# How Tempering Fixes Data Augmentation in Bayesian Neural Networks arXiv: https://arxiv.org/abs/2205.13900 ยท HTML: https://mlsanity.com/paper/2205.13900/ ## Key facts - Cited by 13 papers in the map (data through 14 Oct 2026). - Builds on 28 of its 50 references that are in the map. - First posted on arXiv 27 May 2022. ## Builds on (most cited first, 28 of 28) - [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015) - [Intriguing properties of neural networks](https://mlsanity.com/paper/1312.6199/) (2013) - [Swin Transformer V2: Scaling Up Capacity and Resolution](https://mlsanity.com/paper/2111.09883/) (2021) - [Group Equivariant Convolutional Networks](https://mlsanity.com/paper/1602.07576/) (2016) - [Scaling Vision Transformers](https://mlsanity.com/paper/2106.04560/) (2021) - [Deep Neural Networks are Easily Fooled: High Confidence Predictions for Unrecognizable Images](https://mlsanity.com/paper/1412.1897/) (2014) - [Loss Surfaces, Mode Connectivity, and Fast Ensembling of DNNs](https://mlsanity.com/paper/1802.10026/) (2018) - [CoAtNet: Marrying Convolution and Attention for All Data Sizes](https://mlsanity.com/paper/2106.04803/) (2021) - [Rotation Equivariant CNNs for Digital Pathology](https://mlsanity.com/paper/1806.03962/) (2018) - [Meta Pseudo Labels](https://mlsanity.com/paper/2003.10580/) (2020) - [Essentially No Barriers in Neural Network Energy Landscape](https://mlsanity.com/paper/1803.00885/) (2018) - [What Are Bayesian Neural Network Posteriors Really Like?](https://mlsanity.com/paper/2104.14421/) (2021) - [Probabilistic Backpropagation for Scalable Learning of Bayesian Neural Networks](https://mlsanity.com/paper/1502.05336/) (2015) - [Cyclical Stochastic Gradient MCMC for Bayesian Deep Learning](https://mlsanity.com/paper/1902.03932/) (2019) - [On Translation Invariance in CNNs: Convolutional Layers can Exploit Absolute Spatial Location](https://mlsanity.com/paper/2003.07064/) (2020) - [Preconditioned Stochastic Gradient Langevin Dynamics for Deep Neural Networks](https://mlsanity.com/paper/1512.07666/) (2015) - [Bayesian Neural Network Priors Revisited](https://mlsanity.com/paper/2102.06571/) (2021) - [A Kernel Theory of Modern Data Augmentation](https://mlsanity.com/paper/1803.06084/) (2018) - [Inconsistency of Bayesian Inference for Misspecified Linear Models, and a Proposal for Repairing It](https://mlsanity.com/paper/1412.3730/) (2014) - [The Case for Bayesian Deep Learning](https://mlsanity.com/paper/2001.10995/) (2020) - [A statistical theory of cold posteriors in deep neural networks](https://mlsanity.com/paper/2008.05912/) (2020) - [On the Generalization Effects of Linear Transformations in Data Augmentation](https://mlsanity.com/paper/2005.00695/) (2020) - [Data augmentation in Bayesian neural networks and the cold posterior effect](https://mlsanity.com/paper/2106.05586/) (2021) - [Cold Posteriors and Aleatoric Uncertainty](https://mlsanity.com/paper/2008.00029/) (2020) - [Disentangling the Roles of Curation, Data-Augmentation and the Prior in the Cold Posterior Effect](https://mlsanity.com/paper/2106.06596/) (2021) - [Generalization capabilities of translationally equivariant neural networks](https://mlsanity.com/paper/2103.14686/) (2021) - [Stride and Translation Invariance in CNNs](https://mlsanity.com/paper/2103.10097/) (2021) - [Posterior Temperature Optimization in Variational Inference for Inverse Problems](https://mlsanity.com/paper/2106.07533/) (2021) ## Built on by (most cited first, 13 of 13) - [A Primer on Bayesian Neural Networks: Review and Debates](https://mlsanity.com/paper/2309.16314/) (2023) - [Inferring the Langevin Equation with Uncertainty via Bayesian Neural Networks](https://mlsanity.com/paper/2402.01338/) (2024) - [Cold Posteriors through PAC-Bayes](https://mlsanity.com/paper/2206.11173/) (2022) - [The fine print on tempered posteriors](https://mlsanity.com/paper/2309.05292/) (2023) - [If there is no underfitting, there is no Cold Posterior Effect](https://mlsanity.com/paper/2310.01189/) (2023) - [Robust Classification by Coupling Data Mollification with Label Smoothing](https://mlsanity.com/paper/2406.01494/) (2024) - [Temperature Optimization for Bayesian Deep Learning](https://mlsanity.com/paper/2410.05757/) (2024) - [Optimizing Data Augmentation through Bayesian Model Selection](https://mlsanity.com/paper/2505.21813/) (2025) - [Tempering the Bayes Filter towards Improved Model-Based Estimation](https://mlsanity.com/paper/2512.02823/) (2025) - [Position: The Time for Sampling Is Now! Charting a New Course for Bayesian Deep Learning](https://mlsanity.com/paper/2605.21765/) (2026) - [Sparse Data Augmentation for Optimization with Provable Guarantees](https://mlsanity.com/paper/2609.08133/) (2026) - [On Uniform, Bayesian, and PAC-Bayesian Deep Ensembles](https://mlsanity.com/paper/2406.05469/) (2024) - [Gaussian Mean Field Variational Inference can Overestimate Predictive Variance](https://mlsanity.com/paper/2606.25745/) (2026) ## Abstract (arXiv) While Bayesian neural networks (BNNs) provide a sound and principled alternative to standard neural networks, an artificial sharpening of the posterior usually needs to be applied to reach comparable performance. This is in stark contrast to theory, dictating that given an adequate prior and a well-specified model, the untempered Bayesian posterior should achieve optimal performance. Despite the community's extensive efforts, the observed gains in performance still remain disputed with several plausible causes pointing at its origin. While data augmentation has been empirically recognized as one of the main drivers of this effect, a theoretical account of its role, on the other hand, is largely missing. In this work we identify two interlaced factors concurrently influencing the strength of the cold posterior effect, namely the correlated nature of augmentations and the degree of invariance of the employed model to such transformations. By theoretically analyzing simplified settings, we prove that tempering implicitly reduces the misspecification arising from modeling augmentations as i.i.d. data. The temperature mimics the role of the effective sample size, reflecting the gain in information provided by the augmentations. We corroborate our theoretical findings with extensive empirical evaluations, scaling to realistic BNNs. By relying on the framework of group convolutions, we experiment with models of varying inherent degree of invariance, confirming its hypothesized relationship with the optimal temperature.