A Comparative Study of Rule Extraction for Recurrent Neural Networks

Understanding recurrent networks through rule extraction has a long history. This has taken on new interests due to the need for interpreting or verifying neural networks. One basic form for representing stateful rules is deterministic finite automata (DFA). Previous research shows that extracting DFAs from trained second-order recurrent networks is not only possible but also relatively stable. Recently, several new types of recurrent networks with more complicated architectures have been introduced. These handle challenging learning tasks usually involving sequential data. However, it remains an open problem whether DFAs can be adequately extracted from these models. Specifically, it is not clear how DFA extraction will be affected when applied to different recurrent networks trained on data sets with different levels of complexity. Here, we investigate DFA extraction on several widely adopted recurrent networks that are trained to learn a set of seven regular Tomita grammars. We first formally analyze the complexity of Tomita grammars and categorize these grammars according to that complexity. Then we empirically evaluate different recurrent networks for their performance of DFA extraction on all Tomita grammars. Our experiments show that for most recurrent networks, their extraction performance decreases as the complexity of the underlying grammar increases. On grammars of lower complexity, most recurrent networks obtain desirable extraction performance. As for grammars with the highest level of complexity, while several complicated models fail with only certain recurrent networks having satisfactory extraction performance.