Title: (Unconstrained) Beam Search is Sensitive to Large Search Discrepancies. Abstract: Beam search is the most popular inference algorithm for decoding neural sequence models. Unlike greedy search, beam search allows for a non-greedy local decisions that can potentially lead to a sequence with a higher overall probability. However, previous work found that the performance of beam search tends to degrade with large beam widths. In this work, we perform an empirical study of the behavior of the beam search algorithm across three sequence synthesis tasks. We find that increasing the beam width leads to sequences that are disproportionately based on early and highly non-greedy decisions. These sequences typically include a very low probability token that is followed by a sequence of tokens with higher (conditional) probability leading to an overall higher probability sequence. However, as beam width increases, such sequences are more likely to have a lower evaluation score. Based on our empirical analysis we propose to constrain the beam search from taking highly non-greedy decisions early in the search. We evaluate two methods to constrain the search and show that constrained beam search effectively eliminates the problem of beam search degradation and in some cases even leads to higher evaluation scores. Our results generalize and improve upon previous observations on copies and training set predictions.