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fix README
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qiauil committed Aug 13, 2024
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10 changes: 5 additions & 5 deletions README.md
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<h6 align="center">Towards Conflict-free Training for everything!</h6>

<p align="center">
[<a href="https://arxiv.org/abs/2312.05320">Arxiv</a>][<a href="https://qiauil.github.io/ConFIG/">📖 Documentation & Examples</a>]
[<a href="https://arxiv.org/abs/2312.05320">Arxiv</a>][<a href="https://tum-pbs.github.io/ConFIG/">📖 Documentation & Examples</a>]
</p>

## About
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​ The ConFIG method obtains the conflict-free direction by calculating the inverse of the loss-specific gradients matrix:

$$
\boldsymbol{g}_{ConFIG}=\left(\sum_{i=1}^m \boldsymbol{g}_i^\top\boldsymbol{g}_u\right)\boldsymbol{g}_u,
\boldsymbol{g}_{ConFIG}=\left(\sum_{i=1}^{m} \boldsymbol{g}_{i}^\top\boldsymbol{g}_{u}\right)\boldsymbol{g}_u,
$$

$$
\boldsymbol{g}_u = \mathcal{U}\left[
[\mathcal{U}(\boldsymbol{g}_1),\mathcal{U}(\boldsymbol{g}_2),\cdots, \mathcal{U}(\boldsymbol{g}_m)]^{-\top} \mathbf{1}_m\right].
$$

Then the dot product between $\boldsymbol{g}_{ConFIG}$ and each loss-specific gradient is always positive and equal, i.e., $\boldsymbol{g}_i^\top\boldsymbol{g}_{ConFIG}=\boldsymbol{g}_i^\top\boldsymbol{g}_{ConFIG} \quad \forall i,j \in [1,m]$​.
Then the dot product between $\boldsymbol{g}_{ConFIG}$ and each loss-specific gradient is always positive and equal, i.e., $\boldsymbol{g}_{i}^{\top}\boldsymbol{g}_{ConFIG}=\boldsymbol{g}_{i}^{\top}\boldsymbol{g}_{ConFIG} \quad \forall i,j \in [1,m]$​.

* **Is the ConFIG Computationally expensive?**

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## Paper Info

<h4 align="center">ConFIG: Towards Conflict-free Training of Physics Informed Neural Networks</h4>
<h6 align="center"><img src="./docs/assets/TUM.svg" width="16"><a href="https://qiauil.github.io/">Qiang Liu</a>, <img src="./docs/assets/PKU.svg" width="16"><a href="https://rachelcmy.github.io/">Mengyu Chu</a> and <img src="./docs/assets/TUM.svg" width="16"> <a href="https://ge.in.tum.de/about/n-thuerey/">Nils Thuerey</a></h6>
<h6 align="center"><img src="./docs/assets/TUM.svg" width="16"><a href="https://tum-pbs.github.io/">Qiang Liu</a>, <img src="./docs/assets/PKU.svg" width="16"><a href="https://rachelcmy.github.io/">Mengyu Chu</a> and <img src="./docs/assets/TUM.svg" width="16"> <a href="https://ge.in.tum.de/about/n-thuerey/">Nils Thuerey</a></h6>

<h6 align="center">
<img src="./docs/assets/TUM.svg" width="16"> Technical University of Munich
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optimizer.step()
```

More details and examples can be found in our [doc page](https://qiauil.github.io/ConFIG/).
More details and examples can be found in our [doc page](https://tum-pbs.github.io/ConFIG/).

To reproduce the result in our paper, please check the [experiments](https://github.com/tum-pbs/ConFIG/tree/main/experiments) folder.

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2 changes: 1 addition & 1 deletion mkdocs.yml
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site_name: ConFIG
site_description: Official Implementation for Conflict-Free Inverse Gradients Method.
site_author: Qiang Liu
site_url: https://qiauil.github.io/ConFIG
site_url: https://tum-pbs.github.io/ConFIG

repo_url: https://github.com/tum-pbs/ConFIG
repo_name: tum-pbs/ConFIG
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