# Formalizing Generalization and Robustness of Neural Networks to Weight Perturbations

arXiv: https://arxiv.org/abs/2103.02200 · HTML: https://mlsanity.com/paper/2103.02200/

## Key facts

- Cited by 22 papers in the map (data through 14 Oct 2026).
- Builds on 19 of its 39 references that are in the map.
- First posted on arXiv 3 Mar 2021.

## Builds on (most cited first, 19 of 19)

- [Towards Deep Learning Models Resistant to Adversarial Attacks](https://mlsanity.com/paper/1706.06083/) (2017)
- [Theoretically Principled Trade-off between Robustness and Accuracy](https://mlsanity.com/paper/1901.08573/) (2019)
- [Sharpness-Aware Minimization for Efficiently Improving Generalization](https://mlsanity.com/paper/2010.01412/) (2020)
- [On Large-Batch Training for Deep Learning: Generalization Gap and Sharp Minima](https://mlsanity.com/paper/1609.04836/) (2016)
- [Robustness May Be at Odds with Accuracy](https://mlsanity.com/paper/1805.12152/) (2018)
- [Exploring Generalization in Deep Learning](https://mlsanity.com/paper/1706.08947/) (2017)
- [Computing Nonvacuous Generalization Bounds for Deep (Stochastic) Neural Networks with Many More Parameters than Training Data](https://mlsanity.com/paper/1703.11008/) (2017)
- [Quantized Neural Networks: Training Neural Networks with Low Precision Weights and Activations](https://mlsanity.com/paper/1609.07061/) (2016)
- [A PAC-Bayesian Approach to Spectrally-Normalized Margin Bounds for Neural Networks](https://mlsanity.com/paper/1707.09564/) (2017)
- [Norm-Based Capacity Control in Neural Networks](https://mlsanity.com/paper/1503.00036/) (2015)
- [Size-Independent Sample Complexity of Neural Networks](https://mlsanity.com/paper/1712.06541/) (2017)
- [Uniform convergence may be unable to explain generalization in deep learning](https://mlsanity.com/paper/1902.04742/) (2019)
- [Is Robustness the Cost of Accuracy? -- A Comprehensive Study on the Robustness of 18 Deep Image Classification Models](https://mlsanity.com/paper/1808.01688/) (2018)
- [Rademacher Complexity for Adversarially Robust Generalization](https://mlsanity.com/paper/1810.11914/) (2018)
- [Bridging Mode Connectivity in Loss Landscapes and Adversarial Robustness](https://mlsanity.com/paper/2005.00060/) (2020)
- [Fault Sneaking Attack: a Stealthy Framework for Misleading Deep Neural Networks](https://mlsanity.com/paper/1905.12032/) (2019)
- [Approximation and Estimation for High-Dimensional Deep Learning Networks](https://mlsanity.com/paper/1809.03090/) (2018)
- [Diametrical Risk Minimization: Theory and Computations](https://mlsanity.com/paper/1910.10844/) (2019)
- [Global Capacity Measures for Deep ReLU Networks via Path Sampling](https://mlsanity.com/paper/1910.10245/) (2019)

## Built on by (most cited first, 22 of 22)

- [Rashomon Capacity: A Metric for Predictive Multiplicity in Classification](https://mlsanity.com/paper/2206.01295/) (2022)
- [Formalising the Robustness of Counterfactual Explanations for Neural Networks](https://mlsanity.com/paper/2208.14878/) (2022)
- [Computing-In-Memory Neural Network Accelerators for Safety-Critical Systems: Can Small Device Variations Be Disastrous?](https://mlsanity.com/paper/2207.07626/) (2022)
- [Holistic Adversarial Robustness of Deep Learning Models](https://mlsanity.com/paper/2202.07201/) (2022)
- [A.I. Robustness: a Human-Centered Perspective on Technological Challenges and Opportunities](https://mlsanity.com/paper/2210.08906/) (2022)
- [Improving Realistic Worst-Case Performance of NVCiM DNN Accelerators through Training with Right-Censored Gaussian Noise](https://mlsanity.com/paper/2307.15853/) (2023)
- [DPAdapter: Improving Differentially Private Deep Learning through Noise Tolerance Pre-training](https://mlsanity.com/paper/2403.02571/) (2024)
- [Interval Abstractions for Robust Counterfactual Explanations](https://mlsanity.com/paper/2404.13736/) (2024)
- [StealthAttack: Robust 3D Gaussian Splatting Poisoning via Density-Guided Illusions](https://mlsanity.com/paper/2510.02314/) (2025)
- [Exploring the cloud of feature interaction scores in a Rashomon set](https://mlsanity.com/paper/2305.10181/) (2023)
- [Investigating Weight-Perturbed Deep Neural Networks With Application in Iris Presentation Attack Detection](https://mlsanity.com/paper/2311.12764/) (2023)
- [Compute-in-Memory based Neural Network Accelerators for Safety-Critical Systems: Worst-Case Scenarios and Protections](https://mlsanity.com/paper/2312.06137/) (2023)
- [Practical Attribution Guidance for Rashomon Sets](https://mlsanity.com/paper/2407.18482/) (2024)
- [Adversarial Defence without Adversarial Defence: Enhancing Language Model Robustness via Instance-level Principal Component Removal](https://mlsanity.com/paper/2507.21750/) (2025)
- [Enhancing Offline Model-Based RL via Active Model Selection: A Bayesian Optimization Perspective](https://mlsanity.com/paper/2502.11480/) (2025)
- [A2SG:Adaptive and Asymmetric Surrogate Gradients for Training Deep Spiking Neural Networks](https://mlsanity.com/paper/2606.11236/) (2026)
- [Verification of Neural Networks Local Differential Classification Privacy](https://mlsanity.com/paper/2310.20299/) (2023)
- [Enhancing selectivity using Wasserstein distance based reweighing](https://mlsanity.com/paper/2401.11562/) (2024)
- [Beyond topography: Topographic regularization improves robustness and reshapes representations in convolutional neural networks](https://mlsanity.com/paper/2508.00043/) (2025)
- [MEASER: Malware embedding attacks on open-source LLMs](https://mlsanity.com/paper/2510.10486/) (2025)
- [NNV3: Expanding Neural Network Verification to New Architectures and Domains](https://mlsanity.com/paper/2609.30050/) (2026)
- [Security Properties of Neural Networks as Decision Problems](https://mlsanity.com/paper/2609.39768/) (2026)

## Abstract (arXiv)

Studying the sensitivity of weight perturbation in neural networks and its impacts on model performance, including generalization and robustness, is an active research topic due to its implications on a wide range of machine learning tasks such as model compression, generalization gap assessment, and adversarial attacks. In this paper, we provide the first integral study and analysis for feed-forward neural networks in terms of the robustness in pairwise class margin and its generalization behavior under weight perturbation. We further design a new theory-driven loss function for training generalizable and robust neural networks against weight perturbations. Empirical experiments are conducted to validate our theoretical analysis. Our results offer fundamental insights for characterizing the generalization and robustness of neural networks against weight perturbations.