  When training a Neural Network, it is optimized using the available training
data with the hope that it generalizes well to new or unseen testing data. At
the same absolute value, a flat minimum in the loss landscape is presumed to
generalize better than a sharp minimum. Methods for determining flat minima
have been mostly researched for independent and identically distributed (i. i.
d.) data such as images. Graphs are inherently non-i. i. d. since the vertices
are edge-connected. We investigate flat minima methods and combinations of
those methods for training graph neural networks (GNNs). We use GCN and GAT as
well as extend Graph-MLP to work with more layers and larger graphs. We conduct
experiments on small and large citation, co-purchase, and protein datasets with
different train-test splits in both the transductive and inductive training
procedure. Results show that flat minima methods can improve the performance of
GNN models by over 2 points, if the train-test split is randomized. Following
Shchur et al., randomized splits are essential for a fair evaluation of GNNs,
as other (fixed) splits like 'Planetoid' are biased. Overall, we provide
important insights for improving and fairly evaluating flat minima methods on
GNNs. We recommend practitioners to always use weight averaging techniques, in
particular EWA when using early stopping. While weight averaging techniques are
only sometimes the best performing method, they are less sensitive to
hyperparameters, need no additional training, and keep the original model
unchanged. All source code is available in
https://github.com/Foisunt/FMMs-in-GNNs.
