mlsanityData to 7 Oct 2026

Understanding Softmax Confidence and Uncertainty

arXiv 2106.04972 ↗First posted 9 Jun 2021cs.LG cs.AI stat.MLcited by 62

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Abstract (arXiv)

It is often remarked that neural networks fail to increase their uncertainty when predicting on data far from the training distribution. Yet naively using softmax confidence as a proxy for uncertainty achieves modest success in tasks exclusively testing for this, e.g., out-of-distribution (OOD) detection. This paper investigates this contradiction, identifying two implicit biases that do encourage softmax confidence to correlate with epistemic uncertainty: 1) Approximately optimal decision boundary structure, and 2) Filtering effects of deep networks. It describes why low-dimensional intuitions about softmax confidence are misleading. Diagnostic experiments quantify reasons softmax confidence can fail, finding that extrapolations are less to blame than overlap between training and OOD data in final-layer representations. Pre-trained/fine-tuned networks reduce this overlap.

Key facts. Cited by 62 papers in the map (data through 7 Oct 2026). Builds on 21 of its 46 references that are in the map. First posted on arXiv 9 Jun 2021.

Builds on

21 of 46 references.

References · 21

  1. 2013Intriguing properties of neural networkscited by 5,114
  2. 2017On Calibration of Modern Neural Networkscited by 4,860
  3. 2015Dropout as a Bayesian Approximation: Representing Model Uncertainty in Deep Learningcited by 4,416
  4. 2016Simple and Scalable Predictive Uncertainty Estimation using Deep Ensemblescited by 3,888
  5. 2016A Baseline for Detecting Misclassified and Out-of-Distribution Examples in Neural Networkscited by 2,362
  6. 2013Visualizing and Understanding Convolutional Networkscited by 2,278
  7. 2018A Simple Unified Framework for Detecting Out-of-Distribution Samples and Adversarial Attackscited by 1,472
  8. 2017Deep Bayesian Active Learning with Image Datacited by 812
  9. 2015Deep Learning and the Information Bottleneck Principlecited by 793
  10. 2014Deep Neural Networks are Easily Fooled: High Confidence Predictions for Unrecognizable Imagescited by 774
  11. 2018Predictive Uncertainty Estimation via Prior Networkscited by 555
  12. 2019Using Self-Supervised Learning Can Improve Model Robustness and Uncertaintycited by 511
9 more
  1. 2020Simple and Principled Uncertainty Estimation with Deterministic Deep Learning via Distance Awarenesscited by 389
  2. 2019Using Pre-Training Can Improve Model Robustness and Uncertaintycited by 373
  3. 2018Why ReLU networks yield high-confidence predictions far away from the training data and how to mitigate the problemcited by 323
  4. 2020Pretrained Transformers Improve Out-of-Distribution Robustnesscited by 293
  5. 2018Strike (with) a Pose: Neural Networks Are Easily Fooled by Strange Poses of Familiar Objectscited by 143
  6. 2020Topology of deep neural networkscited by 111
  7. 2020Uncertainty Estimation Using a Single Deep Deterministic Neural Networkcited by 37
  8. 2019Robustness properties of Facebook's ResNeXt WSL modelscited by 17
  9. 2018How the Softmax Output is Misleading for Evaluating the Strength of Adversarial Examplescited by 4

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2021: 5; 2022: 9; 2023: 15; 2024: 19; 2025: 7; 2026: 7.

62 papers.

