HyperLogic: Enhancing Diversity and Accuracy in Rule Learning with HyperNets

Exploring the integration of if-then logic rules within neural network architectures presents an intriguing area. This integration seamlessly transforms the rule learning task into neural network training using backpropagation and stochastic gradient descent. From a well-trained sparse and shallow neural network, one can interpret each layer and neuron through the language of logic rules, and a global explanatory rule set can be directly extracted. However, ensuring interpretability may impose constraints on the flexibility, depth, and width of neural networks. In this paper, we propose HyperLogic: a flexible approach leveraging hypernetworks to generate weights of the main network. HyperLogic can be combined with existing differentiable rule learning methods to generate diverse rule sets, each capable of capturing heterogeneous patterns in data. This provides a simple yet effective method to increase model flexibility and preserve interpretability. We theoretically analyze the benefits of the HyperLogic by examining the approximation error and generalization capabilities under two types of regularization terms: sparsity and diversity regularization. Experiments on real data demonstrate that our method can learn more diverse, accurate, and concise rules.