Representing Formal Languages: A Comparison Between Finite Automata and Recurrent Neural Networks

Joshua J. Michalenko, Ameesh Shah, Abhinav Verma, Richard G. Baraniuk, Swarat Chaudhuri, Ankit B. Patel

Sep 27, 2018 ICLR 2019 Conference Blind Submission readers: everyone Show Bibtex
  • Abstract: 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.
  • Keywords: Language recognition, Recurrent Neural Networks, Representation Learning, deterministic finite automaton, automaton
  • TL;DR: Finite Automata Can be Linearly decoded from Language-Recognizing RNNs using low coarseness abstraction functions and high accuracy decoders.
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