# Enhancing Certifiable Semantic Robustness via Robust Pruning of Deep Neural Networks

arXiv: https://arxiv.org/abs/2510.00083 · HTML: https://mlsanity.com/paper/2510.00083/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 28 of its 31 references that are in the map.
- First posted on arXiv 30 Sep 2025.

## Builds on (most cited first, 28 of 28)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Towards Deep Learning Models Resistant to Adversarial Attacks](https://mlsanity.com/paper/1706.06083/) (2017)
- [Towards Evaluating the Robustness of Neural Networks](https://mlsanity.com/paper/1608.04644/) (2016)
- [Deep Compression: Compressing Deep Neural Networks with Pruning, Trained Quantization and Huffman Coding](https://mlsanity.com/paper/1510.00149/) (2015)
- [The Lottery Ticket Hypothesis: Finding Sparse, Trainable Neural Networks](https://mlsanity.com/paper/1803.03635/) (2018)
- [Theoretically Principled Trade-off between Robustness and Accuracy](https://mlsanity.com/paper/1901.08573/) (2019)
- [Certified Adversarial Robustness via Randomized Smoothing](https://mlsanity.com/paper/1902.02918/) (2019)
- [Rethinking the Value of Network Pruning](https://mlsanity.com/paper/1810.05270/) (2018)
- [Efficient Neural Network Robustness Certification with General Activation Functions](https://mlsanity.com/paper/1811.00866/) (2018)
- [Lipschitz regularity of deep neural networks: analysis and efficient estimation](https://mlsanity.com/paper/1805.10965/) (2018)
- [Algorithms for Verifying Deep Neural Networks](https://mlsanity.com/paper/1903.06758/) (2019)
- [Statistical Aspects of Wasserstein Distances](https://mlsanity.com/paper/1806.05500/) (2018)
- [A Survey on Deep Neural Network Pruning-Taxonomy, Comparison, Analysis, and Recommendations](https://mlsanity.com/paper/2308.06767/) (2023)
- [Training robust neural networks using Lipschitz bounds](https://mlsanity.com/paper/2005.02929/) (2020)
- [Numerical Coordinate Regression with Convolutional Neural Networks](https://mlsanity.com/paper/1801.07372/) (2018)
- [RoboDepth: Robust Out-of-Distribution Depth Estimation under Corruptions](https://mlsanity.com/paper/2310.15171/) (2023)
- [On the Effect of Pruning on Adversarial Robustness](https://mlsanity.com/paper/2108.04890/) (2021)
- [The RoboDrive Challenge: Drive Anytime Anywhere in Any Condition](https://mlsanity.com/paper/2405.08816/) (2024)
- [Investigating the Impact of Multi-LiDAR Placement on Object Detection for Autonomous Driving](https://mlsanity.com/paper/2105.00373/) (2021)
- [Can pruning improve certified robustness of neural networks?](https://mlsanity.com/paper/2206.07311/) (2022)
- [Certifiable 3D Object Pose Estimation: Foundations, Learning Models, and Self-Training](https://mlsanity.com/paper/2206.11215/) (2022)
- [Linearity Grafting: Relaxed Neuron Pruning Helps Certifiable Robustness](https://mlsanity.com/paper/2206.07839/) (2022)
- [SeasonDepth: Cross-Season Monocular Depth Prediction Dataset and Benchmark under Multiple Environments](https://mlsanity.com/paper/2011.04408/) (2020)
- [Retrieval-based Localization Based on Domain-invariant Feature Learning under Changing Environments](https://mlsanity.com/paper/1909.10184/) (2019)
- [ModelVerification.jl: a Comprehensive Toolbox for Formally Verifying Deep Neural Networks](https://mlsanity.com/paper/2407.01639/) (2024)
- [Certifying Robustness of Learning-Based Keypoint Detection and Pose Estimation Methods](https://mlsanity.com/paper/2408.00117/) (2024)
- [Robustness Certification of Visual Perception Models via Camera Motion Smoothing](https://mlsanity.com/paper/2210.04625/) (2022)
- [Pixel-wise Smoothing for Certified Robustness against Camera Motion Perturbations](https://mlsanity.com/paper/2309.13150/) (2023)

## Abstract (arXiv)

Deep neural networks have been widely adopted in many vision and robotics applications with visual inputs. It is essential to verify its robustness against semantic transformation perturbations, such as brightness and contrast. However, current certified training and robustness certification methods face the challenge of over-parameterization, which hinders the tightness and scalability due to the over-complicated neural networks. To this end, we first analyze stability and variance of layers and neurons against input perturbation, showing that certifiable robustness can be indicated by a fundamental Unbiased and Smooth Neuron metric (USN). Based on USN, we introduce a novel neural network pruning method that removes neurons with low USN and retains those with high USN, thereby preserving model expressiveness without over-parameterization. To further enhance this pruning process, we propose a new Wasserstein distance loss to ensure that pruned neurons are more concentrated across layers. We validate our approach through extensive experiments on the challenging robust keypoint detection task, which involves realistic brightness and contrast perturbations, demonstrating that our method achieves superior robustness certification performance and efficiency compared to baselines.