  A common problem of classical neural network architectures is that additional
information or expert knowledge cannot be naturally integrated into the
learning process. To overcome this limitation, we propose a two-step approach
consisting of (1) generating rule functions from knowledge and (2) using these
rules to define rule based layers -- a new type of dynamic neural network
layer. The focus of this work is on the second step, i.e., rule based layers
that are designed to dynamically arrange learnable parameters in the weight
matrices and bias vectors depending on the input samples. Indeed, we prove that
our approach generalizes classical feed-forward layers such as fully connected
and convolutional layers by choosing appropriate rules. As a concrete
application we present rule based graph neural networks (RuleGNNs) that
overcome some limitations of ordinary graph neural networks. Our experiments
show that the predictive performance of RuleGNNs is comparable to
state-of-the-art graph classifiers using simple rules based on Weisfeiler-Leman
labeling and pattern counting. Moreover, we introduce new synthetic benchmark
graph datasets to show how to integrate expert knowledge into RuleGNNs making
them more powerful than ordinary graph neural networks.
