Probabilistically-sound beam search with masked language models

Beam search with masked language models (MLMs) is challenging in part because joint probability distributions over sequences are not readily available, unlike for autoregressive models. Nevertheless, estimating such distributions has applications in many domains, including protein engineering and ancient text restoration. We present probabilistically-sound methods for beam search with MLMs. First, we clarify the conditions under which it is theoretically sound to perform text infilling with MLMs using standard beam search. When these conditions fail, we provide a probabilistically-sound modification with no additional computational complexity and demonstrate that it is superior to the aforementioned beam search in the expected conditions. We then present empirical results comparing several infilling approaches with MLMs across several domains.