Integrating machine learning into the internals of database management systems requires significant feature engineering, a human effort-intensive process to determine the best way to represent the pieces of information that are relevant to a task. In addition to being labor intensive, the process of hand-engineering features must generally be repeated for each data management task, and may make assumptions about the underlying database that are not universally true. We introduce flexible

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... r embeddings, a deep learning technique for automatically transforming query operators into feature vectors that are useful for a multiple data management tasks and is custom-tailored to the underlying database. Our approach works by taking advantage of an operator's context, resulting in a neural network that quickly transforms sparse representations of query operators into dense, information-rich feature vectors. Experimentally, we show that our flexible operator embeddings perform well across a number of data management tasks, using both synthetic and real-world datasets.