# Bridging Robustness and Generalization Against Word Substitution Attacks in NLP via the Growth Bound Matrix Approach

arXiv: https://arxiv.org/abs/2507.10330 · HTML: https://mlsanity.com/paper/2507.10330/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 29 of its 52 references that are in the map.
- First posted on arXiv 14 Jul 2025.

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

- [Explaining and Harnessing Adversarial Examples](https://mlsanity.com/paper/1412.6572/) (2014)
- [Towards Deep Learning Models Resistant to Adversarial Attacks](https://mlsanity.com/paper/1706.06083/) (2017)
- [Mamba: Linear-Time Sequence Modeling with Selective State Spaces](https://mlsanity.com/paper/2312.00752/) (2023)
- [Character-level Convolutional Networks for Text Classification](https://mlsanity.com/paper/1509.01626/) (2015)
- [Convolutional Neural Networks for Sentence Classification](https://mlsanity.com/paper/1408.5882/) (2014)
- [Is BERT Really Robust? A Strong Baseline for Natural Language Attack on Text Classification and Entailment](https://mlsanity.com/paper/1907.11932/) (2019)
- [Generating Natural Language Adversarial Examples](https://mlsanity.com/paper/1804.07998/) (2018)
- [FreeLB: Enhanced Adversarial Training for Natural Language Understanding](https://mlsanity.com/paper/1909.11764/) (2019)
- [Algorithms for Verifying Deep Neural Networks](https://mlsanity.com/paper/1903.06758/) (2019)
- [Survey of Vulnerabilities in Large Language Models Revealed by Adversarial Attacks](https://mlsanity.com/paper/2310.10844/) (2023)
- [Certified Robustness to Adversarial Word Substitutions](https://mlsanity.com/paper/1909.00986/) (2019)
- [Combating Adversarial Misspellings with Robust Word Recognition](https://mlsanity.com/paper/1905.11268/) (2019)
- [InfoBERT: Improving Robustness of Language Models from An Information Theoretic Perspective](https://mlsanity.com/paper/2010.02329/) (2020)
- [Achieving Verified Robustness to Symbol Substitutions via Interval Bound Propagation](https://mlsanity.com/paper/1909.01492/) (2019)
- [OpenAttack: An Open-source Textual Adversarial Attack Toolkit](https://mlsanity.com/paper/2009.09191/) (2020)
- [SAFER: A Structure-free Approach for Certified Robustness to Adversarial Word Substitutions](https://mlsanity.com/paper/2005.14424/) (2020)
- [Towards Robustness Against Natural Language Word Substitutions](https://mlsanity.com/paper/2107.13541/) (2021)
- [Certified Robustness to Text Adversarial Attacks by Randomized [MASK]](https://mlsanity.com/paper/2105.03743/) (2021)
- [Searching for an Effective Defender: Benchmarking Defense against Adversarial Word Substitution](https://mlsanity.com/paper/2108.12777/) (2021)
- [Universal Adversarial Attacks with Natural Triggers for Text Classification](https://mlsanity.com/paper/2005.00174/) (2020)
- [Generating Natural Language Attacks in a Hard Label Black Box Setting](https://mlsanity.com/paper/2012.14956/) (2020)
- [Natural Language Adversarial Defense through Synonym Encoding](https://mlsanity.com/paper/1909.06723/) (2019)
- [From Hero to Z'eroe: A Benchmark of Low-Level Adversarial Attacks](https://mlsanity.com/paper/2010.05648/) (2020)
- [Text-CRS: A Generalized Certified Robustness Framework against Textual Adversarial Attacks](https://mlsanity.com/paper/2307.16630/) (2023)
- [Defense against Adversarial Attacks in NLP via Dirichlet Neighborhood Ensemble](https://mlsanity.com/paper/2006.11627/) (2020)
- [Achieving Model Robustness through Discrete Adversarial Training](https://mlsanity.com/paper/2104.05062/) (2021)
- [Assessing Adversarial Robustness of Large Language Models: An Empirical Study](https://mlsanity.com/paper/2405.02764/) (2024)
- [Certified Robustness to Programmable Transformations in LSTMs](https://mlsanity.com/paper/2102.07818/) (2021)
- [Safety verification of Neural-Network-based controllers: a set invariance approach](https://mlsanity.com/paper/2312.11352/) (2023)

## Built on by (most cited first, 1 of 1)

- [S-GBT: Smooth Growth Bound Tensor for Certified Robustness Against Word Substitution Attacks in NLP](https://mlsanity.com/paper/2606.13439/) (2026)

## Abstract (arXiv)

Despite advancements in Natural Language Processing (NLP), models remain vulnerable to adversarial attacks, such as synonym substitutions. While prior work has focused on improving robustness for feed-forward and convolutional architectures, the robustness of recurrent networks and modern state space models (SSMs), such as S4, remains understudied. These architectures pose unique challenges due to their sequential processing and complex parameter dynamics. In this paper, we introduce a novel regularization technique based on Growth Bound Matrices (GBM) to improve NLP model robustness by reducing the impact of input perturbations on model outputs. We focus on computing the GBM for three architectures: Long Short-Term Memory (LSTM), State Space models (S4), and Convolutional Neural Networks (CNN). Our method aims to (1) enhance resilience against word substitution attacks, (2) improve generalization on clean text, and (3) providing the first systematic analysis of SSM (S4) robustness. Extensive experiments across multiple architectures and benchmark datasets demonstrate that our method improves adversarial robustness by up to 8.8% over existing baselines. These results highlight the effectiveness of our approach, outperforming several state-of-the-art methods in adversarial defense. Codes are available at https://github.com/BouriMohammed/GBM