# Robustness Certificates for Neural Networks Against Data Poisoning and Evasion Attacks

arXiv: https://arxiv.org/abs/2512.20865 · HTML: https://mlsanity.com/paper/2512.20865/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Backdoor and data poisoning attacks, one of 12 directions in LLM safety and security.
- Builds on 29 of its 39 references that are in the map.
- First posted on arXiv 24 Dec 2025.

## Placed in

- LLM safety and security / [Backdoor and data poisoning attacks](https://mlsanity.com/safety/backdoor-and-data-poisoning-attacks/)

## Builds on (most cited first, 29 of 29)

- [Towards Deep Learning Models Resistant to Adversarial Attacks](https://mlsanity.com/paper/1706.06083/) (2017)
- [Understanding Black-box Predictions via Influence Functions](https://mlsanity.com/paper/1703.04730/) (2017)
- [Reliable evaluation of adversarial robustness with an ensemble of diverse parameter-free attacks](https://mlsanity.com/paper/2003.01690/) (2020)
- [Certified Adversarial Robustness via Randomized Smoothing](https://mlsanity.com/paper/1902.02918/) (2019)
- [BadNets: Identifying Vulnerabilities in the Machine Learning Model Supply Chain](https://mlsanity.com/paper/1708.06733/) (2017)
- [Poison Frogs! Targeted Clean-Label Poisoning Attacks on Neural Networks](https://mlsanity.com/paper/1804.00792/) (2018)
- [Poisoning Web-Scale Training Datasets is Practical](https://mlsanity.com/paper/2302.10149/) (2023)
- [Dataset Security for Machine Learning: Data Poisoning, Backdoor Attacks, and Defenses](https://mlsanity.com/paper/2012.10544/) (2020)
- [Stronger Data Poisoning Attacks Break Data Sanitization Defenses](https://mlsanity.com/paper/1811.00741/) (2018)
- [MetaPoison: Practical General-purpose Clean-label Data Poisoning](https://mlsanity.com/paper/2004.00225/) (2020)
- [RAB: Provable Robustness Against Backdoor Attacks](https://mlsanity.com/paper/2003.08904/) (2020)
- [Just How Toxic is Data Poisoning? A Unified Benchmark for Backdoor and Data Poisoning Attacks](https://mlsanity.com/paper/2006.12557/) (2020)
- [Deep Partition Aggregation: Provable Defense against General Poisoning Attacks](https://mlsanity.com/paper/2006.14768/) (2020)
- [Certified Robustness to Label-Flipping Attacks via Randomized Smoothing](https://mlsanity.com/paper/2002.03018/) (2020)
- [Intrinsic Certified Robustness of Bagging against Data Poisoning Attacks](https://mlsanity.com/paper/2008.04495/) (2020)
- [Data Poisoning against Differentially-Private Learners: Attacks and Defenses](https://mlsanity.com/paper/1903.09860/) (2019)
- [On Certifying Robustness against Backdoor Attacks via Randomized Smoothing](https://mlsanity.com/paper/2002.11750/) (2020)
- [Bullseye Polytope: A Scalable Clean-Label Poisoning Attack with Improved Transferability](https://mlsanity.com/paper/2005.00191/) (2020)
- [Certified Robustness of Nearest Neighbors against Data Poisoning and Backdoor Attacks](https://mlsanity.com/paper/2012.03765/) (2020)
- [Improved Certified Defenses against Data Poisoning with (Deterministic) Finite Aggregation](https://mlsanity.com/paper/2202.02628/) (2022)
- [Certifying Robustness to Programmable Data Bias in Decision Trees](https://mlsanity.com/paper/2110.04363/) (2021)
- [BagFlip: A Certified Defense against Data Poisoning](https://mlsanity.com/paper/2205.13634/) (2022)
- [Certified Robustness to Data Poisoning in Gradient-Based Training](https://mlsanity.com/paper/2406.05670/) (2024)
- [Run-Off Election: Improved Provable Defense against Data Poisoning Attacks](https://mlsanity.com/paper/2302.02300/) (2023)
- [Unraveling the Connections between Privacy and Certified Robustness in Federated Learning Against Poisoning Attacks](https://mlsanity.com/paper/2209.04030/) (2022)
- [Analysis of Convolutions, Non-linearity and Depth in Graph Neural Networks using Neural Tangent Kernel](https://mlsanity.com/paper/2210.09809/) (2022)
- [SEEV: Synthesis with Efficient Exact Verification for ReLU Neural Barrier Functions](https://mlsanity.com/paper/2410.20326/) (2024)
- [Exact Certification of (Graph) Neural Networks Against Label Poisoning](https://mlsanity.com/paper/2412.00537/) (2024)
- [Provable Robustness of (Graph) Neural Networks Against Data Poisoning and Backdoor Attacks](https://mlsanity.com/paper/2407.10867/) (2024)

## Abstract (arXiv)

The increasing use of machine learning in safety-critical domains amplifies the risk of adversarial threats, especially data poisoning attacks that corrupt training data to degrade performance or induce unsafe behavior. Most existing defenses lack formal guarantees or rely on restrictive assumptions about the model class, attack type, extent of poisoning, or point-wise certification, limiting their practical reliability. This paper introduces a principled formal robustness certification framework that models gradient-based training as a discrete-time dynamical system (dt-DS) and formulates poisoning robustness as a formal safety verification problem. By adapting the concept of barrier certificates (BCs) from control theory, we introduce sufficient conditions to certify a robust radius ensuring that the terminal model remains safe under worst-case ℓp-norm-based poisoning. To make this practical, we parameterize BCs as neural networks trained on finite sets of poisoned trajectories. We further derive probably approximately correct (PAC) bounds by solving a scenario convex program (SCP), which yields a confidence lower bound on the certified robustness radius generalizing beyond the training set. Importantly, our framework also extends to certification against test-time attacks, making it the first unified framework to provide formal guarantees in both training and test-time attack settings. Experiments on MNIST, SVHN, CIFAR-10, and CIFAR-100 show that our approach certifies non-trivial perturbation budgets while being model-agnostic and requiring no prior knowledge of the attack or contamination level.