by aligning and differentiating the sensitivity to parameters. These properties are demonstrated with an illustrative example and an application to a representation problem in solid mechanics.