Add optimal transport to Geometric Deep Learning

[CaiYitao]

I was wondering if this package is based on the geometric deep learning by Michael Bronstein et.al.? Can this package do the 5G(Grids,Graphs,Groups,Geodesics&Gauges) thing?

Is it possible to add a geometric understanding of deep learning into the arsenal? it basically uses optimal transport(Brenier's potential, Monge-Ampere PDE) to study geometric deep learning. and there are a great optimal transport course for this topic for reference.

[yuehhua]

Currently, this package is towards the goal of geometric deep learning by Michael Bronstein. However, most of the things for the goal is not ready yet. For the 5G, Grids and Graphs are available.

It's welcome to contribute models from the paper a geometric understanding of deep learning into this package.

[CaiYitao]

That sounds very exciting!!!
Right now, my skill is not up to contribute to the package, I will try to practice Julia more often, when I feel I am ready I will, till then perhaps also gonna need your help: )

[yuehhua]

@CaiYitao Do you refer this paper?

[CaiYitao]

yeah, I am aware of this paper, and I like the idea of this paper, but haven't dug deep into it yet, (I was planning to do Practical AI with this paper but the source code was not published yet, so my supervisor suggested me to do CONFGF and SEGNN) .

I was thinking of applying a geometric understanding of deep learning which is a geometric way of Optimal transport (core methods based on monge-ampere PDE and Brenier polar factorization) to geometric deep learning /GNN

[yuehhua]

I just check the paper. I seems to analyze and establish the relationship between optimal transportation (OT) and generative adversarial networks (GANs). In this paper, it proposed a novel generative model AE-OT model, and it uses an autoencoder (AE) for manifold learning and OT map for probability distribution transformation. I am sure it is a kind of deep learning model, but should not under the umbrella of geometric deep learning. Although there are some relationship between geometric deep learning and OT, the relationship remains not mentioned in this paper.

[yuehhua]

ConfGF to be https://github.com/DeepGraphLearning/ConfGF? And SEGNN to be https://github.com/EnyanDai/SEGNN?

[CaiYitao]

Yeah, ConfGF is that one, but SEGNN is this SEGNN This paper is from Johannes Brandstetter et.al who is a prof. of our university JKU.
I think their method is pretty general not constrained by what is presented in the paper AE-OT model and plausible cause this method developed together with Shingtung Yau(丘成桐）
Perhaps when they wrote the paper they are not aware of Geometric deep learning by Bronstein et.al. since they never mentioned it.

[yuehhua]

I think it's OK they didn't aware of geometric deep learning developed by Bronstein et.al. I didn't go deeper in this paper but I think it is surely general enough to extend to geometric deep learning. However, this package should collect the models under the umbrella of geometric deep learning, at least. There might be some work to be done and we can have models in this package.

[CaiYitao]

I am very glad and grateful that you are developing these amazing packages, I am planning to use this package to write my master thesis, and I hope in the meantime I will be proficient enough to contribute : ).

[CaiYitao]

The code for applying OT,GNN to protein analysis, was out here