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.

通过将规则函数从知识中生成并使用这些规则定义基于规则的层，我们提出了一种解决经典神经网络体系结构中难以自然整合额外信息或专家知识进入学习过程的问题的两步方法。我们的研究重点是第二步，即基于规则的层，它们旨在根据输入样本动态地安排可学习参数在权重矩阵和偏差向量中。我们证明了我们的方法通过选择适当的规则来广义化传统前馈层，如全连接层和卷积层。我们提出了基于规则的图神经网络（RuleGNNs）作为一个具体的应用，克服了普通图神经网络的一些限制。我们的实验结果表明，RuleGNNs 的预测性能与使用基于 Weisfeiler-Leman 标签和模式计数的简单规则的最先进图分类器相当。此外，我们引入了新的合成基准图数据集，展示了如何将专家知识整合到 RuleGNNs 中，使它们比普通图神经网络更强大。