This repository contains the source code for the ICLR 2023 paper (link) "Learning Proximal Operators to Discover Multiple Optima" by Lingxiao Li, Noam Aigerman, Vladimir G. Kim, Jiajin Li, Kristjan Greenewald, Mikhail Yurochkin, Justin Solomon.

The only core dependency is PyTorch. We will also need the CUDAToolkit to compile the CUDA library geomlib for symmetry detection only (CUDAToolkit should come with pytorch if installed using conda).

Additional dependencies:

• Logging + plotting:
  • h5py
  • tqdm
  • matplotlib
  • jupyterlab + ipywidgets
  • tensorboard
• Symmetry detection dependencies:
  • pybind11
  • ninja
  • meshio
  • pyvista (for visualization)
• Object detection dependencies:
  • PIL
  • fiftyone
  • albumentations

The core implementation is contained in pol package (pol is short for proximal operator learning). The organization of pol package is as follows.

• problems folder contains classes inherited from ProblemBase (defined in problem_base.py) specialized for different applications. We implemented the following applications.
  • AnalyticalProblem: the problem class where the objective function is given analytically and its evaluation does not have stochasticity. This class is used in the "sampling from conic sections" experiment (Section 5.1) as well as the experiments in Section D.2, D.3 of the paper.
  • SupervisedLearningProblem: the problem class for supervised learning, where the objective function can only be evaluated stochastically on batches of the dataset. This class is used in the "sparse recovery" experiment (Section 5.2) in the paper.
  • MaxCutProblem: the problem class for the "rank-2 relaxation of max-cut" experiment (Section 5.3) of the paper.
  • SymmetryDetection: the problem class for the "symmetry detection of 3D shapes" experiment (Section 5.4) of the paper.
  • ObjectDetection: the problem class for the "object detection in images" experiment (Section 5.5) of the paper.
• solvers folder contains a list of solver classes. Universal solvers (child classes of UniversalSolverBase) are those that can generalize to new problems with different parameters.
  • ParticleDescent: a baseline solver that simply runs gradient descent independently on initial particles.
  • POL: the proximal operator learning solver, a universal solver that is the main contribution of the paper.
  • GOL: the gradient operator learning solver, a universal solver proposed in the paper as an alternative to compare against.
  • FRCNN and FixedNumberSolver: specialized universal solvers for object detection only for comparison purposes.
  • configs folder contains classes used to configure experiments.
  • nn folder contains neural network architectures used.
• datasets folder contains classes used to prepare the datasets.
• runners folder contains runner classes used to run experiments (e.g. saving/loading checkpoints, training for loops).

In addition to pol package, there are a few other folders in the root directory:

• assets folder is used to store assets (e.g. MCB dataset for symmetry detection).
• notebooks folder contains jupyter notebooks used to make plots in the paper.
• geomlib is a standalone package used in symmetry detection to query the distance field of points to a 3D mesh.
• tests folder contains the working directories of all experiments (running experiments is detailed in the next section).

First, you will need to install the package pol in order to run it. This can be done by either pip install -e . (using pip) or conda develop . (using conda). Either way, you will be able to modify the source code and the changes will be reflected immediately the next time you use the package pol.

The tests folder contains the working directories of the experiments. The folders analytical, linear_regression, maxcut, symmetry_detection, and objdetect correspond to the five experiments in Section 5 of the paper respectively. In each working directory, there is a config.py file that is the entry point of the corresponding experiment. There is also a script.sh which includes the command line used to run the experiment for each method. Evaluation scripts named eval.py are also included (though not so well-maintained).

For example, to run the "sampling from conic sections" experiment, from the project root directory, execute

cd tests/analytical
python config.py --problem_list=conic --method_list=pol_res_lot --train_step=200000 --restart

If you wish to run the symmetry detection experiment (Section 5.4 in the paper), the setup is slightly more involved as we need to compile the CUDA library geomlib. Be sure to install pybind11 and ninja through conda, in addtional to PyTorch (we need the CUDAToolkit that comes with it). Then run the script install.sh or adapt the script to your needs. You also need to download the MCB dataset A and then extract the .tar.gz file into assets/MCB. The resulting assets/MCB should contain a folder called dataset_org_norm along with train_catalog.txt and test_catalog.txt which are lists of meshes after filtering (as described in the appendix, we filter out meshes with more than 5000 triangles and keep up to 100 meshes per category). Then follow the script.py in tests/symmetry_detection to run various methods.

To run the object detection experiment (Section 5.5 in the paper), we use fiftyone library to fetch COCO17 dataset. Be aware that running the commands in tests/objdetect/script.py will first download COCO17 dataset which can be huge (around 40GB, and this only happens one time).

To apply the proximal operator learning (POL) framework to a custom problem, you will need to

• inherit a problem class from ProblemBase and implement the abstract methods;
• create a folder in tests/, and then create a config Python file that suits your need.

An example is the spring equilibrium problem defined by the problem class pol/problems/spring_equilibrium.py, with a config file tests/spring_equilibrium/config.py. These two files (and the ProblemBase class) are documented.

To run it, cd into tests/spring_equilibrium and then call python config.py. To visualize the results, start a Jupyter lab at notebooks/spring. The plot.ipynb inside can be run directly.