# HODA: Hardness-Oriented Detection of Model Extraction Attacks

arXiv: https://arxiv.org/abs/2106.11424 · HTML: https://mlsanity.com/paper/2106.11424/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 41 of its 64 references that are in the map.
- First posted on arXiv 21 Jun 2021.

## Builds on (most cited first, 30 of 41)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Explaining and Harnessing Adversarial Examples](https://mlsanity.com/paper/1412.6572/) (2014)
- [Densely Connected Convolutional Networks](https://mlsanity.com/paper/1608.06993/) (2016)
- [Towards Deep Learning Models Resistant to Adversarial Attacks](https://mlsanity.com/paper/1706.06083/) (2017)
- [Intriguing properties of neural networks](https://mlsanity.com/paper/1312.6199/) (2013)
- [MobileNetV2: Inverted Residuals and Linear Bottlenecks](https://mlsanity.com/paper/1801.04381/) (2018)
- [Towards Evaluating the Robustness of Neural Networks](https://mlsanity.com/paper/1608.04644/) (2016)
- [A Baseline for Detecting Misclassified and Out-of-Distribution Examples in Neural Networks](https://mlsanity.com/paper/1610.02136/) (2016)
- [Membership Inference Attacks against Machine Learning Models](https://mlsanity.com/paper/1610.05820/) (2016)
- [Reliable evaluation of adversarial robustness with an ensemble of diverse parameter-free attacks](https://mlsanity.com/paper/2003.01690/) (2020)
- [Enhancing The Reliability of Out-of-distribution Image Detection in Neural Networks](https://mlsanity.com/paper/1706.02690/) (2017)
- [Practical Black-Box Attacks against Machine Learning](https://mlsanity.com/paper/1602.02697/) (2016)
- [An Empirical Study of Example Forgetting during Deep Neural Network Learning](https://mlsanity.com/paper/1812.05159/) (2018)
- [Stealing Machine Learning Models via Prediction APIs](https://mlsanity.com/paper/1609.02943/) (2016)
- [Generalized ODIN: Detecting Out-of-distribution Image without Learning from Out-of-distribution Data](https://mlsanity.com/paper/2002.11297/) (2020)
- [Turning Your Weakness Into a Strength: Watermarking Deep Neural Networks by Backdooring](https://mlsanity.com/paper/1802.04633/) (2018)
- [Knockoff Nets: Stealing Functionality of Black-Box Models](https://mlsanity.com/paper/1812.02766/) (2018)
- [High Accuracy and High Fidelity Extraction of Neural Networks](https://mlsanity.com/paper/1909.01838/) (2019)
- [PRADA: Protecting against DNN Model Stealing Attacks](https://mlsanity.com/paper/1805.02628/) (2018)
- [Entangled Watermarks as a Defense against Model Extraction](https://mlsanity.com/paper/2002.12200/) (2020)
- [Deep Learning Through the Lens of Example Difficulty](https://mlsanity.com/paper/2106.09647/) (2021)
- [Thieves on Sesame Street! Model Extraction of BERT-based APIs](https://mlsanity.com/paper/1910.12366/) (2019)
- [Data-Free Model Extraction](https://mlsanity.com/paper/2011.14779/) (2020)
- [Stealing Hyperparameters in Machine Learning](https://mlsanity.com/paper/1802.05351/) (2018)
- [Stealing Links from Graph Neural Networks](https://mlsanity.com/paper/2005.02131/) (2020)
- [DAWN: Dynamic Adversarial Watermarking of Neural Networks](https://mlsanity.com/paper/1906.00830/) (2019)
- [MAZE: Data-Free Model Stealing Attack Using Zeroth-Order Gradient Estimation](https://mlsanity.com/paper/2005.03161/) (2020)
- [Characterizing Structural Regularities of Labeled Data in Overparameterized Models](https://mlsanity.com/paper/2002.03206/) (2020)
- [Exploring Connections Between Active Learning and Model Extraction](https://mlsanity.com/paper/1811.02054/) (2018)
- [Prediction Poisoning: Towards Defenses Against DNN Model Stealing Attacks](https://mlsanity.com/paper/1906.10908/) (2019)

## Built on by (most cited first, 3 of 3)

- [I Know What You Trained Last Summer: A Survey on Stealing Machine Learning Models and Defences](https://mlsanity.com/paper/2206.08451/) (2022)
- [AI Security in the Foundation Model Era: A Comprehensive Survey from a Unified Perspective](https://mlsanity.com/paper/2603.24857/) (2026)
- [The Limits of Query Monitoring against Distributed Model Extraction](https://mlsanity.com/paper/2610.13083/) (2026)

## Abstract (arXiv)

Model Extraction attacks exploit the target model's prediction API to create a surrogate model in order to steal or reconnoiter the functionality of the target model in the black-box setting. Several recent studies have shown that a data-limited adversary who has no or limited access to the samples from the target model's training data distribution can use synthesis or semantically similar samples to conduct model extraction attacks. In this paper, we define the hardness degree of a sample using the concept of learning difficulty. The hardness degree of a sample depends on the epoch number that the predicted label of that sample converges. We investigate the hardness degree of samples and demonstrate that the hardness degree histogram of a data-limited adversary's sample sequences is distinguishable from the hardness degree histogram of benign users' samples sequences. We propose Hardness-Oriented Detection Approach (HODA) to detect the sample sequences of model extraction attacks. The results demonstrate that HODA can detect the sample sequences of model extraction attacks with a high success rate by only monitoring 100 samples of them, and it outperforms all previous model extraction detection methods.