# Cautious Deep Learning

arXiv: https://arxiv.org/abs/1805.09460 · HTML: https://mlsanity.com/paper/1805.09460/

## Key facts

- Cited by 35 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 24 May 2018.

## Built on by (most cited first, 30 of 35)

- [A Gentle Introduction to Conformal Prediction and Distribution-Free Uncertainty Quantification](https://mlsanity.com/paper/2107.07511/) (2021)
- [Distribution-Free, Risk-Controlling Prediction Sets](https://mlsanity.com/paper/2101.02703/) (2021)
- [Learn then Test: Calibrating Predictive Algorithms to Achieve Risk Control](https://mlsanity.com/paper/2110.01052/) (2021)
- [Testing for Outliers with Conformal p-values](https://mlsanity.com/paper/2104.08279/) (2021)
- [Learning Optimal Conformal Classifiers](https://mlsanity.com/paper/2110.09192/) (2021)
- [Class-Conditional Conformal Prediction with Many Classes](https://mlsanity.com/paper/2306.09335/) (2023)
- [Image-to-Image Regression with Distribution-Free Uncertainty Quantification and Applications in Imaging](https://mlsanity.com/paper/2202.05265/) (2022)
- [A Survey on Uncertainty Quantification Methods for Deep Learning](https://mlsanity.com/paper/2302.13425/) (2023)
- [Training Uncertainty-Aware Classifiers with Conformalized Deep Learning](https://mlsanity.com/paper/2205.05878/) (2022)
- [Conformal Prediction for Natural Language Processing: A Survey](https://mlsanity.com/paper/2405.01976/) (2024)
- [Probabilistically robust conformal prediction](https://mlsanity.com/paper/2307.16360/) (2023)
- [Adaptive conformal classification with noisy labels](https://mlsanity.com/paper/2309.05092/) (2023)
- [Conformal Prediction: A Data Perspective](https://mlsanity.com/paper/2410.06494/) (2024)
- [Semantic uncertainty intervals for disentangled latent spaces](https://mlsanity.com/paper/2207.10074/) (2022)
- [Integrative conformal p-values for powerful out-of-distribution testing with labeled outliers](https://mlsanity.com/paper/2208.11111/) (2022)
- [Private Prediction Sets](https://mlsanity.com/paper/2102.06202/) (2021)
- [Conformal inference is (almost) free for neural networks trained with early stopping](https://mlsanity.com/paper/2301.11556/) (2023)
- [Backward Conformal Prediction](https://mlsanity.com/paper/2505.13732/) (2025)
- [Predictive Inference with Weak Supervision](https://mlsanity.com/paper/2201.08315/) (2022)
- [Do Multi-Document Summarization Models Synthesize?](https://mlsanity.com/paper/2301.13844/) (2023)
- [Conformal Risk Control for Ordinal Classification](https://mlsanity.com/paper/2405.00417/) (2024)
- [Building a stable classifier with the inflated argmax](https://mlsanity.com/paper/2405.14064/) (2024)
- [Conformal Prediction for Long-Tailed Classification](https://mlsanity.com/paper/2507.06867/) (2025)
- [Towards Certification of Uncertainty Calibration under Adversarial Attacks](https://mlsanity.com/paper/2405.13922/) (2024)
- [Distribution-Free Finite-Sample Guarantees and Split Conformal Prediction](https://mlsanity.com/paper/2210.14735/) (2022)
- [CAMMARL: Conformal Action Modeling in Multi Agent Reinforcement Learning](https://mlsanity.com/paper/2306.11128/) (2023)
- [Efficient Online Set-valued Classification with Bandit Feedback](https://mlsanity.com/paper/2405.04393/) (2024)
- [An Empirical Study of Conformal Prediction in LLM with ASP Scaffolds for Robust Reasoning](https://mlsanity.com/paper/2503.05439/) (2025)
- [Conformalized Semi-supervised Random Forest for Classification and Abnormality Detection](https://mlsanity.com/paper/2302.02237/) (2023)
- [Distribution-free Conformal Prediction for Ordinal Classification](https://mlsanity.com/paper/2404.16610/) (2024)

## Abstract (arXiv)

Most classifiers operate by selecting the maximum of an estimate of the conditional distribution p(y|x) where x stands for the features of the instance to be classified and y denotes its label. This often results in a em hubristic bias: overconfidence in the assignment of a definite label. Usually, the observations are concentrated on a small volume but the classifier provides definite predictions for the entire space. We propose constructing conformal prediction sets which contain a set of labels rather than a single label. These conformal prediction sets contain the true label with probability 1-α. Our construction is based on p(x|y) rather than p(y|x) which results in a classifier that is very cautious: it outputs the null set --- meaning "I don't know" --- when the object does not resemble the training examples. An important property of our approach is that adversarial attacks are likely to be predicted as the null set or would also include the true label. We demonstrate the performance on the ImageNet ILSVRC dataset and the CelebA and IMDB-Wiki facial datasets using high dimensional features obtained from state of the art convolutional neural networks.