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  1. 2023A Survey of Confidence Estimation and Calibration in Large Language Modelscited by 253
  2. 2021Prior and Posterior Networks: A Survey on Evidential Deep Learning Methods For Uncertainty Estimationcited by 71
  3. 2023Fusing Models with Complementary Expertisecited by 45
  4. 2022Augmenting Softmax Information for Selective Classification with Out-of-Distribution Datacited by 27
  5. 2023Think Twice Before Selection: Federated Evidential Active Learning for Medical Image Analysis with Domain Shiftscited by 26
  6. 2024EDGE-LLM: Enabling Efficient Large Language Model Adaptation on Edge Devices via Layerwise Unified Compression and Adaptive Layer Tuning and Votingcited by 26
  7. 2023Beyond Confidence: Reliable Models Should Also Consider Atypicalitycited by 25
  8. 2021Calibrating the Dice loss to handle neural network overconfidence for biomedical image segmentationcited by 17
  9. 2021FF-NSL: Feed-Forward Neural-Symbolic Learnercited by 15
  10. 2023Unsupervised Layer-wise Score Aggregation for Textual OOD Detectioncited by 15
  11. 2023Window-Based Early-Exit Cascades for Uncertainty Estimation: When Deep Ensembles are More Efficient than Single Modelscited by 15
  12. 2023The Co-12 Recipe for Evaluating Interpretable Part-Prototype Image Classifierscited by 15
38 more
  1. 2022On the Usefulness of Deep Ensemble Diversity for Out-of-Distribution Detectioncited by 14
  2. 2023A Reliable and Interpretable Framework of Multi-view Learning for Liver Fibrosis Stagingcited by 13
  3. 2023Multi-stage Large Language Model Correction for Speech Recognitioncited by 13
  4. 2024MERIT: Multi-view evidential learning for reliable and interpretable liver fibrosis stagingcited by 12
  5. 2024Towards Understanding and Quantifying Uncertainty for Text-to-Image Generationcited by 11
  6. 2025The Confidence Paradox: Can LLM Know When It's Wrongcited by 11
  7. 2021Generalisation effects of predictive uncertainty estimation in deep learning for digital pathologycited by 9
  8. 2024A Structured Review of Literature on Uncertainty in Machine Learning & Deep Learningcited by 9
  9. 2024Privacy Preserving Federated Learning in Medical Imaging with Uncertainty Estimationcited by 9
  10. 2022Curved Representation Space of Vision Transformerscited by 8
  11. 2023Uncertainty Estimation of Transformers' Predictions via Topological Analysis of the Attention Matricescited by 8
  12. 2024Advancing Deep Active Learning & Data Subset Selection: Unifying Principles with Information-Theory Intuitionscited by 7
  13. 2024Out-of-Distribution Detection Should Use Conformal Prediction (and Vice-versa?)cited by 7
  14. 2023Confidence-Based Model Selection: When to Take Shortcuts for Subpopulation Shiftscited by 5
  15. 2024Improving Local Training in Federated Learning via Temperature Scalingcited by 5
  16. 2023Reliable Prediction Intervals with Directly Optimized Inductive Conformal Regression for Deep Learningcited by 4
  17. 2022To Softmax, or not to Softmax: that is the question when applying Active Learning for Transformer Modelscited by 3
  18. 2024Investigating the Impact of Model Instability on Explanations and Uncertaintycited by 3
  19. 2026Energy-Aware Reinforcement Learning for Robotic Manipulation of Articulated Components in Infrastructure Operation and Maintenancecited by 3
  20. 2022Perception Over Time: Temporal Dynamics for Robust Image Understandingcited by 2
  21. 2022Quantifying Model Uncertainty for Semantic Segmentation using Operators in the RKHScited by 2
  22. 2025Adaptive Conformal Guidance for Learning under Uncertaintycited by 2
  23. 2025Recursive Offloading for LLM Serving in Multi-tier Networkscited by 2
  24. 2022A Principled Evaluation Protocol for Comparative Investigation of the Effectiveness of DNN Classification Models on Similar-but-non-identical Datasetscited by 1
  25. 2022Statistical process monitoring of artificial neural networkscited by 1
  26. 2022On the calibration of underrepresented classes in LiDAR-based semantic segmentationcited by 1
  27. 2023Simple and Efficient Confidence Score for Grading Whole Slide Imagescited by 1
  28. 2023Deep Neural Networks Tend To Extrapolate Predictablycited by 1
  29. 2024Confidence Preservation Property in Knowledge Distillation Abstractionscited by 1
  30. 2024Taking Class Imbalance Into Account in Open Set Recognition Evaluationcited by 1
  31. 2024Predictive uncertainty estimation in deep learning for lung carcinoma classification in digital pathology under real dataset shiftscited by 1
  32. 2025DiTOX: Fault Detection and Localization in the ONNX Optimizercited by 1
  33. 2021HOMRS: High Order Metamorphic Relations Selector for Deep Neural Networkscited by 0
  34. 2023Elongated Physiological Structure Segmentation via Spatial and Scale Uncertainty-aware Networkcited by 0
  35. 2024Awareness of uncertainty in classification using a multivariate model and multi-viewscited by 0
  36. 2024Application of Deep Learning Methods to Processing of Noisy Medical Video Datacited by 0
  37. 2024Improving Explainability of Softmax Classifiers Using a Prototype-Based Joint Embedding Methodcited by 0
  38. 2024Trimming the Risk: Towards Reliable Continuous Training for Deep Learning Inspection Systemscited by 0

50 most cited of 62 All 62 (JSON)