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Gradients as a Measure of Uncertainty in Neural Networks

arXiv 2008.08030 ↗First posted 18 Aug 2020cs.CVcited by 55

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Abstract (arXiv)

Despite tremendous success of modern neural networks, they are known to be overconfident even when the model encounters inputs with unfamiliar conditions. Detecting such inputs is vital to preventing models from making naive predictions that may jeopardize real-world applications of neural networks. In this paper, we address the challenging problem of devising a simple yet effective measure of uncertainty in deep neural networks. Specifically, we propose to utilize backpropagated gradients to quantify the uncertainty of trained models. Gradients depict the required amount of change for a model to properly represent given inputs, thus providing a valuable insight into how familiar and certain the model is regarding the inputs. We demonstrate the effectiveness of gradients as a measure of model uncertainty in applications of detecting unfamiliar inputs, including out-of-distribution and corrupted samples. We show that our gradient-based method outperforms state-of-the-art methods by up to 4.8% of AUROC score in out-of-distribution detection and 35.7% in corrupted input detection.

Key facts. Cited by 55 papers in the map (data through 14 Oct 2026). First posted on arXiv 18 Aug 2020.

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Citing papers per year: 2021: 5; 2022: 11; 2023: 15; 2024: 14; 2025: 7; 2026: 3.

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  1. 2021A Survey of Uncertainty in Deep Neural Networkscited by 680
  2. 2021On the Importance of Gradients for Detecting Distributional Shifts in the Wildcited by 339
  3. 2024A Survey on Uncertainty Quantification of Large Language Models: Taxonomy, Open Research Challenges, and Future Directionscited by 121
  4. 2024LUQ: Long-text Uncertainty Quantification for LLMscited by 81
  5. 2023Single-model uncertainty quantification in neural network potentials does not consistently outperform model ensemblescited by 30
  6. 2022Gradient-based Uncertainty for Monocular Depth Estimationcited by 26
  7. 2024Out-of-Distribution Detection: A Task-Oriented Survey of Recent Advancescited by 26
  8. 2024A Comprehensive Survey on Evidential Deep Learning and Its Applicationscited by 25
  9. 2023GradOrth: A Simple yet Efficient Out-of-Distribution Detection with Orthogonal Projection of Gradientscited by 21
  10. 2022How Useful are Gradients for OOD Detection Really?cited by 20
  11. 2022Introspective Learning : A Two-Stage Approach for Inference in Neural Networkscited by 20
  12. 2024Predictive Dynamic Fusioncited by 17
38 more
  1. 2022Fine-grained TLS services classification with reject optioncited by 14
  2. 2022Gradient-Based Adversarial and Out-of-Distribution Detectioncited by 14
  3. 2024Ctrl-U: Robust Conditional Image Generation via Uncertainty-aware Reward Modelingcited by 14
  4. 2021Extracting Causal Visual Features for Limited label Classificationcited by 12
  5. 2023GAIA: Delving into Gradient-based Attribution Abnormality for Out-of-distribution Detectioncited by 12
  6. 2021Contrastive Reasoning in Neural Networkscited by 11
  7. 2022Explanatory Paradigms in Neural Networkscited by 11
  8. 2021Gradient-based Novelty Detection Boosted by Self-supervised Binary Classificationcited by 10
  9. 2023Gaussian Switch Sampling: A Second Order Approach to Active Learningcited by 10
  10. 2023Revisiting Deep Ensemble for Out-of-Distribution Detection: A Loss Landscape Perspectivecited by 10
  11. 2024Epistemic Uncertainty Quantification For Pre-trained Neural Networkcited by 10
  12. 2024A Structured Review of Literature on Uncertainty in Machine Learning & Deep Learningcited by 10
  13. 2022Highlighting Object Category Immunity for the Generalization of Human-Object Interaction Detectioncited by 9
  14. 2023WDiscOOD: Out-of-Distribution Detection via Whitened Linear Discriminant Analysiscited by 9
  15. 2023Probing the Purview of Neural Networks via Gradient Analysiscited by 9
  16. 2024Harnessing Uncertainty-aware Bounding Boxes for Unsupervised 3D Object Detectioncited by 9
  17. 2023Forgetful Active Learning with Switch Events: Efficient Sampling for Out-of-Distribution Datacited by 8
  18. 2022Open-Set Recognition with Gradient-Based Representationscited by 7
  19. 2023Explaining Deep Models through Forgettable Learning Dynamicscited by 7
  20. 2025Probabilistic Machine Learning for Noisy Labels in Earth Observationcited by 6
  21. 2023Example Forgetting: A Novel Approach to Explain and Interpret Deep Neural Networks in Seismic Interpretationcited by 4
  22. 2025Uncertainty-Aware Deep Learning for Wildfire Danger Forecastingcited by 4
  23. 2022TEDL: A Two-stage Evidential Deep Learning Method for Classification Uncertainty Quantificationcited by 3
  24. 2023Compiled Models, Built-In Exploits: Uncovering Pervasive Bit-Flip Attack Surfaces in DNN Executablescited by 3
  25. 2024VOICE: Variance of Induced Contrastive Explanations to quantify Uncertainty in Neural Network Interpretabilitycited by 3
  26. 2024Understanding the Dependence of Perception Model Competency on Regions in an Imagecited by 3
  27. 2022A Benchmark for Out of Distribution Detection in Point Cloud 3D Semantic Segmentationcited by 2
  28. 2023Generalized Uncertainty of Deep Neural Networks: Taxonomy and Applicationscited by 2
  29. 2023Delay-SDE-net: A deep learning approach for time series modelling with memory and uncertainty estimatescited by 2
  30. 2024Generalizable Physics-Informed Learning for Stochastic Safety-Critical Systemscited by 2
  31. 2024Estimating Environmental Cost Throughout Model's Adaptive Life Cyclecited by 2
  32. 2025GradPCA: Leveraging NTK Alignment for Reliable Out-of-Distribution Detectioncited by 2
  33. 2022Explainable Machine Learning for Hydrocarbon Prospect Riskingcited by 1
  34. 2023GIT: Detecting Uncertainty, Out-Of-Distribution and Adversarial Samples using Gradients and Invariance Transformationscited by 0
  35. 2023GROOD: GRadient-Aware Out-of-Distribution Detectioncited by 0
  36. 2024RESQUE: Quantifying Estimator to Task and Distribution Shift for Sustainable Model Reusabilitycited by 0
  37. 2025Model uncertainty quantification using feature confidence sets for outcome excursionscited by 0
  38. 2025ELMAR: Enhancing LiDAR Detection with 4D Radar Motion Awareness and Cross-modal Uncertaintycited by 0

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