# Certified Training for Convolutional Perturbations

arXiv: https://arxiv.org/abs/2607.18195 · HTML: https://mlsanity.com/paper/2607.18195/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 44 of its 66 references that are in the map.
- First posted on arXiv 20 Jul 2026.

## Builds on (most cited first, 30 of 44)

- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Explaining and Harnessing Adversarial Examples](https://mlsanity.com/paper/1412.6572/) (2014)
- [Batch Normalization: Accelerating Deep Network Training by Reducing Internal Covariate Shift](https://mlsanity.com/paper/1502.03167/) (2015)
- [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)
- [Towards Evaluating the Robustness of Neural Networks](https://mlsanity.com/paper/1608.04644/) (2016)
- [Theoretically Principled Trade-off between Robustness and Accuracy](https://mlsanity.com/paper/1901.08573/) (2019)
- [The Limitations of Deep Learning in Adversarial Settings](https://mlsanity.com/paper/1511.07528/) (2015)
- [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)
- [Efficient Neural Network Robustness Certification with General Activation Functions](https://mlsanity.com/paper/1811.00866/) (2018)
- [On the Effectiveness of Interval Bound Propagation for Training Verifiably Robust Models](https://mlsanity.com/paper/1810.12715/) (2018)
- [Beta-CROWN: Efficient Bound Propagation with Per-neuron Split Constraints for Complete and Incomplete Neural Network Robustness Verification](https://mlsanity.com/paper/2103.06624/) (2021)
- [Algorithms for Verifying Deep Neural Networks](https://mlsanity.com/paper/1903.06758/) (2019)
- [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 Security Analysis of Neural Networks using Symbolic Intervals](https://mlsanity.com/paper/1804.10829/) (2018)
- [Efficient Formal Safety Analysis of Neural Networks](https://mlsanity.com/paper/1809.08098/) (2018)
- [Physically Realizable Adversarial Examples for LiDAR Object Detection](https://mlsanity.com/paper/2004.00543/) (2020)
- [SoK: Certified Robustness for Deep Neural Networks](https://mlsanity.com/paper/2009.04131/) (2020)
- [General Cutting Planes for Bound-Propagation-Based Neural Network Verification](https://mlsanity.com/paper/2208.05740/) (2022)
- [Complete Verification via Multi-Neuron Relaxation Guided Branch-and-Bound](https://mlsanity.com/paper/2205.00263/) (2022)
- [Robustness Verification for Transformers](https://mlsanity.com/paper/2002.06622/) (2020)
- [Training for Faster Adversarial Robustness Verification via Inducing ReLU Stability](https://mlsanity.com/paper/1809.03008/) (2018)
- [Certified Training: Small Boxes are All You Need](https://mlsanity.com/paper/2210.04871/) (2022)
- [Fast Certified Robust Training with Short Warmup](https://mlsanity.com/paper/2103.17268/) (2021)
- [Improved Branch and Bound for Neural Network Verification via Lagrangian Decomposition](https://mlsanity.com/paper/2104.06718/) (2021)
- [Scaling Polyhedral Neural Network Verification on GPUs](https://mlsanity.com/paper/2007.10868/) (2020)
- [Scalable Neural Network Verification with Branch-and-bound Inferred Cutting Planes](https://mlsanity.com/paper/2501.00200/) (2024)
- [Understanding Certified Training with Interval Bound Propagation](https://mlsanity.com/paper/2306.10426/) (2023)

## Abstract (arXiv)

Vision models have been found to be susceptible to perturbations such as motion blur induced at runtime by a shaking camera. This impedes their deployment in critical applications since phenomena such as slightly blurred vision might lead to failures, for example an object detector missing objects. While methods such as data augmentation or Adversarial Training can improve empirical robustness, they lack formal safety guarantees, making it difficult to identify and mitigate hidden vulnerabilities. We introduce a novel Certified Training approach that leverages an efficient encoding of convolutional perturbations to train provably robust models. Our method significantly outperforms Adversarial Training, achieving, for example, over 80% robust accuracy against motion blur of reasonable intensity on CIFAR10 while maintaining comparable standard accuracy.