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We present an algorithm for extraction of a probabilistic deterministicfinite automaton (PDFA) from a given black-box language model, such as arecurrent neural network (RNN). The algorithm is a variant of theexact-learning algorithm L*, adapted to a probabilistic setting with noise. Thekey insight is the use of conditional probabilities for observations, and theintroduction of a local tolerance when comparing them. When applied to RNNs,our algorithm often achieves better word error rate (WER) and normaliseddistributed cumulative gain (NDCG) than that achieved by spectral extraction ofweighted finite automata (WFA) from the same networks. PDFAs are substantiallymore expressive than n-grams, and are guaranteed to be stochastic anddeterministic - unlike spectrally extracted WFAs.

Learning Deterministic Weighted Automata with Queries and Counterexamples