# Quantification of Uncertainty with Adversarial Models

arXiv: https://arxiv.org/abs/2307.03217 · HTML: https://mlsanity.com/paper/2307.03217/

## Key facts

- Cited by 28 papers in the map (data through 14 Oct 2026).
- Builds on 59 of its 109 references that are in the map.
- First posted on arXiv 6 Jul 2023.

## Builds on (most cited first, 30 of 59)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [LoRA: Low-Rank Adaptation of Large Language Models](https://mlsanity.com/paper/2106.09685/) (2021)
- [Explaining and Harnessing Adversarial Examples](https://mlsanity.com/paper/1412.6572/) (2014)
- [EfficientNet: Rethinking Model Scaling for Convolutional Neural Networks](https://mlsanity.com/paper/1905.11946/) (2019)
- [Intriguing properties of neural networks](https://mlsanity.com/paper/1312.6199/) (2013)
- [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)
- [Fashion-MNIST: a Novel Image Dataset for Benchmarking Machine Learning Algorithms](https://mlsanity.com/paper/1708.07747/) (2017)
- [Parameter-Efficient Transfer Learning for NLP](https://mlsanity.com/paper/1902.00751/) (2019)
- [Simple and Scalable Predictive Uncertainty Estimation using Deep Ensembles](https://mlsanity.com/paper/1612.01474/) (2016)
- [Axiomatic Attribution for Deep Networks](https://mlsanity.com/paper/1703.01365/) (2017)
- [What Uncertainties Do We Need in Bayesian Deep Learning for Computer Vision?](https://mlsanity.com/paper/1703.04977/) (2017)
- [Natural Adversarial Examples](https://mlsanity.com/paper/1907.07174/) (2019)
- [Can You Trust Your Model's Uncertainty? Evaluating Predictive Uncertainty Under Dataset Shift](https://mlsanity.com/paper/1906.02530/) (2019)
- [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)
- [Evasion Attacks against Machine Learning at Test Time](https://mlsanity.com/paper/1708.06131/) (2017)
- [A Survey of Uncertainty in Deep Neural Networks](https://mlsanity.com/paper/2107.03342/) (2021)
- [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)
- [Weight Uncertainty in Neural Networks](https://mlsanity.com/paper/1505.05424/) (2015)
- [Bayesian Deep Learning and a Probabilistic Perspective of Generalization](https://mlsanity.com/paper/2002.08791/) (2020)
- [Deep Ensembles: A Loss Landscape Perspective](https://mlsanity.com/paper/1912.02757/) (2019)
- [Deep Learning for Classical Japanese Literature](https://mlsanity.com/paper/1812.01718/) (2018)
- [Simple and Principled Uncertainty Estimation with Deterministic Deep Learning via Distance Awareness](https://mlsanity.com/paper/2006.10108/) (2020)
- [Last Layer Re-Training is Sufficient for Robustness to Spurious Correlations](https://mlsanity.com/paper/2204.02937/) (2022)
- [Laplace Redux -- Effortless Bayesian Deep Learning](https://mlsanity.com/paper/2106.14806/) (2021)
- [The Pitfalls of Simplicity Bias in Neural Networks](https://mlsanity.com/paper/2006.07710/) (2020)
- [Snapshot Ensembles: Train 1, get M for free](https://mlsanity.com/paper/1704.00109/) (2017)

