  Neural networks efficiently encode learned information within their
parameters. Consequently, many tasks can be unified by treating neural networks
themselves as input data. When doing so, recent studies demonstrated the
importance of accounting for the symmetries and geometry of parameter spaces.
However, those works developed architectures tailored to specific networks such
as MLPs and CNNs without normalization layers, and generalizing such
architectures to other types of networks can be challenging. In this work, we
overcome these challenges by building new metanetworks - neural networks that
take weights from other neural networks as input. Put simply, we carefully
build graphs representing the input neural networks and process the graphs
using graph neural networks. Our approach, Graph Metanetworks (GMNs),
generalizes to neural architectures where competing methods struggle, such as
multi-head attention layers, normalization layers, convolutional layers, ResNet
blocks, and group-equivariant linear layers. We prove that GMNs are expressive
and equivariant to parameter permutation symmetries that leave the input neural
network functions unchanged. We validate the effectiveness of our method on
several metanetwork tasks over diverse neural network architectures.
