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Work in information retrieval has traditionally focused on ranking and relevance: given a query, return some number of results ordered by relevance to the user. However, the problem of determining how many results to return, i.e. how to optimally truncate the ranked result list, has received less attention despite being of critical importance in a range of applications. Such truncation is a balancing act between the overall relevance, or usefulness of the results, with the user cost of processing more results. In this work, we propose Choppy, an assumption-free model based on the widely successful Transformer architecture, to the ranked list truncation problem. Needing nothing more than the relevance scores of the results, the model uses a powerful multi-head attention mechanism to directly optimize any user-defined IR metric. We show Choppy improves upon recent state-of-the-art methods.