# Calibrated Sampling-Free Uncertainty Estimation in Bayesian Deep Learning

arXiv: https://arxiv.org/abs/2606.16214 · HTML: https://mlsanity.com/paper/2606.16214/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 34 of its 52 references that are in the map.
- First posted on arXiv 15 Jun 2026.

## Builds on (most cited first, 30 of 34)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Learning Transferable Visual Models From Natural Language Supervision](https://mlsanity.com/paper/2103.00020/) (2021)
- [An Image is Worth 16x16 Words: Transformers for Image Recognition at Scale](https://mlsanity.com/paper/2010.11929/) (2020)
- [Batch Normalization: Accelerating Deep Network Training by Reducing Internal Covariate Shift](https://mlsanity.com/paper/1502.03167/) (2015)
- [Layer Normalization](https://mlsanity.com/paper/1607.06450/) (2016)
- [On Calibration of Modern Neural Networks](https://mlsanity.com/paper/1706.04599/) (2017)
- [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)
- [Making the V in VQA Matter: Elevating the Role of Image Understanding in Visual Question Answering](https://mlsanity.com/paper/1612.00837/) (2016)
- [ViLT: Vision-and-Language Transformer Without Convolution or Region Supervision](https://mlsanity.com/paper/2102.03334/) (2021)
- [Selective Classification for Deep Neural Networks](https://mlsanity.com/paper/1705.08500/) (2017)
- [VizWiz Grand Challenge: Answering Visual Questions from Blind People](https://mlsanity.com/paper/1802.08218/) (2018)
- [A Simple Baseline for Bayesian Uncertainty in Deep Learning](https://mlsanity.com/paper/1902.02476/) (2019)
- [A Corpus for Reasoning About Natural Language Grounded in Photographs](https://mlsanity.com/paper/1811.00491/) (2018)
- [Measuring Calibration in Deep Learning](https://mlsanity.com/paper/1904.01685/) (2019)
- [Probabilistic Backpropagation for Scalable Learning of Bayesian Neural Networks](https://mlsanity.com/paper/1502.05336/) (2015)
- [Why Language Models Hallucinate](https://mlsanity.com/paper/2509.04664/) (2025)
- [Practical Deep Learning with Bayesian Principles](https://mlsanity.com/paper/1906.02506/) (2019)
- [Large Legal Fictions: Profiling Legal Hallucinations in Large Language Models](https://mlsanity.com/paper/2401.01301/) (2024)
- [AbstentionBench: Reasoning LLMs Fail on Unanswerable Questions](https://mlsanity.com/paper/2506.09038/) (2025)
- [Reliable Visual Question Answering: Abstain Rather Than Answer Incorrectly](https://mlsanity.com/paper/2204.13631/) (2022)
- [Lightweight Probabilistic Deep Networks](https://mlsanity.com/paper/1805.11327/) (2018)
- [Sampling-free Epistemic Uncertainty Estimation Using Approximated Variance Propagation](https://mlsanity.com/paper/1908.00598/) (2019)
- [Variational Learning is Effective for Large Deep Networks](https://mlsanity.com/paper/2402.17641/) (2024)
- [Filter Response Normalization Layer: Eliminating Batch Dependence in the Training of Deep Neural Networks](https://mlsanity.com/paper/1911.09737/) (2019)
- [Fast Predictive Uncertainty for Classification with Bayesian Deep Networks](https://mlsanity.com/paper/2003.01227/) (2020)
- [Overpruning in Variational Bayesian Neural Networks](https://mlsanity.com/paper/1801.06230/) (2018)
- [Semi-analytical approximations to statistical moments of sigmoid and softmax mappings of normal variables](https://mlsanity.com/paper/1703.00091/) (2017)
- [Mean-Field Approximation to Gaussian-Softmax Integral with Application to Uncertainty Estimation](https://mlsanity.com/paper/2006.07584/) (2020)
- [An Analytic Solution to Covariance Propagation in Neural Networks](https://mlsanity.com/paper/2403.16163/) (2024)

## Abstract (arXiv)

Modern deep learning models remain notoriously prone to overconfidence, limiting their reliability in high-stakes applications. Bayesian methods aim to counter this by learning a distribution over model parameters, and recent advances now make this feasible for large-scale architectures at costs comparable to AdamW. However, a challenge remains at test time: predictions must be averaged across many forward passes with weights sampled from the posterior, which is prohibitively expensive. Variance propagation offers an efficient alternative, computing layer-wise analytical approximations of uncertainty in a single forward pass. While such techniques are effective for MLPs, their extension to modern architectures remains challenging, due to increased depth and diversity of layer types. To fill this gap, we propose Calibrated Variance Propagation (CVP), which introduces a new propagation method for normalization layers, combines it with recent techniques for handling activation functions, and absorbs residual error through a light calibration step. CVP yields comparably accurate uncertainty estimates to MC sampling across transformers and CNNs, at a fraction of the cost. Against prior variance propagation work, CVP improves coverage at 0.5% risk from 8.2% to 14.6% with BEiT-3 on Visual Reasoning (NLVR2) and from 2.6% to 10.8% with ViLT on VQAv2, with gains extending to convolutional architectures.