Abstract. Software systems often use specialized combinations of data structures to store and retrieve data. Designing and maintaining custom data structures particularly concurrent ones is time-consuming and error-prone. We let the user declare the required data as a high-level specification of a relation and method interface, and automatically synthesize correct and efficient concurrent data representations. We present provably sound syntactic derivations to synthesize structures that efficiently support the interface. We then synthesize synchronization to support concurrent execution on the structures. Multiple candidate representations may satisfy the same specification and we aim at quantitative selection of the most efficient candidate. Previous works have either used dynamic auto-tuners to execute and measure the performance of the candidates or used static cost functions to estimate their performance. However, repeating the execution for many candidates is time-consuming and a single performance model cannot be an effective predictor of all workloads across all platforms. We present a novel approach to quantitative synthesis that learns the performance model. We developed a synthesis tool called Leqsy that trains an artificial neural network to statically predict the performance of candidate representations. Experimental evaluations demonstrate that Leqsy can synthesize near-optimum representations.