# Deep Deterministic Uncertainty: A Simple Baseline

arXiv: https://arxiv.org/abs/2102.11582 · HTML: https://mlsanity.com/paper/2102.11582/

## Key facts

- Cited by 200 papers in the map (data through 14 Oct 2026).
- Builds on 49 of its 77 references that are in the map.
- First posted on arXiv 23 Feb 2021.

## Builds on (most cited first, 30 of 49)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Very Deep Convolutional Networks for Large-Scale Image Recognition](https://mlsanity.com/paper/1409.1556/) (2014)
- [Densely Connected Convolutional Networks](https://mlsanity.com/paper/1608.06993/) (2016)
- [On Calibration of Modern Neural Networks](https://mlsanity.com/paper/1706.04599/) (2017)
- [Fully Convolutional Networks for Semantic Segmentation](https://mlsanity.com/paper/1411.4038/) (2014)
- [Dropout as a Bayesian Approximation: Representing Model Uncertainty in Deep Learning](https://mlsanity.com/paper/1506.02142/) (2015)
- [Fashion-MNIST: a Novel Image Dataset for Benchmarking Machine Learning Algorithms](https://mlsanity.com/paper/1708.07747/) (2017)
- [Auto-Encoding Variational Bayes](https://mlsanity.com/paper/1312.6114/) (2013)
- [Simple and Scalable Predictive Uncertainty Estimation using Deep Ensembles](https://mlsanity.com/paper/1612.01474/) (2016)
- [Wide Residual Networks](https://mlsanity.com/paper/1605.07146/) (2016)
- [Benchmarking Neural Network Robustness to Common Corruptions and Perturbations](https://mlsanity.com/paper/1903.12261/) (2019)
- [A Baseline for Detecting Misclassified and Out-of-Distribution Examples in Neural Networks](https://mlsanity.com/paper/1610.02136/) (2016)
- [What Uncertainties Do We Need in Bayesian Deep Learning for Computer Vision?](https://mlsanity.com/paper/1703.04977/) (2017)
- [Improved Training of Wasserstein GANs](https://mlsanity.com/paper/1704.00028/) (2017)
- [Rethinking Atrous Convolution for Semantic Image Segmentation](https://mlsanity.com/paper/1706.05587/) (2017)
- [Spectral Normalization for Generative Adversarial Networks](https://mlsanity.com/paper/1802.05957/) (2018)
- [A Simple Unified Framework for Detecting Out-of-Distribution Samples and Adversarial Attacks](https://mlsanity.com/paper/1807.03888/) (2018)
- [Natural Adversarial Examples](https://mlsanity.com/paper/1907.07174/) (2019)
- [Enhancing The Reliability of Out-of-distribution Image Detection in Neural Networks](https://mlsanity.com/paper/1706.02690/) (2017)
- [Energy-based Out-of-distribution Detection](https://mlsanity.com/paper/2010.03759/) (2020)
- [Can You Trust Your Model's Uncertainty? Evaluating Predictive Uncertainty Under Dataset Shift](https://mlsanity.com/paper/1906.02530/) (2019)
- [NICE: Non-linear Independent Components Estimation](https://mlsanity.com/paper/1410.8516/) (2014)
- [Deep Anomaly Detection with Outlier Exposure](https://mlsanity.com/paper/1812.04606/) (2018)
- [Revisiting Unreasonable Effectiveness of Data in Deep Learning Era](https://mlsanity.com/paper/1707.02968/) (2017)
- [Deep Bayesian Active Learning with Image Data](https://mlsanity.com/paper/1703.02910/) (2017)
- [A Simple Baseline for Bayesian Uncertainty in Deep Learning](https://mlsanity.com/paper/1902.02476/) (2019)
- [Predictive Uncertainty Estimation via Prior Networks](https://mlsanity.com/paper/1802.10501/) (2018)
- [Bayesian Deep Learning and a Probabilistic Perspective of Generalization](https://mlsanity.com/paper/2002.08791/) (2020)
- [BatchBALD: Efficient and Diverse Batch Acquisition for Deep Bayesian Active Learning](https://mlsanity.com/paper/1906.08158/) (2019)