## Built on by (most cited first, 28 of 28)

- [Rethinking Aleatoric and Epistemic Uncertainty](https://mlsanity.com/paper/2412.20892/) (2024)
- [Improving Uncertainty Estimation through Semantically Diverse Language Generation](https://mlsanity.com/paper/2406.04306/) (2024)
- [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)
- [Rethinking Uncertainty Estimation in LLMs: A Principled Single-Sequence Measure](https://mlsanity.com/paper/2412.15176/) (2024)
- [On Information-Theoretic Measures of Predictive Uncertainty](https://mlsanity.com/paper/2410.10786/) (2024)
- [Uncertainty Quantification for Machine Learning in Healthcare: A Survey](https://mlsanity.com/paper/2505.02874/) (2025)
- [Uncertainty Quantification for Hallucination Detection in Large Language Models: Foundations, Methodology, and Future Directions](https://mlsanity.com/paper/2510.12040/) (2025)
- [Epistemic Uncertainty Quantification For Pre-trained Neural Network](https://mlsanity.com/paper/2404.10124/) (2024)
- [Function Space Diversity for Uncertainty Prediction via Repulsive Last-Layer Ensembles](https://mlsanity.com/paper/2412.15758/) (2024)
- [Addressing Pitfalls in the Evaluation of Uncertainty Estimation Methods for Natural Language Generation](https://mlsanity.com/paper/2510.02279/) (2025)
- [Out-of-Distribution Data: An Acquaintance of Adversarial Examples -- A Survey](https://mlsanity.com/paper/2404.05219/) (2024)
- [Achieving Well-Informed Decision-Making in Drug Discovery: A Comprehensive Calibration Study using Neural Network-Based Structure-Activity Models](https://mlsanity.com/paper/2407.14185/) (2024)
- [The Disparate Benefits of Deep Ensembles](https://mlsanity.com/paper/2410.13831/) (2024)
- [Robust Adversarial Quantification via Conflict-Aware Evidential Deep Learning](https://mlsanity.com/paper/2506.05937/) (2025)
- [Probabilistic Scores of Classifiers, Calibration is not Enough](https://mlsanity.com/paper/2408.03421/) (2024)
- [PH-Dropout: Practical Epistemic Uncertainty Quantification for View Synthesis](https://mlsanity.com/paper/2410.05468/) (2024)
- [Temporal Distribution Shift in Real-World Pharmaceutical Data: Implications for Uncertainty Quantification in QSAR Models](https://mlsanity.com/paper/2502.03982/) (2025)
- [Adversarial Examples in Environment Perception for Automated Driving (Review)](https://mlsanity.com/paper/2504.08414/) (2025)
- [A Ground-Truth Framework for Uncertainty Disentanglement with Posterior Risk](https://mlsanity.com/paper/2608.05995/) (2026)
- [CONTINA: Confidence Interval for Traffic Demand Prediction with Coverage Guarantee](https://mlsanity.com/paper/2504.13961/) (2025)
- [Feature Fitted Online Conformal Prediction for Deep Time Series Forecasting Model](https://mlsanity.com/paper/2505.08158/) (2025)
- [Objectomaly: Objectness-Aware Refinement for OoD Segmentation with Structural Consistency and Boundary Precision](https://mlsanity.com/paper/2507.07460/) (2025)
- [PEdger++: Practical Edge Detection via Assembling Cross Information](https://mlsanity.com/paper/2508.11961/) (2025)
- [Post-Hoc Split-Point Self-Consistency Verification for Efficient, Unified Quantification of Aleatoric and Epistemic Uncertainty in Deep Learning](https://mlsanity.com/paper/2509.13262/) (2025)
- [Guided Uncertainty Learning Using a Post-Hoc Evidential Meta-Model](https://mlsanity.com/paper/2509.24492/) (2025)
- [Quantification of Uncertainty with Adversarial Models in Medical Image Segmentation](https://mlsanity.com/paper/2606.18860/) (2026)
- [Uncertainty quantification for trustworthy deep learning: Methods and measures](https://mlsanity.com/paper/2607.28248/) (2026)

## Abstract (arXiv)

Quantifying uncertainty is important for actionable predictions in real-world applications. A crucial part of predictive uncertainty quantification is the estimation of epistemic uncertainty, which is defined as an integral of the product between a divergence function and the posterior. Current methods such as Deep Ensembles or MC dropout underperform at estimating the epistemic uncertainty, since they primarily consider the posterior when sampling models. We suggest Quantification of Uncertainty with Adversarial Models (QUAM) to better estimate the epistemic uncertainty. QUAM identifies regions where the whole product under the integral is large, not just the posterior. Consequently, QUAM has lower approximation error of the epistemic uncertainty compared to previous methods. Models for which the product is large correspond to adversarial models (not adversarial examples!). Adversarial models have both a high posterior as well as a high divergence between their predictions and that of a reference model. Our experiments show that QUAM excels in capturing epistemic uncertainty for deep learning models and outperforms previous methods on challenging tasks in the vision domain.