Renormalized Graph Neural Networks
Francesco Caso Giovanni Trappolini Andrea Bacciu Pietro Liò Fabrizio Silvestri
Graph Neural Networks (GNNs) have become essential for studying complex data,
particularly when represented as graphs. Their value is underpinned by their
ability to reflect the intricacies of numerous areas, ranging from social to
biological networks. GNNs can grapple with non-linear behaviors, emerging
patterns, and complex connections; these are also typical characteristics of
complex systems. The renormalization group (RG) theory has emerged as the
language for studying complex systems. It is recognized as the preferred lens
through which to study complex systems, offering a framework that can untangle
their intricate dynamics. Despite the clear benefits of integrating RG theory
with GNNs, no existing methods have ventured into this promising territory.
This paper proposes a new approach that applies RG theory to devise a novel
graph rewiring to improve GNNs' performance on graph-related tasks. We support
our proposal with extensive experiments on standard benchmarks and baselines.
The results demonstrate the effectiveness of our method and its potential to
remedy the current limitations of GNNs. Finally, this paper marks the beginning
of a new research direction. This path combines the theoretical foundations of
RG, the magnifying glass of complex systems, with the structural capabilities
of GNNs. By doing so, we aim to enhance the potential of GNNs in modeling and
unraveling the complexities inherent in diverse systems.