# Towards One-for-All Robustness Across a Continuum of Threat Levels

arXiv: https://arxiv.org/abs/2609.02440 · HTML: https://mlsanity.com/paper/2609.02440/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 21 of its 27 references that are in the map.
- First posted on arXiv 2 Sep 2026.

## Builds on (most cited first, 21 of 21)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [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)
- [FiLM: Visual Reasoning with a General Conditioning Layer](https://mlsanity.com/paper/1709.07871/) (2017)
- [Theoretically Principled Trade-off between Robustness and Accuracy](https://mlsanity.com/paper/1901.08573/) (2019)
- [Reliable evaluation of adversarial robustness with an ensemble of diverse parameter-free attacks](https://mlsanity.com/paper/2003.01690/) (2020)
- [WILDS: A Benchmark of in-the-Wild Distribution Shifts](https://mlsanity.com/paper/2012.07421/) (2020)
- [Overfitting in adversarially robust deep learning](https://mlsanity.com/paper/2002.11569/) (2020)
- [Uncovering the Limits of Adversarial Training against Norm-Bounded Adversarial Examples](https://mlsanity.com/paper/2010.03593/) (2020)
- [Improving Adversarial Robustness via Promoting Ensemble Diversity](https://mlsanity.com/paper/1901.08846/) (2019)
- [Adversarial Training and Robustness for Multiple Perturbations](https://mlsanity.com/paper/1904.13000/) (2019)
- [Perceptual Adversarial Robustness: Defense Against Unseen Threat Models](https://mlsanity.com/paper/2006.12655/) (2020)
- [Curriculum Adversarial Training](https://mlsanity.com/paper/1805.04807/) (2018)
- [Adversarial Robustness Against the Union of Multiple Perturbation Models](https://mlsanity.com/paper/1909.04068/) (2019)
- [Ensemble Methods as a Defense to Adversarial Perturbations Against Deep Neural Networks](https://mlsanity.com/paper/1709.03423/) (2017)
- [Robust Graph Neural Networks via Unbiased Aggregation](https://mlsanity.com/paper/2311.14934/) (2023)
- [Mixture of Robust Experts (MoRE):A Robust Denoising Method towards multiple perturbations](https://mlsanity.com/paper/2104.10586/) (2021)
- [ProTransformer: Robustify Transformers via Plug-and-Play Paradigm](https://mlsanity.com/paper/2410.23182/) (2024)
- [OODRobustBench: a Benchmark and Large-Scale Analysis of Adversarial Robustness under Distribution Shift](https://mlsanity.com/paper/2310.12793/) (2023)
- [Robustness Reprogramming for Representation Learning](https://mlsanity.com/paper/2410.04577/) (2024)
- [Boosting Adversarial Robustness and Generalization with Dictionary Structure](https://mlsanity.com/paper/2502.00834/) (2025)

## Abstract (arXiv)

Adversarially robust models often overfit to a specific attack budget, necessitating multiple specialized models for diverse and dynamic adversarial environments, a strategy that becomes fundamentally intractable as the threat space grows. This raises an open challenge: can we achieve strong robustness across a continuum of threat levels within a single model? We propose the Threat Conditional Network (TCN), grounded in a representation factorization framework that decomposes representation learning into a threat-invariant shared backbone and a lightweight threat-conditional adaptor. TCN conditions a single model on the perturbation level via Fourier-based embeddings and channel-wise affine modulation, and is trained against a distribution over perturbation budgets, enabling flexible and seamless adaptation across an infinite continuum of threat levels during inference. Extensive experiments on CIFAR-10, CIFAR-100, and Tiny-ImageNet show that TCN matches or surpasses a full ensemble of budget-specialized models with a single set of parameters, generalizes to unseen perturbation budgets, and transfers robustly under mismatched threat conditions, with only 4.6% parameter overhead. These contributions chart a promising path toward adaptive and generalizable robustness in dynamic and diverse threat environments.