# Robust CurveMoE: Multi-Norm Adversarial Defense for Mixture-of-Experts Models via Mode Connectivity

arXiv: https://arxiv.org/abs/2608.26043 · HTML: https://mlsanity.com/paper/2608.26043/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Vision mixture-of-experts, one of 12 directions in Mixture-of-experts.
- Builds on 20 of its 24 references that are in the map.
- First posted on arXiv 26 Aug 2026.

## Placed in

- Mixture-of-experts / [Vision mixture-of-experts](https://mlsanity.com/moe/vision-mixture-of-experts/)

## Builds on (most cited first, 20 of 20)

- [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)
- [Intriguing properties of neural networks](https://mlsanity.com/paper/1312.6199/) (2013)
- [Training data-efficient image transformers & distillation through attention](https://mlsanity.com/paper/2012.12877/) (2020)
- [Outrageously Large Neural Networks: The Sparsely-Gated Mixture-of-Experts Layer](https://mlsanity.com/paper/1701.06538/) (2017)
- [Switch Transformers: Scaling to Trillion Parameter Models with Simple and Efficient Sparsity](https://mlsanity.com/paper/2101.03961/) (2021)
- [Wide Residual Networks](https://mlsanity.com/paper/1605.07146/) (2016)
- [Reliable evaluation of adversarial robustness with an ensemble of diverse parameter-free attacks](https://mlsanity.com/paper/2003.01690/) (2020)
- [Model soups: averaging weights of multiple fine-tuned models improves accuracy without increasing inference time](https://mlsanity.com/paper/2203.05482/) (2022)
- [Scaling Vision with Sparse Mixture of Experts](https://mlsanity.com/paper/2106.05974/) (2021)
- [Linear Mode Connectivity and the Lottery Ticket Hypothesis](https://mlsanity.com/paper/1912.05671/) (2019)
- [Loss Surfaces, Mode Connectivity, and Fast Ensembling of DNNs](https://mlsanity.com/paper/1802.10026/) (2018)
- [Essentially No Barriers in Neural Network Energy Landscape](https://mlsanity.com/paper/1803.00885/) (2018)
- [Adversarial Training and Robustness for Multiple Perturbations](https://mlsanity.com/paper/1904.13000/) (2019)
- [Bridging Mode Connectivity in Loss Landscapes and Adversarial Robustness](https://mlsanity.com/paper/2005.00060/) (2020)
- [Adversarial Robustness Against the Union of Multiple Perturbation Models](https://mlsanity.com/paper/1909.04068/) (2019)
- [Robust Mixture-of-Expert Training for Convolutional Neural Networks](https://mlsanity.com/paper/2308.10110/) (2023)
- [On the Adversarial Robustness of Mixture of Experts](https://mlsanity.com/paper/2210.10253/) (2022)
- [Adversarial Robustness against Multiple and Single lp-Threat Models via Quick Fine-Tuning of Robust Classifiers](https://mlsanity.com/paper/2105.12508/) (2021)
- [Optimizing Robustness and Accuracy in Mixture of Experts: A Dual-Model Approach](https://mlsanity.com/paper/2502.06832/) (2025)

## Abstract (arXiv)

Multi-norm adversarial defense aims to protect neural networks against perturbations defined by different norm constraints, but existing methods typically optimize competing robustness objectives within a single parameter configuration, leading to substantial training cost and unfavorable robustness trade-offs. We propose Robust CurveMoE, an efficient mixture-of-experts framework that connects models specialized for different perturbation norms through a low-loss path and exploits the complementary robustness profiles of models along this path. Robust CurveMoE derives clean and norm-specialized experts from robustness-constrained curve locations and selectively expertizes only influential layers, while sharing the remaining parameters across routing paths. To further reduce curve-construction cost, we introduce contribution-guided partial updating, which selects influential curve parameters using initialization-based gradient scores. We also theoretically bound the objective gap between partial and full curve optimization. Experiments on CIFAR-100 and ImageNet-100 with WideResNet and Vision Transformer architectures show that Robust CurveMoE consistently improves clean, norm-specific, and Union accuracy over MSD and ERMC. In particular, it improves Union accuracy by 2.37 and 2.13 percentage points over the strongest baseline on CIFAR-100 and ImageNet-100, respectively. Extensive ablations further validate the effectiveness of partial updating, selective expertization, and robustness-constrained expert selection.