# Robustness Analysis of Classification Using Recurrent Neural Networks with Perturbed Sequential Input

arXiv: https://arxiv.org/abs/2203.05403 · HTML: https://mlsanity.com/paper/2203.05403/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 12 of its 33 references that are in the map.
- First posted on arXiv 10 Mar 2022.

## Builds on (most cited first, 12 of 12)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Very Deep Convolutional Networks for Large-Scale Image Recognition](https://mlsanity.com/paper/1409.1556/) (2014)
- [On Evaluating Adversarial Robustness](https://mlsanity.com/paper/1902.06705/) (2019)
- [The Limits and Potentials of Deep Learning for Robotics](https://mlsanity.com/paper/1804.06557/) (2018)
- [Learning Control Barrier Functions from Expert Demonstrations](https://mlsanity.com/paper/2004.03315/) (2020)
- [Stable Recurrent Models](https://mlsanity.com/paper/1805.10369/) (2018)
- [Structured Adversarial Attack: Towards General Implementation and Better Interpretability](https://mlsanity.com/paper/1808.01664/) (2018)
- [POPQORN: Quantifying Robustness of Recurrent Neural Networks](https://mlsanity.com/paper/1905.07387/) (2019)
- [Multi-Agent Image Classification via Reinforcement Learning](https://mlsanity.com/paper/1905.04835/) (2019)
- [Improved Network Robustness with Adversary Critic](https://mlsanity.com/paper/1810.12576/) (2018)
- [Robust Learning of Recurrent Neural Networks in Presence of Exogenous Noise](https://mlsanity.com/paper/2105.00996/) (2021)
- [A Layered Architecture for Active Perception: Image Classification using Deep Reinforcement Learning](https://mlsanity.com/paper/1909.09705/) (2019)

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

- [Robustness Certification of Visual Perception Models via Camera Motion Smoothing](https://mlsanity.com/paper/2210.04625/) (2022)
- [Symbolic Perception Risk in Autonomous Driving](https://mlsanity.com/paper/2303.09416/) (2023)

## Abstract (arXiv)

For a given stable recurrent neural network (RNN) that is trained to perform a classification task using sequential inputs, we quantify explicit robustness bounds as a function of trainable weight matrices. The sequential inputs can be perturbed in various ways, e.g., streaming images can be deformed due to robot motion or imperfect camera lens. Using the notion of the Voronoi diagram and Lipschitz properties of stable RNNs, we provide a thorough analysis and characterize the maximum allowable perturbations while guaranteeing the full accuracy of the classification task. We illustrate and validate our theoretical results using a map dataset with clouds as well as the MNIST dataset.