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Poster
Generalization and Representational Limits of Graph Neural Networks
Vikas K Garg · Stefanie Jegelka · Tommi Jaakkola

Thu Jul 16 08:00 AM -- 08:45 AM & Thu Jul 16 07:00 PM -- 07:45 PM (PDT) @
in Poster Session 43 »

We address two fundamental questions about graph neural networks (GNNs). First, we prove that several important graph properties cannot be discriminated by GNNs that rely entirely on local information. Such GNNs include the standard message passing models, and more powerful spatial variants that exploit local graph structure (e.g., via relative orientation of messages, or local port ordering) to distinguish neighbors of each node. Our treatment includes a novel graph-theoretic formalism. Second, we provide the first data dependent generalization bounds for message passing GNNs. This analysis explicitly accounts for the local permutation invariance of GNNs. Our bounds are much tighter than existing VC-dimension based guarantees for GNNs, and are comparable to Rademacher bounds for recurrent neural networks.

Keywords: Deep Learning Theory · Network Analysis · Deep Learning - Theory

Author Information

Vikas K Garg (Massachusetts Institute of Technology)
Stefanie Jegelka (Massachusetts Institute of Technology)
Tommi Jaakkola (MIT)

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