Consistency of a Recurrent Language Model With Respect to Incomplete Decoding

Abstract: Despite strong performance on a variety of tasks, neural sequence models trained with maximum likelihood have been shown to exhibit issues such as length bias and degenerate repetition. We study the related issue of receiving infinite-length sequences from a recurrent LLM when using common decoding algorithms. To analyze this issue, we first define inconsistency of a decoding algorithm, meaning that the algorithm can yield an infinite-length sequence that has zero probability under the model. We prove that commonly used incomplete decoding algorithms - greedy search, beam search, top-k sampling, and nucleus sampling - are inconsistent, despite the fact that recurrent LLMs are trained to produce sequences of finite length. Based on these insights, we propose two remedies which address inconsistency: consistent variants of top-k and nucleus sampling, and a self-terminating recurrent LLM. Empirical results show that inconsistency occurs in practice, and that the proposed methods prevent inconsistency.