# Estimating Neural Network Robustness via Lipschitz Constant and Architecture Sensitivity

arXiv: https://arxiv.org/abs/2410.23382 · HTML: https://mlsanity.com/paper/2410.23382/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 26 of its 38 references that are in the map.
- First posted on arXiv 30 Oct 2024.

## Builds on (most cited first, 26 of 26)

- [Explaining and Harnessing Adversarial Examples](https://mlsanity.com/paper/1412.6572/) (2014)
- [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)
- [Neural Tangent Kernel: Convergence and Generalization in Neural Networks](https://mlsanity.com/paper/1806.07572/) (2018)
- [Spectrally-normalized margin bounds for neural networks](https://mlsanity.com/paper/1706.08498/) (2017)
- [Efficient Neural Network Robustness Certification with General Activation Functions](https://mlsanity.com/paper/1811.00866/) (2018)
- [A Survey of Deep Learning Techniques for Autonomous Driving](https://mlsanity.com/paper/1910.07738/) (2019)
- [Safe Learning in Robotics: From Learning-Based Control to Safe Reinforcement Learning](https://mlsanity.com/paper/2108.06266/) (2021)
- [On the Effectiveness of Interval Bound Propagation for Training Verifiably Robust Models](https://mlsanity.com/paper/1810.12715/) (2018)
- [Efficient and Accurate Estimation of Lipschitz Constants for Deep Neural Networks](https://mlsanity.com/paper/1906.04893/) (2019)
- [Towards Fast Computation of Certified Robustness for ReLU Networks](https://mlsanity.com/paper/1804.09699/) (2018)
- [Algorithms for Verifying Deep Neural Networks](https://mlsanity.com/paper/1903.06758/) (2019)
- [Spectral Norm Regularization for Improving the Generalizability of Deep Learning](https://mlsanity.com/paper/1705.10941/) (2017)
- [Evaluating the Robustness of Neural Networks: An Extreme Value Theory Approach](https://mlsanity.com/paper/1801.10578/) (2018)
- [Using Simulation and Domain Adaptation to Improve Efficiency of Deep Robotic Grasping](https://mlsanity.com/paper/1709.07857/) (2017)
- [The Limits and Potentials of Deep Learning for Robotics](https://mlsanity.com/paper/1804.06557/) (2018)
- [Preventing Gradient Attenuation in Lipschitz Constrained Convolutional Networks](https://mlsanity.com/paper/1911.00937/) (2019)
- [Lipschitz constant estimation of Neural Networks via sparse polynomial optimization](https://mlsanity.com/paper/2004.08688/) (2020)
- [Tight Bounds on the Smallest Eigenvalue of the Neural Tangent Kernel for Deep ReLU Networks](https://mlsanity.com/paper/2012.11654/) (2020)
- [Rethinking Lipschitz Neural Networks and Certified Robustness: A Boolean Function Perspective](https://mlsanity.com/paper/2210.01787/) (2022)
- [Efficiently Computing Local Lipschitz Constants of Neural Networks via Bound Propagation](https://mlsanity.com/paper/2210.07394/) (2022)
- [GUARD: A Safe Reinforcement Learning Benchmark](https://mlsanity.com/paper/2305.13681/) (2023)
- [Adversarial Feature Training for Generalizable Robotic Visuomotor Control](https://mlsanity.com/paper/1909.07745/) (2019)
- [Robust Online Model Adaptation by Extended Kalman Filter with Exponential Moving Average and Dynamic Multi-Epoch Strategy](https://mlsanity.com/paper/1912.01790/) (2019)
- [Adaptable Human Intention and Trajectory Prediction for Human-Robot Collaboration](https://mlsanity.com/paper/1909.05089/) (2019)
- [Proactive Human-Robot Co-Assembly: Leveraging Human Intention Prediction and Robust Safe Control](https://mlsanity.com/paper/2306.11862/) (2023)

## Built on by (most cited first, 2 of 2)

- [Trends in Motion Prediction Toward Deployable and Generalizable Autonomy: A Revisit and Perspectives](https://mlsanity.com/paper/2505.09074/) (2025)
- [Failure Cases Are Better Learned But Boundary Says Sorry: Facilitating Smooth Perception Change for Accuracy-Robustness Trade-Off in Adversarial Training](https://mlsanity.com/paper/2508.02186/) (2025)

## Abstract (arXiv)

Ensuring neural network robustness is essential for the safe and reliable operation of robotic learning systems, especially in perception and decision-making tasks within real-world environments. This paper investigates the robustness of neural networks in perception systems, specifically examining their sensitivity to targeted, small-scale perturbations. We identify the Lipschitz constant as a key metric for quantifying and enhancing network robustness. We derive an analytical expression to compute the Lipschitz constant based on neural network architecture, providing a theoretical basis for estimating and improving robustness. Several experiments reveal the relationship between network design, the Lipschitz constant, and robustness, offering practical insights for developing safer, more robust robot learning systems.