SODEF

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# Stable Neural ODE with Lyapunov-Stable Equilibrium Points for Defending Against Adversarial Attacks
  
[Stable Neural ODE with Lyapunov-Stable Equilibrium Points for Defending Against Adversarial Attacks](https://openreview.net/forum?id=9CPc4EIr2t1).

Qiyu Kang, Yang Song, Qinxu Ding, Wee Peng Tay

## Environment settings

- OS: Ubuntu 18.04
- GPU: RTX 2080 Ti, RTX a5000, RTX 3090
- Cuda: 11.1 or 10.2
- Python: >=3.6
- PyTorch: >= 1.6.0
- Torchvision: >= 0.7.0
- pip install git+https://github.com/Lezcano/geotorch.git@0.2.0
- pip install torchdiffeq
- pip install git+https://github.com/RobustBench/robustbench.git

## Notification

__Training code is now added to Rebuffi2021Fixing_70_16_cutmix_extra.__

It seems git lfs is not working very well. The checkpoints can also be found [here](https://drive.google.com/drive/folders/1i7Cj-dvY-7LJWNKACsJDQZmyKiAlCEI9?usp=sharing).

## Empirical Evaluations

### Compatibility of SODEF:

### In this section, we show compatibility of SODEF using [TRADES](https://github.com/P2333/Bag-of-Tricks-for-AT/):

We append our SODEF after TRADES net to improve the model robustness against adversarial attacks. TRADES works as the feature extractor <img src="https://render.githubusercontent.com/render/math?math=h_{\boldsymbol{\phi}}"> as in our paper. Please note TRADES weights are kept fixed during the training. We use the pretrained model provided by [TRADES Repo](https://github.com/P2333/Bag-of-Tricks-for-AT/).

| Attack / Model | TRADES ℒ∞ | TRADES+SODEF ℒ∞ | TRADES ℒ2 | TRADES+SODEF ℒ2 |
|:------------------------------:|:--------------------:|:--------------------------:|:--------------------:|:--------------------------:|
| Clean | 85.48 | 85.18 | 85.48 | 85.18 |
| APGDCE | 56.08 | __70.90__ | 61.74 | __74.35__ |
| APGDDLRT | 53.70 | __64.15__ | 59.22 | __68.55__ |
| FABT | 54.18 | __82.92__ | 60.31 | __83.15__ |
| Square | 59.12 | __62.21__ | 72.65 | __76.02__ |
| AutoAttack | 53.69 | __57.76__ | 59.42 | __67.75__ |

Tab 1. Classification accuracy (%) using TRADES (w/ and w/o SODEF) under
[AutoAttack](https://github.com/fra31/auto-attack) on adversarial CIFAR10 examples with ℒ2 norm
(*ϵ* = 0.5) and ℒ∞ norm (*ϵ* = 8/255).

</div>

__Transfer attack__:

Classification accuracy for adv examples generated from original [pretrained model](https://github.com/P2333/Bag-of-Tricks-for-AT/) using AA ℒ∞ (*ϵ* = 8/255) attacks : 61.94%.

```python
cd trades_r
python sodef_eval_ode.py
```
```python
cd trades_r
sodef_eval_transfer.ipynb
```

### In this section, we show compatibility of SODEF using [Rebuffi2021](https://github.com/deepmind/deepmind-research/tree/master/adversarial_robustness):

Similar to the above section, we append SODEF after the pretrained model provided by the [RobustBench](https://github.com/RobustBench/robustbench) with keywords "Rebuffi2021Fixing_70_16_cutmix_extra". The weights are kept fixed during the training except the final FC layer. The pretrained model without SODEF achieves 66.58% accuracy under AutoAttack. We show that with SODEF, the robust accuracy could be improved to over 70%:

| Attack / Model |   Rebuffi2021    | [Rebuffi2021+SODEF](https://drive.google.com/file/d/1aaEPMXg1HI2rh-VZsBnjAFzg_Nh86ntp/view?usp=sharing) | Transfer Attack |
|:--------------:|:-----:|:------:|:---------------:|
|     Clean      | 92.23 |   93.73    |       NA        |  
|   AutoAttack   | 66.58 |   __71.28__    |       __73.38__    |

Tab 2. Classification accuracy (%) using (w/ and w/o SODEF) under AutoAttack on
adversarial CIFAR10 examples with ℒ∞ norm (*ϵ* = 8/255).

</div>

Here again for the transfer attack, adv examples are generated from original pretrained model using AA ℒ∞ (*ϵ* = 8/255) attacks. We will report results under each individual attack as in Tab 1. soon.

```python
cd Rebuffi2021Fixing_70_16_cutmix_extra
python sodef_eval_ode.py
```
```python
cd Rebuffi2021Fixing_70_16_cutmix_extra
python sodef_eval_transfer.py or sodef_eval_transfer.ipynb
```

SODEF

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