# Reverse KL-Divergence Training of Prior Networks: Improved Uncertainty and Adversarial Robustness

arXiv: https://arxiv.org/abs/1905.13472 · HTML: https://mlsanity.com/paper/1905.13472/

## Key facts

- Cited by 104 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 31 May 2019.

## Built on by (most cited first, 30 of 104)

- [Generalized Out-of-Distribution Detection: A Survey](https://mlsanity.com/paper/2110.11334/) (2021)
- [A Survey of Uncertainty in Deep Neural Networks](https://mlsanity.com/paper/2107.03342/) (2021)
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- [Graph Posterior Network: Bayesian Predictive Uncertainty for Node Classification](https://mlsanity.com/paper/2110.14012/) (2021)
- [Provable Guarantees for Understanding Out-of-distribution Detection](https://mlsanity.com/paper/2112.00787/) (2021)
- [Dream the Impossible: Outlier Imagination with Diffusion Models](https://mlsanity.com/paper/2309.13415/) (2023)
- [Prior and Posterior Networks: A Survey on Evidential Deep Learning Methods For Uncertainty Estimation](https://mlsanity.com/paper/2110.03051/) (2021)
- [Pitfalls of Epistemic Uncertainty Quantification through Loss Minimisation](https://mlsanity.com/paper/2203.06102/) (2022)
- [Rethinking Reconstruction Autoencoder-Based Out-of-Distribution Detection](https://mlsanity.com/paper/2203.02194/) (2022)
- [Uncertainty Estimation by Fisher Information-based Evidential Deep Learning](https://mlsanity.com/paper/2303.02045/) (2023)
- [Latent Space Chain-of-Embedding Enables Output-free LLM Self-Evaluation](https://mlsanity.com/paper/2410.13640/) (2024)
- [Benchmarking Bayesian Deep Learning on Diabetic Retinopathy Detection Tasks](https://mlsanity.com/paper/2211.12717/) (2022)
- [On Second-Order Scoring Rules for Epistemic Uncertainty Quantification](https://mlsanity.com/paper/2301.12736/) (2023)
- [How Does Unlabeled Data Provably Help Out-of-Distribution Detection?](https://mlsanity.com/paper/2402.03502/) (2024)
- [Is Epistemic Uncertainty Faithfully Represented by Evidential Deep Learning Methods?](https://mlsanity.com/paper/2402.09056/) (2024)
- [OpenCon: Open-world Contrastive Learning](https://mlsanity.com/paper/2208.02764/) (2022)
- [Post-hoc Uncertainty Learning using a Dirichlet Meta-Model](https://mlsanity.com/paper/2212.07359/) (2022)
- [Learn to Accumulate Evidence from All Training Samples: Theory and Practice](https://mlsanity.com/paper/2306.11113/) (2023)
- [Tailoring Language Generation Models under Total Variation Distance](https://mlsanity.com/paper/2302.13344/) (2023)
- [A Comprehensive Survey on Evidential Deep Learning and Its Applications](https://mlsanity.com/paper/2409.04720/) (2024)
- [Out-of-distribution Detection in Medical Image Analysis: A survey](https://mlsanity.com/paper/2404.18279/) (2024)
- [Uncertainty Estimation by Density Aware Evidential Deep Learning](https://mlsanity.com/paper/2409.08754/) (2024)
- [Region-Based Evidential Deep Learning to Quantify Uncertainty and Improve Robustness of Brain Tumor Segmentation](https://mlsanity.com/paper/2208.06038/) (2022)
- [Scaling Ensemble Distribution Distillation to Many Classes with Proxy Targets](https://mlsanity.com/paper/2105.06987/) (2021)
- [Random-Set Neural Networks (RS-NN)](https://mlsanity.com/paper/2307.05772/) (2023)
- [Provably Robust Detection of Out-of-distribution Data (almost) for free](https://mlsanity.com/paper/2106.04260/) (2021)

## Abstract (arXiv)

Ensemble approaches for uncertainty estimation have recently been applied to the tasks of misclassification detection, out-of-distribution input detection and adversarial attack detection. Prior Networks have been proposed as an approach to efficiently emulate an ensemble of models for classification by parameterising a Dirichlet prior distribution over output distributions. These models have been shown to outperform alternative ensemble approaches, such as Monte-Carlo Dropout, on the task of out-of-distribution input detection. However, scaling Prior Networks to complex datasets with many classes is difficult using the training criteria originally proposed. This paper makes two contributions. First, we show that the appropriate training criterion for Prior Networks is the reverse KL-divergence between Dirichlet distributions. This addresses issues in the nature of the training data target distributions, enabling prior networks to be successfully trained on classification tasks with arbitrarily many classes, as well as improving out-of-distribution detection performance. Second, taking advantage of this new training criterion, this paper investigates using Prior Networks to detect adversarial attacks and proposes a generalized form of adversarial training. It is shown that the construction of successful adaptive whitebox attacks, which affect the prediction and evade detection, against Prior Networks trained on CIFAR-10 and CIFAR-100 using the proposed approach requires a greater amount of computational effort than against networks defended using standard adversarial training or MC-dropout.