We describe a new deep learning approach to cardinality estimation. MSCN is a multi-set convolutional network, tailored to representing relational query plans, that employs set semantics to capture query features and true cardinalities. MSCN builds on sampling-based estimation, addressing its weaknesses when no sampled tuples qualify a predicate, and in capturing join-crossing correlations. Our evaluation of MSCN using a real-world dataset shows that deep learning significantly enhances the quality of cardinality estimation, which is the core problem in query optimization.