# Classification Uncertainty of Deep Neural Networks Based on Gradient Information

arXiv: https://arxiv.org/abs/1805.08440 · HTML: https://mlsanity.com/paper/1805.08440/

## Key facts

- Cited by 43 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 22 May 2018.

## Built on by (most cited first, 30 of 43)

- [A Survey of Uncertainty in Deep Neural Networks](https://mlsanity.com/paper/2107.03342/) (2021)
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- [Gradient-based Uncertainty for Monocular Depth Estimation](https://mlsanity.com/paper/2208.02005/) (2022)
- [A Comprehensive Survey on Evidential Deep Learning and Its Applications](https://mlsanity.com/paper/2409.04720/) (2024)
- [Gradient-Based Quantification of Epistemic Uncertainty for Deep Object Detectors](https://mlsanity.com/paper/2107.04517/) (2021)
- [Out-of-Distribution Detection by Leveraging Between-Layer Transformation Smoothness](https://mlsanity.com/paper/2310.02832/) (2023)
- [Gradient-Based Adversarial and Out-of-Distribution Detection](https://mlsanity.com/paper/2206.08255/) (2022)
- [Resisting Out-of-Distribution Data Problem in Perturbation of XAI](https://mlsanity.com/paper/2107.14000/) (2021)
- [Pixel-wise Gradient Uncertainty for Convolutional Neural Networks applied to Out-of-Distribution Segmentation](https://mlsanity.com/paper/2303.06920/) (2023)
- [A Structured Review of Literature on Uncertainty in Machine Learning & Deep Learning](https://mlsanity.com/paper/2406.00332/) (2024)
- [Improving Variational Autoencoder based Out-of-Distribution Detection for Embedded Real-time Applications](https://mlsanity.com/paper/2107.11750/) (2021)
- [Benchmark for Out-of-Distribution Detection in Deep Reinforcement Learning](https://mlsanity.com/paper/2112.02694/) (2021)
- [WOOD: Wasserstein-based Out-of-Distribution Detection](https://mlsanity.com/paper/2112.06384/) (2021)
- [Probing the Purview of Neural Networks via Gradient Analysis](https://mlsanity.com/paper/2304.02834/) (2023)
- [Open-Set Recognition with Gradient-Based Representations](https://mlsanity.com/paper/2206.08229/) (2022)
- [Learning Complementary Policies for Human-AI Teams](https://mlsanity.com/paper/2302.02944/) (2023)
- [Revisiting Gradient-based Uncertainty for Monocular Depth Estimation](https://mlsanity.com/paper/2502.05964/) (2025)
- [Probabilistic Machine Learning for Noisy Labels in Earth Observation](https://mlsanity.com/paper/2504.03478/) (2025)
- [Compensation Learning in Semantic Segmentation](https://mlsanity.com/paper/2304.13428/) (2023)
- [Exploring the Limits of Epistemic Uncertainty Quantification in Low-Shot Settings](https://mlsanity.com/paper/2111.09808/) (2021)
- [Uncertainty-Aware Deep Learning for Wildfire Danger Forecasting](https://mlsanity.com/paper/2509.25017/) (2025)
- [Understanding the Dependence of Perception Model Competency on Regions in an Image](https://mlsanity.com/paper/2407.10543/) (2024)
- [Guiding Reinforcement Learning Using Uncertainty-Aware Large Language Models](https://mlsanity.com/paper/2411.14457/) (2024)
- [Generalized Uncertainty of Deep Neural Networks: Taxonomy and Applications](https://mlsanity.com/paper/2302.01440/) (2023)
- [Delay-SDE-net: A deep learning approach for time series modelling with memory and uncertainty estimates](https://mlsanity.com/paper/2303.08587/) (2023)

## Abstract (arXiv)

We study the quantification of uncertainty of Convolutional Neural Networks (CNNs) based on gradient metrics. Unlike the classical softmax entropy, such metrics gather information from all layers of the CNN. We show for the EMNIST digits data set that for several such metrics we achieve the same meta classification accuracy -- i.e. the task of classifying predictions as correct or incorrect without knowing the actual label -- as for entropy thresholding. We apply meta classification to unknown concepts (out-of-distribution samples) -- EMNIST/Omniglot letters, CIFAR10 and noise -- and demonstrate that meta classification rates for unknown concepts can be increased when using entropy together with several gradient based metrics as input quantities for a meta classifier. Meta classifiers only trained on the uncertainty metrics of known concepts, i.e. EMNIST digits, usually do not perform equally well for all unknown concepts. If we however allow the meta classifier to be trained on uncertainty metrics for some out-of-distribution samples, meta classification for concepts remote from EMNIST digits (then termed known unknowns) can be improved considerably.