Recurrent Neural Language Models as Probabilistic Finite-state Automata
This work provides foundational insights into the capabilities and limitations of RNN LMs for researchers in computational linguistics and machine learning, though it is incremental in extending formal language theory to probabilistic models.
The paper tackled the problem of characterizing the representational capacity of recurrent neural network language models (RNN LMs) by analyzing them as probabilistic finite-state automata, showing that simple RNNs can model only a strict subset of probability distributions expressible by finite-state models and requiring Ω(N|Σ|) neurons to represent arbitrary deterministic finite-state LMs with N states over an alphabet Σ.
Studying language models (LMs) in terms of well-understood formalisms allows us to precisely characterize their abilities and limitations. Previous work has investigated the representational capacity of recurrent neural network (RNN) LMs in terms of their capacity to recognize unweighted formal languages. However, LMs do not describe unweighted formal languages -- rather, they define \emph{probability distributions} over strings. In this work, we study what classes of such probability distributions RNN LMs can represent, which allows us to make more direct statements about their capabilities. We show that simple RNNs are equivalent to a subclass of probabilistic finite-state automata, and can thus model a strict subset of probability distributions expressible by finite-state models. Furthermore, we study the space complexity of representing finite-state LMs with RNNs. We show that, to represent an arbitrary deterministic finite-state LM with $N$ states over an alphabet $\alphabet$, an RNN requires $Ω\left(N |Σ|\right)$ neurons. These results present a first step towards characterizing the classes of distributions RNN LMs can represent and thus help us understand their capabilities and limitations.