Timezone: »
We study properties of Graph Convolutional Networks (GCNs) by analyzing their behavior on standard models of random graphs, where nodes are represented by random latent variables and edges are drawn according to a similarity kernel. This allows us to overcome the difficulties of dealing with discrete notions such as isomorphisms on very large graphs, by considering instead more natural geometric aspects. We first study the convergence of GCNs to their continuous counterpart as the number of nodes grows. Our results are fully non-asymptotic and are valid for relatively sparse graphs with an average degree that grows logarithmically with the number of nodes. We then analyze the stability of GCNs to small deformations of the random graph model. In contrast to previous studies of stability in discrete settings, our continuous setup allows us to provide more intuitive deformation-based metrics for understanding stability, which have proven useful for explaining the success of convolutional representations on Euclidean domains.
Author Information
Nicolas Keriven (CNRS, GIPSA-lab)
Alberto Bietti (NYU)
Samuel Vaiter (CNRS)
Related Events (a corresponding poster, oral, or spotlight)
-
2020 Poster: Convergence and Stability of Graph Convolutional Networks on Large Random Graphs »
Thu. Dec 10th 05:00 -- 07:00 PM Room Poster Session 5 #1720
More from the Same Authors
-
2022 Panel: Panel 1C-4: Fast Bayesian Coresets… & Not too little,… »
Nicolas Keriven · Cian Naik -
2022 Poster: When does return-conditioned supervised learning work for offline reinforcement learning? »
David Brandfonbrener · Alberto Bietti · Jacob Buckman · Romain Laroche · Joan Bruna -
2022 Poster: Learning single-index models with shallow neural networks »
Alberto Bietti · Joan Bruna · Clayton Sanford · Min Jae Song -
2021 Poster: On the Sample Complexity of Learning under Geometric Stability »
Alberto Bietti · Luca Venturi · Joan Bruna -
2021 Poster: On the Universality of Graph Neural Networks on Large Random Graphs »
Nicolas Keriven · Alberto Bietti · Samuel Vaiter -
2019 Poster: On the Inductive Bias of Neural Tangent Kernels »
Alberto Bietti · Julien Mairal -
2019 Poster: Universal Invariant and Equivariant Graph Neural Networks »
Nicolas Keriven · Gabriel Peyré -
2017 Poster: Stochastic Optimization with Variance Reduction for Infinite Datasets with Finite Sum Structure »
Alberto Bietti · Julien Mairal -
2017 Spotlight: Stochastic Optimization with Variance Reduction for Infinite Datasets with Finite Sum Structure »
Alberto Bietti · Julien Mairal -
2017 Poster: Invariance and Stability of Deep Convolutional Representations »
Alberto Bietti · Julien Mairal