We formulate a conceptual model forwhite-box compression,which represents thelogicalcolumns in tabular data as anopenly defined function over some actually storedphysicalcolumns. Each block of data should thus go accompanied bya header that describes this functional mapping. Becausethese compression functions are openly defined, databasesystems can exploit them using query optimization and dur-ing execution, enabling e.g. better filter predicate push-down. In addition, we show that white-box compressionis able to identify a broad variety of new opportunities forcompression, leading to much better compression factors.These opportunities are identified using anautomatic learn-ingprocess that learns the functions from the data. We pro-vide a recursive pattern-driven algorithm for such learning.Finally, we demonstrate the effectiveness of white-box com-pression on a new benchmark we contribute hereby: thePub-lic BI benchmarkprovides a rich set of real-world datasets.We believe our basic prototype for white-box compres-sion opens the way for future research into transparent com-pressed data representations on the one hand and databasesystem architectures that can efficiently exploit these on theother, and should be seen as another step into the direc-tion of data management systems that are self-learning andoptimize themselves for the data they are deployed on.