Probabilistic Deterministic Finite Automata and Recurrent Networks, Revisited

TL;DR

This paper evaluates the predictive capabilities of various neural models on probabilistic finite automata, revealing significant gaps in accuracy and emphasizing the importance of causal state inference methods.

Contribution

It systematically compares RNNs, RCs, and linear models on PDFAs, highlighting their limitations and the need for causal state inference in predictive modeling.

Findings

LSTMs outperform RCs and linear models

Models can be up to 50% less accurate than optimal predictors

Optimized models still fall short of maximal accuracy by ~5%

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".