# Dropout Injection at Test Time for Post Hoc Uncertainty Quantification in Neural Networks

arXiv: https://arxiv.org/abs/2302.02924 · HTML: https://mlsanity.com/paper/2302.02924/

## Key facts

- Cited by 14 papers in the map (data through 14 Oct 2026).
- Builds on 16 of its 31 references that are in the map.
- First posted on arXiv 6 Feb 2023.

## Builds on (most cited first, 16 of 16)

- [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)
- [What Uncertainties Do We Need in Bayesian Deep Learning for Computer Vision?](https://mlsanity.com/paper/1703.04977/) (2017)
- [Aleatoric and Epistemic Uncertainty in Machine Learning: An Introduction to Concepts and Methods](https://mlsanity.com/paper/1910.09457/) (2019)
- [A Review of Uncertainty Quantification in Deep Learning: Techniques, Applications and Challenges](https://mlsanity.com/paper/2011.06225/) (2020)
- [Optimizing Neural Networks with Kronecker-factored Approximate Curvature](https://mlsanity.com/paper/1503.05671/) (2015)
- [Weight Uncertainty in Neural Networks](https://mlsanity.com/paper/1505.05424/) (2015)
- [Accurate Uncertainties for Deep Learning Using Calibrated Regression](https://mlsanity.com/paper/1807.00263/) (2018)
- [Probabilistic Backpropagation for Scalable Learning of Bayesian Neural Networks](https://mlsanity.com/paper/1502.05336/) (2015)
- [Concrete Dropout](https://mlsanity.com/paper/1705.07832/) (2017)
- [To Trust Or Not To Trust A Classifier](https://mlsanity.com/paper/1805.11783/) (2018)
- [A General Framework for Uncertainty Estimation in Deep Learning](https://mlsanity.com/paper/1907.06890/) (2019)
- [Learnable Uncertainty under Laplace Approximations](https://mlsanity.com/paper/2010.02720/) (2020)
- [BayesCap: Bayesian Identity Cap for Calibrated Uncertainty in Frozen Neural Networks](https://mlsanity.com/paper/2207.06873/) (2022)
- [Tractable Inference for Complex Stochastic Processes](https://mlsanity.com/paper/1301.7362/) (2013)
- [Crowd Counting with Decomposed Uncertainty](https://mlsanity.com/paper/1903.07427/) (2019)

## Built on by (most cited first, 14 of 14)

- [A Survey on Uncertainty Quantification of Large Language Models: Taxonomy, Open Research Challenges, and Future Directions](https://mlsanity.com/paper/2412.05563/) (2024)
- [Epistemic Uncertainty Quantification For Pre-trained Neural Network](https://mlsanity.com/paper/2404.10124/) (2024)
- [Rate-In: Information-Driven Adaptive Dropout Rates for Improved Inference-Time Uncertainty Estimation](https://mlsanity.com/paper/2412.07169/) (2024)
- [Efficient Evaluation of Multi-Task Robot Policies With Active Experiment Selection](https://mlsanity.com/paper/2502.09829/) (2025)
- [How Confident are Video Models? Empowering Video Models to Express their Uncertainty](https://mlsanity.com/paper/2510.02571/) (2025)
- [Adversarial Attacks Against Uncertainty Quantification](https://mlsanity.com/paper/2309.10586/) (2023)
- [h-calibration: Rethinking Classifier Recalibration with Probabilistic Error-Bounded Objective](https://mlsanity.com/paper/2506.17968/) (2025)
- [Teaching with Uncertainty: Unleashing the Potential of Knowledge Distillation in Object Detection](https://mlsanity.com/paper/2406.06999/) (2024)
- [PH-Dropout: Practical Epistemic Uncertainty Quantification for View Synthesis](https://mlsanity.com/paper/2410.05468/) (2024)
- [Constructive Approximation of Random Process via Stochastic Interpolation Neural Network Operators](https://mlsanity.com/paper/2512.24106/) (2025)
- [Unsupervised Source-Free Ranking of Biomedical Segmentation Models Under Distribution Shift](https://mlsanity.com/paper/2503.00450/) (2025)
- [Principled Input-Output-Conditioned Post-Hoc Uncertainty Estimation for Regression Networks](https://mlsanity.com/paper/2506.00918/) (2025)
- [Confidence-Uncertainty Boundary Calibration for Bayesian Deep Learning in Medical Image Analysis](https://mlsanity.com/paper/2602.11973/) (2026)
- [Confidence is Not Reliability: Rethinking MC Dropout in Brain Tumour Segmentation](https://mlsanity.com/paper/2606.19300/) (2026)

## Abstract (arXiv)

Among Bayesian methods, Monte-Carlo dropout provides principled tools for evaluating the epistemic uncertainty of neural networks. Its popularity recently led to seminal works that proposed activating the dropout layers only during inference for evaluating uncertainty. This approach, which we call dropout injection, provides clear benefits over its traditional counterpart (which we call embedded dropout) since it allows one to obtain a post hoc uncertainty measure for any existing network previously trained without dropout, avoiding an additional, time-consuming training process. Unfortunately, no previous work compared injected and embedded dropout; therefore, we provide the first thorough investigation, focusing on regression problems. The main contribution of our work is to provide guidelines on the effective use of injected dropout so that it can be a practical alternative to the current use of embedded dropout. In particular, we show that its effectiveness strongly relies on a suitable scaling of the corresponding uncertainty measure, and we discuss the trade-off between negative log-likelihood and calibration error as a function of the scale factor. Experimental results on UCI data sets and crowd counting benchmarks support our claim that dropout injection can effectively behave as a competitive post hoc uncertainty quantification technique.