Thread by @chaitjo

🚀Excited+nervous to share our latest work on understanding geometric GNNs for biomolecules, materials, etc.

"On the Expressive Power of Geometric GNNs" with @crisbodnar @SimMat20 @TacoCohen @pl219_Cambridge

PDF: arxiv.org/abs/2301.09308
Code: github.com/chaitjo/geomet…
Findings👇

How powerful are geometric GNNs? How do design choices influence expressivity?

💡Key idea: Geometric graph isomorphism + Geometric WL framework --> upper bound on geom. GNN expressivity.

Standard GNN tools (WL) are inapplicable due to new physical symmetries (roto-translation).

- GWL formalises role of depth, invariance vs. equivariance, body ordering.

- Invariant GNNs cannot tell apart one-hop identical geom. graphs, fail to compute global properties.

- Equivariant GNNs distinguish more graphs; how? Depth propagates local geom. beyond one-hop.

What about practical implications? Synthetic experiments highlight challenges in building maximally powerful geom. GNNs:

- Oversquashing of geom. info. with increased depth.

- Utility of higher order order spherical tensors over cartesian vectors.

Code: github.com/chaitjo/geomet…

And lots more in the full paper! E.g. deep theoretical connections b/w our discrimination-based perspective and universal approximation.

Looking forward to feedback and discussions at upcoming talks or virtually! 🤗

arxiv.org/abs/2301.09308

Thank you very much to anon. reviewers from @LogConference, @neur_reps and @iclr_conf (rejected 😢), as well as supportive colleagues @IlyesBatatia @davkovacs10 @weihua916 @challenger1987 @DutaIulia and several others, for helping improve our work!

P.S. Are you new to geometric graphs and GNNs?

Try this introductory collab before diving into the more advanced stuff:
colab.research.google.com/drive/1p9vlVAU…
with @charlieharris01 and Ramon Vinās, developed for students at @Cambridge_CL and @AIMS_Next.