Probabilistic Deterministic Finite Automata and Recurrent Networks, Revisited

Sarah E. Marzen

W. M. Keck Science Department
Claremont McKenna, Scripps, and Pitzer College
925 N Mills Ave, Claremont, CA 91711 USA


James P. Crutchfield

Complexity Sciences Center
Physics Department
University of California at Davis
Davis, CA 95616

ABSTRACT: Reservoir computers (RCs) and recurrent neural networks (RNNs) can mimic any finite-state automaton in theory, and some workers demonstrated that this can hold in practice. We test the capability of generalized linear models, RCs, and Long Short-Term Memory (LSTM) RNN architectures to predict the stochastic processes generated by a large suite of probabilistic deterministic finite-state automata (PDFA). PDFAs provide an excellent performance benchmark in that they can be systematically enumerated, the randomness and correlation structure of their generated processes are exactly known, and their optimal memory-limited predictors are easily computed. Unsurprisingly, LSTMs outperform RCs, which outperform generalized linear models. Surprisingly, each of these methods can fall short of the maximal predictive accuracy by as much as 50% after training and, when optimized, tend to fall short of the maximal predictive accuracy by ~5%, even though previously available methods achieve maximal predictive accuracy with orders-of-magnitude less data. Thus, despite the representational universality of RCs and RNNs, using them can engender a surprising predictive gap for simple stimuli. One concludes that there is an important and underappreciated role for methods that infer “causal states” or “predictive state representations”.

Sarah E. Marzen and James P. Crutchfield, "Probabilistic Deterministic Finite Automata and Recurrent Networks, Revisited", Entropy 24:1 (2022) 90.
[pdf] [cs.LG].