# Variation Due to Regularization Tractably Recovers Bayesian Deep Learning

arXiv: https://arxiv.org/abs/2403.10671 · HTML: https://mlsanity.com/paper/2403.10671/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 19 of its 40 references that are in the map.
- First posted on arXiv 15 Mar 2024.

## Builds on (most cited first, 19 of 19)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Dropout as a Bayesian Approximation: Representing Model Uncertainty in Deep Learning](https://mlsanity.com/paper/1506.02142/) (2015)
- [Simple and Scalable Predictive Uncertainty Estimation using Deep Ensembles](https://mlsanity.com/paper/1612.01474/) (2016)
- [Pointer Sentinel Mixture Models](https://mlsanity.com/paper/1609.07843/) (2016)
- [The Pile: An 800GB Dataset of Diverse Text for Language Modeling](https://mlsanity.com/paper/2101.00027/) (2020)
- [What Uncertainties Do We Need in Bayesian Deep Learning for Computer Vision?](https://mlsanity.com/paper/1703.04977/) (2017)
- [Optimizing Neural Networks with Kronecker-factored Approximate Curvature](https://mlsanity.com/paper/1503.05671/) (2015)
- [A Simple Baseline for Bayesian Uncertainty in Deep Learning](https://mlsanity.com/paper/1902.02476/) (2019)
- [Weight Uncertainty in Neural Networks](https://mlsanity.com/paper/1505.05424/) (2015)
- [Laplace Redux -- Effortless Bayesian Deep Learning](https://mlsanity.com/paper/2106.14806/) (2021)
- [Visual Transformers: Token-based Image Representation and Processing for Computer Vision](https://mlsanity.com/paper/2006.03677/) (2020)
- [Optimizing Millions of Hyperparameters by Implicit Differentiation](https://mlsanity.com/paper/1911.02590/) (2019)
- [Approximate Inference Turns Deep Networks into Gaussian Processes](https://mlsanity.com/paper/1906.01930/) (2019)
- ['In-Between' Uncertainty in Bayesian Neural Networks](https://mlsanity.com/paper/1906.11537/) (2019)
- [The Case for Bayesian Deep Learning](https://mlsanity.com/paper/2001.10995/) (2020)
- [Variational Learning is Effective for Large Deep Networks](https://mlsanity.com/paper/2402.17641/) (2024)
- [Position: Bayesian Deep Learning is Needed in the Age of Large-Scale AI](https://mlsanity.com/paper/2402.00809/) (2024)
- [A Variational Analysis of Stochastic Gradient Algorithms](https://mlsanity.com/paper/1602.02666/) (2016)
- [Bootstrapped Thompson Sampling and Deep Exploration](https://mlsanity.com/paper/1507.00300/) (2015)

## Abstract (arXiv)

Uncertainty quantification in deep learning is crucial for safe and reliable decision-making in downstream tasks. Existing methods quantify uncertainty at the last layer or other approximations of the network which may miss some sources of uncertainty in the model. To address this gap, we propose an uncertainty quantification method for large networks based on variation due to regularization. Essentially, predictions that are more (less) sensitive to the regularization of network parameters are less (more, respectively) certain. This principle can be implemented by deterministically tweaking the training loss during the fine-tuning phase and reflects confidence in the output as a function of all layers of the network. We show that regularization variation (RegVar) provides rigorous uncertainty estimates that, in the infinitesimal limit, exactly recover the Laplace approximation in Bayesian deep learning. We demonstrate its success in several deep learning architectures, showing it can scale tractably with the network size while maintaining or improving uncertainty quantification quality. Our experiments across multiple datasets show that RegVar not only identifies uncertain predictions effectively but also provides insights into the stability of learned representations.