Representing Formal Languages: A Comparison Between Finite Automata and Recurrent Neural Networks
This work provides insights into how RNNs process formal languages, which is incremental for understanding neural network interpretability in computational linguistics.
The study investigated whether recurrent neural networks (RNNs) learn internal representations similar to finite automata when recognizing regular formal languages, finding that RNN states map to abstractions of minimal deterministic finite automaton states, revealing a structural relationship.
We investigate the internal representations that a recurrent neural network (RNN) uses while learning to recognize a regular formal language. Specifically, we train a RNN on positive and negative examples from a regular language, and ask if there is a simple decoding function that maps states of this RNN to states of the minimal deterministic finite automaton (MDFA) for the language. Our experiments show that such a decoding function indeed exists, and that it maps states of the RNN not to MDFA states, but to states of an {\em abstraction} obtained by clustering small sets of MDFA states into "superstates". A qualitative analysis reveals that the abstraction often has a simple interpretation. Overall, the results suggest a strong structural relationship between internal representations used by RNNs and finite automata, and explain the well-known ability of RNNs to recognize formal grammatical structure.