This project was done for the Geometric Data Analysis course of the MVA Master (at ENS Paris-Saclay). I analyzed the paper Learning Smooth Neural Functions via Lipschitz Regularization, Liu et al. 2022, published in SIGGRAPH '22 Conference Proceedings. The authors present a novel regularization technique for deep neural networks, in order to learn smooth functions, which are particularly important when dealing with geometric tasks.
| Standard MLP | Lipschitz MLP |
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This repository is an enhanced version the official repository made by the authors, which is a demonstration of 2D interpolation using the proposed method. Although the code is similar here (the files in jaxgptoolbox were not modified), some nonnegligible modifications were made:
- While the demonstration was only for 2D, the code was modified to work for 3D too
- this includes rendering of the results as a video, using the Open3D library
- Improving the way training samples are generated, as the sampling is very time-consuming (especially in 3D) due to the signed distance function
- Adding more hyperparameters to allow more flexibility and experimentation (e.g. the activation function, the resolution, the possibility to use a pre-trained model, etc.)
An illustration of the results is shown above. The left image shows the interpolation of a rabbit to a cat, using a standard MLP. The right image shows the same interpolation, but using the Lipschitz MLP. The results are much smoother, and the interpolation is more natural.
- Hsueh-Ti Derek Liu, Francis Williams, Alec Jacobson, Sanja Fidler, and Or Litany. 2022. Learning Smooth Neural Functions via Lipschitz Regularization. https://doi.org/10.48550/ARXIV.2202.08345