# Dynamical Low-Rank Compression of Neural Networks with Robustness under Adversarial Attacks

arXiv: https://arxiv.org/abs/2505.08022 · HTML: https://mlsanity.com/paper/2505.08022/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Builds on 37 of its 55 references that are in the map.
- First posted on arXiv 12 May 2025.

## Builds on (most cited first, 30 of 37)

- [LoRA: Low-Rank Adaptation of Large Language Models](https://mlsanity.com/paper/2106.09685/) (2021)
- [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)
- [Spectral Normalization for Generative Adversarial Networks](https://mlsanity.com/paper/1802.05957/) (2018)
- [Theoretically Principled Trade-off between Robustness and Accuracy](https://mlsanity.com/paper/1901.08573/) (2019)
- [Adversarial Machine Learning at Scale](https://mlsanity.com/paper/1611.01236/) (2016)
- [Ensemble Adversarial Training: Attacks and Defenses](https://mlsanity.com/paper/1705.07204/) (2017)
- [Intrinsic Dimensionality Explains the Effectiveness of Language Model Fine-Tuning](https://mlsanity.com/paper/2012.13255/) (2020)
- [GaLore: Memory-Efficient LLM Training by Gradient Low-Rank Projection](https://mlsanity.com/paper/2403.03507/) (2024)
- [AdaLoRA: Adaptive Budget Allocation for Parameter-Efficient Fine-Tuning](https://mlsanity.com/paper/2303.10512/) (2023)
- [Nesterov Accelerated Gradient and Scale Invariance for Adversarial Attacks](https://mlsanity.com/paper/1908.06281/) (2019)
- [Exploiting Linear Structure Within Convolutional Networks for Efficient Evaluation](https://mlsanity.com/paper/1404.0736/) (2014)
- [Parseval Networks: Improving Robustness to Adversarial Examples](https://mlsanity.com/paper/1704.08847/) (2017)
- [Dynamic Network Surgery for Efficient DNNs](https://mlsanity.com/paper/1608.04493/) (2016)
- [DyLoRA: Parameter Efficient Tuning of Pre-trained Models using Dynamic Search-Free Low-Rank Adaptation](https://mlsanity.com/paper/2210.07558/) (2022)
- [Sorting out Lipschitz function approximation](https://mlsanity.com/paper/1811.05381/) (2018)
- [Speeding-up Convolutional Neural Networks Using Fine-tuned CP-Decomposition](https://mlsanity.com/paper/1412.6553/) (2014)
- [Formal Guarantees on the Robustness of a Classifier against Adversarial Manipulation](https://mlsanity.com/paper/1705.08475/) (2017)
- [Efficient Riemannian Optimization on the Stiefel Manifold via the Cayley Transform](https://mlsanity.com/paper/2002.01113/) (2020)
- [Adv-BNN: Improved Adversarial Defense through Robust Bayesian Neural Network](https://mlsanity.com/paper/1810.01279/) (2018)
- [Pufferfish: Communication-efficient Models At No Extra Cost](https://mlsanity.com/paper/2103.03936/) (2021)
- [All You Need is Beyond a Good Init: Exploring Better Solution for Training Extremely Deep Convolutional Neural Networks with Orthonormality and Modulation](https://mlsanity.com/paper/1703.01827/) (2017)
- [Learning Low-rank Deep Neural Networks via Singular Vector Orthogonality Regularization and Singular Value Sparsification](https://mlsanity.com/paper/2004.09031/) (2020)
- [Analytic Insights into Structure and Rank of Neural Network Hessian Maps](https://mlsanity.com/paper/2106.16225/) (2021)
- [Low-rank lottery tickets: finding efficient low-rank neural networks via matrix differential equations](https://mlsanity.com/paper/2205.13571/) (2022)
- [DoRA: Enhancing Parameter-Efficient Fine-Tuning with Dynamic Rank Distribution](https://mlsanity.com/paper/2405.17357/) (2024)
- [Exploring Misclassifications of Robust Neural Networks to Enhance Adversarial Attacks](https://mlsanity.com/paper/2105.10304/) (2021)
- [Universal Adversarial Examples in Remote Sensing: Methodology and Benchmark](https://mlsanity.com/paper/2202.07054/) (2022)
- [On the Effect of Pruning on Adversarial Robustness](https://mlsanity.com/paper/2108.04890/) (2021)
- [Generative Adversarial Trainer: Defense to Adversarial Perturbations with GAN](https://mlsanity.com/paper/1705.03387/) (2017)

## Built on by (most cited first, 6 of 6)

- [StelLA: Subspace Learning in Low-rank Adaptation using Stiefel Manifold](https://mlsanity.com/paper/2510.01938/) (2025)
- [A geometric framework for momentum-based optimizers for low-rank training](https://mlsanity.com/paper/2506.17475/) (2025)
- [Mitigating Subject Dependency in EEG Decoding with Subject-Specific Low-Rank Adapters](https://mlsanity.com/paper/2510.08059/) (2025)
- [Compressing Vision Transformers in Geospatial Transfer Learning with Manifold-Constrained Optimization](https://mlsanity.com/paper/2601.08882/) (2026)
- [RepUCB: Representation Learning-Based UCB for Heterogeneous Multi-Task Linear Bandits](https://mlsanity.com/paper/2604.00531/) (2026)
- [Dynamical low-rank equilibrium computation for stochastic games between advanced persistent threats and moving target defense](https://mlsanity.com/paper/2610.06885/) (2026)

## Abstract (arXiv)

Deployment of neural networks on resource-constrained devices demands models that are both compact and robust to adversarial inputs. However, compression and adversarial robustness often conflict. In this work, we introduce a dynamical low-rank training scheme enhanced with a novel spectral regularizer that controls the condition number of the low-rank core in each layer. This approach mitigates the sensitivity of compressed models to adversarial perturbations without sacrificing accuracy on clean data. The method is model- and data-agnostic, computationally efficient, and supports rank adaptivity to automatically compress the network at hand. Extensive experiments across standard architectures, datasets, and adversarial attacks show the regularized networks can achieve over 94% compression while recovering or improving adversarial accuracy relative to uncompressed baselines.