Standard autoregressive language models perform only polynomial-time computation to compute the probability of the next symbol. While this is attractive, it means they cannot model distributions whose next-symbol probability is hard to compute. Indeed, they cannot even model them well enough to solve associated easy decision problems for which an engineer might want to consult a language model. These limitations apply no matter how much computation and data are used to train the model, unless the model is given access to oracle parameters that grow superpolynomially in sequence length. Thus, simply training larger autoregressive language models is not a panacea for NLP. Alternatives include energy-based models (which give up efficient sampling) and latent-variable autoregressive models (which give up efficient scoring of a given string). Both are powerful enough to escape the above limitations.

We introduce neural finite state transducers (NFSTs), a family of string transduction models defining joint and conditional probability distributions over pairs of strings. The probability of a string pair is obtained by marginalizing over all its accepting paths in a finite state transducer. In contrast to ordinary weighted FSTs, however, each path is scored using an arbitrary function such as a recurrent neural network, which breaks the usual conditional independence assumption (Markov property). NFSTs are more powerful than previous finite-state models with neural features (Rastogi et al., 2016.) We present training and inference algorithms for locally and globally normalized variants of NFSTs. In experiments on different transduction tasks, they compete favorably against seq2seq models while offering interpretable paths that correspond to hard monotonic alignments.

We introduce neural particle smoothing, a sequential Monte Carlo method for sampling annotations of an input string from a given probability model. In contrast to conventional particle filtering algorithms, we train a proposal distribution that looks ahead to the end of the input string by means of a right-to-left LSTM. We demonstrate that this innovation can improve the quality of the sample. To motivate our formal choices, we explain how neural transduction models and our sampler can be viewed as low-dimensional but nonlinear approximations to working with HMMs over very large state spaces.