# Learning Security Classifiers with Verified Global Robustness Properties

arXiv: https://arxiv.org/abs/2105.11363 · HTML: https://mlsanity.com/paper/2105.11363/

## Key facts

- Cited by 14 papers in the map (data through 14 Oct 2026).
- Builds on 54 of its 101 references that are in the map.
- First posted on arXiv 24 May 2021.

## Builds on (most cited first, 30 of 54)

- [Towards Deep Learning Models Resistant to Adversarial Attacks](https://mlsanity.com/paper/1706.06083/) (2017)
- [XGBoost: A Scalable Tree Boosting System](https://mlsanity.com/paper/1603.02754/) (2016)
- [Intriguing properties of neural networks](https://mlsanity.com/paper/1312.6199/) (2013)
- [Certified Adversarial Robustness via Randomized Smoothing](https://mlsanity.com/paper/1902.02918/) (2019)
- [Adversarial Machine Learning at Scale](https://mlsanity.com/paper/1611.01236/) (2016)
- [Reluplex: An Efficient SMT Solver for Verifying Deep Neural Networks](https://mlsanity.com/paper/1702.01135/) (2017)
- [Provable defenses against adversarial examples via the convex outer adversarial polytope](https://mlsanity.com/paper/1711.00851/) (2017)
- [Certified Robustness to Adversarial Examples with Differential Privacy](https://mlsanity.com/paper/1802.03471/) (2018)
- [Efficient Neural Network Robustness Certification with General Activation Functions](https://mlsanity.com/paper/1811.00866/) (2018)
- [Provably Robust Deep Learning via Adversarially Trained Smoothed Classifiers](https://mlsanity.com/paper/1906.04584/) (2019)
- [Regularisation of Neural Networks by Enforcing Lipschitz Continuity](https://mlsanity.com/paper/1804.04368/) (2018)
- [Certified Defenses against Adversarial Examples](https://mlsanity.com/paper/1801.09344/) (2018)
- [Parseval Networks: Improving Robustness to Adversarial Examples](https://mlsanity.com/paper/1704.08847/) (2017)
- [Safety Verification of Deep Neural Networks](https://mlsanity.com/paper/1610.06940/) (2016)
- [Towards Fast Computation of Certified Robustness for ReLU Networks](https://mlsanity.com/paper/1804.09699/) (2018)
- [Formal Verification of Piece-Wise Linear Feed-Forward Neural Networks](https://mlsanity.com/paper/1705.01320/) (2017)
- [Sorting out Lipschitz function approximation](https://mlsanity.com/paper/1811.05381/) (2018)
- [Towards Stable and Efficient Training of Verifiably Robust Neural Networks](https://mlsanity.com/paper/1906.06316/) (2019)
- [Fast and Complete: Enabling Complete Neural Network Verification with Rapid and Massively Parallel Incomplete Verifiers](https://mlsanity.com/paper/2011.13824/) (2020)
- [Formal Guarantees on the Robustness of a Classifier against Adversarial Manipulation](https://mlsanity.com/paper/1705.08475/) (2017)
- [Formal Security Analysis of Neural Networks using Symbolic Intervals](https://mlsanity.com/paper/1804.10829/) (2018)
- [Evaluating the Robustness of Neural Networks: An Extreme Value Theory Approach](https://mlsanity.com/paper/1801.10578/) (2018)
- [Certified Adversarial Robustness with Additive Noise](https://mlsanity.com/paper/1809.03113/) (2018)
- [Semidefinite relaxations for certifying robustness to adversarial examples](https://mlsanity.com/paper/1811.01057/) (2018)
- [Efficient Formal Safety Analysis of Neural Networks](https://mlsanity.com/paper/1809.08098/) (2018)
- [Randomized Smoothing of All Shapes and Sizes](https://mlsanity.com/paper/2002.08118/) (2020)
- [Adversarial Robustness through Local Linearization](https://mlsanity.com/paper/1907.02610/) (2019)
- [Scaling provable adversarial defenses](https://mlsanity.com/paper/1805.12514/) (2018)
- [An approach to reachability analysis for feed-forward ReLU neural networks](https://mlsanity.com/paper/1706.07351/) (2017)
- [A Dual Approach to Scalable Verification of Deep Networks](https://mlsanity.com/paper/1803.06567/) (2018)

## Built on by (most cited first, 14 of 14)

- [Trustworthy AI: From Principles to Practices](https://mlsanity.com/paper/2110.01167/) (2021)
- [RS-Del: Edit Distance Robustness Certificates for Sequence Classifiers via Randomized Deletion](https://mlsanity.com/paper/2302.01757/) (2023)
- [Efficient Global Robustness Certification of Neural Networks via Interleaving Twin-Network Encoding](https://mlsanity.com/paper/2203.14141/) (2022)
- [Verification of Neural Networks' Global Robustness](https://mlsanity.com/paper/2402.19322/) (2024)
- [Explainable Global Fairness Verification of Tree-Based Classifiers](https://mlsanity.com/paper/2209.13179/) (2022)
- [Beyond Robustness: Resilience Verification of Tree-Based Classifiers](https://mlsanity.com/paper/2112.02705/) (2021)
- [Verifiable Learning for Robust Tree Ensembles](https://mlsanity.com/paper/2305.03626/) (2023)
- [What Distributions are Robust to Indiscriminate Poisoning Attacks for Linear Learners?](https://mlsanity.com/paper/2307.01073/) (2023)
- [The Pros and Cons of Adversarial Robustness](https://mlsanity.com/paper/2312.10911/) (2023)
- [VeriFlow: Modeling Distributions for Neural Network Verification](https://mlsanity.com/paper/2406.14265/) (2024)
- [Verifiable Boosted Tree Ensembles](https://mlsanity.com/paper/2402.14988/) (2024)
- [Like Oil and Water: Group Robustness Methods and Poisoning Defenses May Be at Odds](https://mlsanity.com/paper/2504.02142/) (2025)
- [Probably Approximately Global Robustness Certification](https://mlsanity.com/paper/2511.06495/) (2025)
- [On Robustness of Linear Classifiers to Targeted Data Poisoning](https://mlsanity.com/paper/2511.12722/) (2025)

## Abstract (arXiv)

Many recent works have proposed methods to train classifiers with local robustness properties, which can provably eliminate classes of evasion attacks for most inputs, but not all inputs. Since data distribution shift is very common in security applications, e.g., often observed for malware detection, local robustness cannot guarantee that the property holds for unseen inputs at the time of deploying the classifier. Therefore, it is more desirable to enforce global robustness properties that hold for all inputs, which is strictly stronger than local robustness. In this paper, we present a framework and tools for training classifiers that satisfy global robustness properties. We define new notions of global robustness that are more suitable for security classifiers. We design a novel booster-fixer training framework to enforce global robustness properties. We structure our classifier as an ensemble of logic rules and design a new verifier to verify the properties. In our training algorithm, the booster increases the classifier's capacity, and the fixer enforces verified global robustness properties following counterexample guided inductive synthesis. We show that we can train classifiers to satisfy different global robustness properties for three security datasets, and even multiple properties at the same time, with modest impact on the classifier's performance. For example, we train a Twitter spam account classifier to satisfy five global robustness properties, with 5.4% decrease in true positive rate, and 0.1% increase in false positive rate, compared to a baseline XGBoost model that doesn't satisfy any property.