feat(MeshCNN): Add MeshCNN's Convolution Layer

[michaelfortunato]

This commit is the first part of a series of pull requests that we will make to PyTorch Geometric in order add MeshCNN! MeshCNN is a complex and important paper. As such its integration into PyG will be via a series of self-contained PRs. The proposed plan to integrate MeshCNN into PyTorch Geometric is posted as a new comment on the original issue: #283. The full PDF is also downloadable here: https://github.com/user-attachments/files/19872710/MeshCNN-PyG.pdf.

Background

It's important to recognize that the original attempt to integrate MeshCNN into PyG, PR #2293, is quite comprehensive and complete. The code we put here for MeshCNN will may very well look like the original PR. The main difference is that we will split up the pull requests into a series of smaller ones.

This is Part 1 of a comprehensive plan to add MeshCNN into PyTorch Geometric and implements the convolutional layer of MeshCNN. Please see #283 for the comprehensive plan. Please add all comments and feedback related to the entire plan or higher level ideas on the original issue #283. I would love critical feedback on the plan and am happy to completely throw it away or change it based on the feedback I get.

PR's Design

A good place to fully-understand MeshCNNConv's design is by rendering the docs for torch.nn.conv.MeshCNNConv and reading it.

The most important aspect of this pull request is ordering we require on the edge_index (edge adjacency). This constraint is documented in the class (torch.nn.conv.MeshCNNConv).

My questions are:

1. Should I write the core logic of MeshCNN's (non-permutation invariant) convolution as a new Aggregate module?
2. MeshCNN's convolution can actually be expressed in terms of the framework of torch_geometric.nn.conv.RGCNConv, where in MeshCNN there are 4 categories. Should we sub-class that instead?
3. Should we implement batch normalization as a performance optimization here?

I have thought about these questions a lot, and if any of these questions are "yes", my rebuttals to them are

1. MeshCNN's aggregation is not generalizable enough to warrant the creation of a new aggregation file. That would introduce two new files to implement MeshCNNConv, that is torch.nn.aggr.MeshCNNConv, and the smaller wrapper torch.nn.conv.MeshCNNConv. That being said, moving to torch.nn.aggr.MeshCNNConv is easy to do.
2. While MeshCNN can be expressed in terms of torch_geometric.nn.conv.RGCNConv, it ties us to any performance characteristics etc that this torch_geometric.nn.conv.RGCNConv may have. I think it is wrong to couple us to this framework, even if conceptually it is important and interesting to recognize MeshCNNConv as a case of torch_geometric.nn.conv.RGCNConv.
3. This can come as a future and enhancement PR after MeshCNN is more situated into PyG. Adding this complexity now obscures the main and lasting design decisions around our implementation of MeshCNN. These first PR's should get the core functionality out in a way that is straightforward, which will increase the odds that our design decisions now can be easily extended to accommodate future enhancements.

Besides that, this is a small PR, most of the lines being documentation.

Thanks. I am a student in Chicago working independently on this project. As of this week, I am working on this project full-time.

Important

I am always reachable directly via instant message or video calling in PyG's slack. My display name is @Michael Fortunato and my account link is https://torchgeometricco.slack.com/team/U08AMAGE318. Please feel free to message or call me directly, at anytime, with questions or comments. I am also always happy to meet if that helps get things moving.

Thanks so much. Once again, for background on the entire plan please see my comments on
the original issue #283 along with the attached PDF of the plan. To get started with this PR, I recommend viewing the rendered class documentation for torch.nn.conv.MeshCNNConv: https://pytorch-geometric--10222.org.readthedocs.build/en/10222/generated/torch_geometric.nn.conv.MeshCNNConv.html.

Best,
Michael

Slack: @Michael Fortunato on Slack
Original Issue Along With Plan Summary: #283
Full Proposal: MeshCNN-PyG.pdf

[rusty1s]

Very in-depth documentation, love it :) Thank you so much.

[codecov]

Codecov Report

❌ Patch coverage is 91.11111% with 4 lines in your changes missing coverage. Please review.
✅ Project coverage is 85.81%. Comparing base (c211214) to head (4b865c9).
⚠️ Report is 94 commits behind head on master.

Files with missing lines	Patch %	Lines
torch_geometric/nn/conv/meshcnn_conv.py	90.90%	4 Missing ⚠️

Additional details and impacted files

@@            Coverage Diff             @@
##           master   #10222      +/-   ##
==========================================
- Coverage   86.11%   85.81%   -0.30%     
==========================================
  Files         496      498       +2     
  Lines       33655    34128     +473     
==========================================
+ Hits        28981    29286     +305     
- Misses       4674     4842     +168     

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