I changed Chamfer distance to unbiased Sinkhorn divergence (via GeomLoss), bumped arity to 4, moved randomness out of the training loop (with the goal of making training more stable), and added a LR scheduler.
Here's my notebook: https://colab.research.google.com/drive/154ffvEWpD7tTW_AIqTD...
This tree parameter set is quite nice and interpretable: https://users.renyi.hu/~daniel/tmp/ifs-christmas-tree-arity-...
Do you have a recommendation for a good reference that teaches about the various metrics for point-cloud distance? (I only used Chamfer distance because I hazily recalled it from some undergrad class taken a while ago...)
I'm glad you did, thank you for that! Disclaimer: I'm not claiming that any of my modifications actually help, there's too much randomness introduced by local minima, and I only did a few training runs. Unbiased Sinkhorn is fancier than Chamfer, but who knows if it's better or not for this use case. Starting from a much higher learning rate did speed up convergence, though.
Re point cloud distance, there's lots of good stuff referenced in the GeomLoss documentation: https://www.kernel-operations.io/geomloss/api/geomloss.html , for example the author's GTTI 2019 slides are an excellent overview. For a very deep dive into Optimal Transport there is Computational Optimal Transport by Peyré and Cuturi: https://arxiv.org/abs/1803.00567 . Note: these mention MMD and Hausdorff, but it's all very Optimal Transport centric.
