11 papers
Graph Learning Should Move Beyond Restrictive Views of Spectral and Message-Passing GNNs
Antonis Vasileiou, Juan Cervino, Pascal Frossard +7
Graph neural networks (GNNs) are commonly divided into message-passing neural networks (MPNNs) and spectral GNNs, reflecting two largely separate research traditions in machine lea…
A Graphop Analysis of Graph Neural Networks on Sparse Graphs: Generalization and Universal Approximation
Ofek Amran, Tom Gilat, Ron Levie
Generalization and approximation capabilities of message passing graph neural networks (MPNNs) are often studied by defining a compact metric on a space of input graphs under which…
Neural Networks With Dense Weights Are Not Universal Approximators
Levi Rauchwerger, Stefanie Jegelka, Ron Levie
We investigate the approximation capabilities of dense neural networks. While universal approximation theorems establish that sufficiently large architectures can approximate arbit…
Beyond Oversquashing: Understanding Signal Propagation in GNNs Via Observables
Eden Nagar, Ya-Wei Eileen Lin, Ron Levie
Graph Neural Networks (GNNs) perform computations on graphs by routing the signal between graph regions using a graph shift operator or a message passing scheme. Often, the propaga…
Adaptive Canonicalization with Application to Invariant Anisotropic Geometric Networks
Ya-Wei Eileen Lin, Ron Levie
Canonicalization is a widely used strategy in equivariant machine learning, enforcing symmetry in neural networks by mapping each input to a standard form. Yet, it often introduces…
Efficient Learning on Large Graphs using a Densifying Regularity Lemma
Jonathan Kouchly, Ben Finkelshtein, Michael Bronstein +1
Learning on large graphs presents significant challenges, with traditional Message Passing Neural Networks suffering from computational and memory costs scaling linearly with the n…