Ron Levie

Spectral and message-passing GNNs are often studied by different communities, with little interaction. In arxiv.org/abs/2602.10031, we argue that the two architecture types have distinct strengths and should be studied in a unified way.

@Anthony_Bonato So, the continuum hypothesis is part of the Code of Canon Law of the Catholic Church?

Not everyone will get this

Want to know about the current understanding of the generalization abilities of GNNs? Please have a look at our survey paper arxiv.org/abs/2503.15650. Joint work with Antonis Vasileiou, Stefanie Jegelka, and @levie_ron.

@benfinkelshtein Ideas so grand, the poster outgrew the bulletin board

Come check out Learning on Large Graphs using Intersecting Communities! (With a “hint” of Game of Throne references) @NeurIPS 📌East Exhibit Hall A-C #3001, Session 3

Check out our #NeurIPS2024 paper: Equivariant Machine Learning on Graphs with Nonlinear Spectral Filters arxiv.org/abs/2406.01249 With Ronen Talmon and @levie_ron, we consider graph functional shifts as a symmetry group and propose NLSFs that are equivariant to these shifts

If you're a Game of Thrones ⚔️ or Graph Learning fan, I'll present "Learning on Large Graphs using Intersecting Communities" @NeurIPS 📌East Exhibit Hall A-C #3001, Session 3 ⏲️Thu 12 Dec 11-14 Reach out to chat about Geometric DL! Thanks @ismaililkanc @mmbronstein @levie_ron

Learning on Large Graphs using Intersecting Communities is accepted to @NeurIPSConf #neurips2024! An efficient algorithm with linear memory/time following our constructive Weak Graph Regularity Lemma Thanks to @ismaililkanc @mmbronstein @levie_ron Paper:arxiv.org/abs/2405.20724

@n_keriven @ERC_Research Congrats!

I'm thrilled to announce that my #ERCStG project has been accepted 🤓 **MALAGA: Reinventing the Theory of Machine Learning on Large Graphs** Many job openings coming up, see nkeriven.github.io/malaga for updates! Thank you @ERC_Research and all my collaborators past and future

@chrsmrrs Congrats!

🙂

@xbresson Get well soon!

I was in a bike accident last Thu and badly broke my knee. I'm scheduled for surgery tmw, and it will take at least 1.5 months of immobilization. I'll miss out on some great events in the coming months :(

@mmbronstein You can approximate “targeted” messages m(x_i,x_j) by linear combinations of simple tensors of the form a(x_i)b(x_j). If you use sum aggregation, you can then use linearity and reduce to the “flooded” case. I use this trick in my analysis here: arxiv.org/pdf/2305.15987…

Martin Grohe questions whether there is a difference between messages of the form m(x_i,x_j) (“targeted”) and m(x_j) (“flooded”) in message passing GNNs

Link to the paper: arxiv.org/abs/2305.15987 Link to the poster, for NeurIPS participants: neurips.cc/virtual/2023/p…

Check out my #NeurIPS paper “A Graphon-Signal Analysis of GNNs.” I introduce a metric on the space of graphs with node features, which reveals that the input space of GNNs has Euclidean-like properties. This allows us to derive nice analysis like generalization theorems.

GNNs typically exploit permutation symmetry. Yet for learning tasks on a fixed graph, we show that enforcing active/approximate symmetries improves generalization. Check out our work "Approximately Equivariant Graph Networks" #NeurIPS23 (joint work w/ @levie_ron @SoledadVillar5 )

1-WL enhanced our understanding of the ultimate limitations of GNNs. However, it doesn't reveal similarities between graphs in the feature space. Check out our new NeurIPS paper, where we develop a continuous variant to better understand the topology of GNNs' feature space.

arxiv.org/abs/2306.03698 arxiv.org/abs/2308.10436 arxiv.org/abs/2305.15987 3/3

We prove new generalization and universal approximation theorems, alignment of GNNs with graph metrics inspired by 1WL, and novel GNN architectures which are equivariant to approximate symmetries. 2/3

3/3 accepted papers at #NeurIPS2023 ! In the papers, with @chrsmrrs, @SoledadVillar5, @TeresaNHuang and Jan Böker, we analyze GNNs by considering meaningful notions of graph metrics using graphon theory, which give structure to the domain of definition of GNNs. By that: 1/3

@ruthcfong @maxhbain @TengdaHan @RamananDeva @yatskar This is actually @KolekDe in the photo. I was not there 🙂

#CVPR2023 Thu 6/22 AM poster session! Saw a few neat works in XAI on saliency maps and concept-based explanations using vision+language as well as posters by old and new friends on accessibility (ie audio descriptions for movies) and learning street maps :)

* (capacity) is some complexity measure of the hypothesis class of message passing networks

* Here, we deal with inductive learning on a dataset of graphs. The term (dataset size) is the number of graphs in the training set. * The (size of graphs) term is the average number of nodes in graphs in the dataset, to some positive power.

Generalization bounds in #DeepLearning are typically: capacity / dataset size For message passing NNs, @SohirMaskey, Y. Lee, @GittaKutyniok and I proved the bound: capacity / (dataset size * size of graphs) facilitating generalization on large graphs. arxiv.org/abs/2202.00645