# Towards Provably Unlearnable Examples via Bayes Error Optimisation

arXiv: https://arxiv.org/abs/2511.08191 · HTML: https://mlsanity.com/paper/2511.08191/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 20 of its 36 references that are in the map.
- First posted on arXiv 11 Nov 2025.

## Builds on (most cited first, 20 of 20)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Scaling Laws for Neural Language Models](https://mlsanity.com/paper/2001.08361/) (2020)
- [Towards Deep Learning Models Resistant to Adversarial Attacks](https://mlsanity.com/paper/1706.06083/) (2017)
- [SGDR: Stochastic Gradient Descent with Warm Restarts](https://mlsanity.com/paper/1608.03983/) (2016)
- [Glow: Generative Flow with Invertible 1x1 Convolutions](https://mlsanity.com/paper/1807.03039/) (2018)
- [Theoretically Principled Trade-off between Robustness and Accuracy](https://mlsanity.com/paper/1901.08573/) (2019)
- [Unlearnable Examples: Making Personal Data Unexploitable](https://mlsanity.com/paper/2101.04898/) (2021)
- [Adversarial Examples Make Strong Poisons](https://mlsanity.com/paper/2106.10807/) (2021)
- [Beyond Sparsity: Tree Regularization of Deep Models for Interpretability](https://mlsanity.com/paper/1711.06178/) (2017)
- [Robust Unlearnable Examples: Protecting Data Against Adversarial Learning](https://mlsanity.com/paper/2203.14533/) (2022)
- [Can Vision Transformers Learn without Natural Images?](https://mlsanity.com/paper/2103.13023/) (2021)
- [Stable Unlearnable Example: Enhancing the Robustness of Unlearnable Examples via Stable Error-Minimizing Noise](https://mlsanity.com/paper/2311.13091/) (2023)
- [Exploring the Limits of Model-Targeted Indiscriminate Data Poisoning Attacks](https://mlsanity.com/paper/2303.03592/) (2023)
- [Evaluating State-of-the-Art Classification Models Against Bayes Optimality](https://mlsanity.com/paper/2106.03357/) (2021)
- [Empirically Estimable Classification Bounds Based on a New Divergence Measure](https://mlsanity.com/paper/1412.6534/) (2014)
- [Learning to Bound the Multi-class Bayes Error](https://mlsanity.com/paper/1811.06419/) (2018)
- [Evaluating Bayes Error Estimators on Real-World Datasets with FeeBee](https://mlsanity.com/paper/2108.13034/) (2021)
- [Certified Robust Accuracy of Neural Networks Are Bounded due to Bayes Errors](https://mlsanity.com/paper/2405.11547/) (2024)
- [Reliable Robustness Evaluation via Automatically Constructed Attack Ensembles](https://mlsanity.com/paper/2211.12713/) (2022)
- [How Does Bayes Error Limit Probabilistic Robust Accuracy](https://mlsanity.com/paper/2405.14923/) (2024)

## Abstract (arXiv)

The recent success of machine learning models, especially large-scale classifiers and language models, relies heavily on training with massive data. These data are often collected from online sources. This raises serious concerns about the protection of user data, as individuals may not have given consent for their data to be used in training. To address this concern, recent studies introduce the concept of unlearnable examples, i.e., data instances that appear natural but are intentionally altered to prevent models from effectively learning from them. While existing methods demonstrate empirical effectiveness, they typically rely on heuristic trials and lack formal guarantees. Besides, when unlearnable examples are mixed with clean data, as is often the case in practice, their unlearnability disappears. In this work, we propose a novel approach to constructing unlearnable examples by systematically maximising the Bayes error, a measurement of irreducible classification error. We develop an optimisation-based approach and provide an efficient solution using projected gradient ascent. Our method provably increases the Bayes error and remains effective when the unlearning examples are mixed with clean samples. Experimental results across multiple datasets and model architectures are consistent with our theoretical analysis and show that our approach can restrict data learnability, effectively in practice.