## Built on by (most cited first, 30 of 200)

- [Out-of-Distribution Detection and Selective Generation for Conditional Language Models](https://mlsanity.com/paper/2209.15558/) (2022)
- [Kernel Language Entropy: Fine-grained Uncertainty Quantification for LLMs from Semantic Similarities](https://mlsanity.com/paper/2405.20003/) (2024)
- [Benchmarking Uncertainty Disentanglement: Specialized Uncertainties for Specialized Tasks](https://mlsanity.com/paper/2402.19460/) (2024)
- [Calibrating Large Language Models Using Their Generations Only](https://mlsanity.com/paper/2403.05973/) (2024)
- [A Survey of Uncertainty Estimation in LLMs: Theory Meets Practice](https://mlsanity.com/paper/2410.15326/) (2024)
- [Estimating Epistemic and Aleatoric Uncertainty with a Single Model](https://mlsanity.com/paper/2402.03478/) (2024)
- [Rethinking Aleatoric and Epistemic Uncertainty](https://mlsanity.com/paper/2412.20892/) (2024)
- [Stochastic Batch Acquisition: A Simple Baseline for Deep Active Learning](https://mlsanity.com/paper/2106.12059/) (2021)
- [Mahalanobis++: Improving OOD Detection via Feature Normalization](https://mlsanity.com/paper/2505.18032/) (2025)
- [Position: Uncertainty Quantification Needs Reassessment for Large-language Model Agents](https://mlsanity.com/paper/2505.22655/) (2025)
- [Quantification of Uncertainty with Adversarial Models](https://mlsanity.com/paper/2307.03217/) (2023)
- [Introducing an Improved Information-Theoretic Measure of Predictive Uncertainty](https://mlsanity.com/paper/2311.08309/) (2023)
- [From Risk to Uncertainty: Generating Predictive Uncertainty Measures via Bayesian Estimation](https://mlsanity.com/paper/2402.10727/) (2024)
- [Beyond Confidence: Reliable Models Should Also Consider Atypicality](https://mlsanity.com/paper/2305.18262/) (2023)
- [ValUES: A Framework for Systematic Validation of Uncertainty Estimation in Semantic Segmentation](https://mlsanity.com/paper/2401.08501/) (2024)
- [On the Variance of Neural Network Training with respect to Test Sets and Distributions](https://mlsanity.com/paper/2304.01910/) (2023)
- [Continual Learning in Medical Image Analysis: A Comprehensive Review of Recent Advancements and Future Prospects](https://mlsanity.com/paper/2312.17004/) (2023)
- [Uncertainty Estimation by Density Aware Evidential Deep Learning](https://mlsanity.com/paper/2409.08754/) (2024)
- [Conformal Semantic Image Segmentation: Post-hoc Quantification of Predictive Uncertainty](https://mlsanity.com/paper/2405.05145/) (2024)
- [Understanding Model Calibration -- A gentle introduction and visual exploration of calibration and the expected calibration error (ECE)](https://mlsanity.com/paper/2501.19047/) (2025)
- [Toward Real-world BEV Perception: Depth Uncertainty Estimation via Gaussian Splatting](https://mlsanity.com/paper/2504.01957/) (2025)
- [Random-Set Neural Networks (RS-NN)](https://mlsanity.com/paper/2307.05772/) (2023)
- [Deep Bayesian Active Learning for Preference Modeling in Large Language Models](https://mlsanity.com/paper/2406.10023/) (2024)
- [On Information-Theoretic Measures of Predictive Uncertainty](https://mlsanity.com/paper/2410.10786/) (2024)
- [DUDES: Deep Uncertainty Distillation using Ensembles for Semantic Segmentation](https://mlsanity.com/paper/2303.09843/) (2023)
- [Uncertainty-based Fairness Measures](https://mlsanity.com/paper/2312.11299/) (2023)
- [Interpreting Predictive Probabilities: Model Confidence or Human Label Variation?](https://mlsanity.com/paper/2402.16102/) (2024)
- [(Implicit) Ensembles of Ensembles: Epistemic Uncertainty Collapse in Large Models](https://mlsanity.com/paper/2409.02628/) (2024)
- [How Reliable is Your Regression Model's Uncertainty Under Real-World Distribution Shifts?](https://mlsanity.com/paper/2302.03679/) (2023)
- [A Data-Driven Measure of Relative Uncertainty for Misclassification Detection](https://mlsanity.com/paper/2306.01710/) (2023)

## Abstract (arXiv)

Reliable uncertainty from deterministic single-forward pass models is sought after because conventional methods of uncertainty quantification are computationally expensive. We take two complex single-forward-pass uncertainty approaches, DUQ and SNGP, and examine whether they mainly rely on a well-regularized feature space. Crucially, without using their more complex methods for estimating uncertainty, a single softmax neural net with such a feature-space, achieved via residual connections and spectral normalization, *outperforms* DUQ and SNGP's epistemic uncertainty predictions using simple Gaussian Discriminant Analysis *post-training* as a separate feature-space density estimator -- without fine-tuning on OoD data, feature ensembling, or input pre-procressing. This conceptually simple *Deep Deterministic Uncertainty (DDU)* baseline can also be used to disentangle aleatoric and epistemic uncertainty and performs as well as Deep Ensembles, the state-of-the art for uncertainty prediction, on several OoD benchmarks (CIFAR-10/100 vs SVHN/Tiny-ImageNet, ImageNet vs ImageNet-O) as well as in active learning settings across different model architectures, yet is *computationally cheaper*.