The Lee-Carter model is a fundamental approach to forecasting mortality rates of a single population. Although extensions of the model to forecasting rates for multiple populations have recently been proposed, the structure of these extended models is hard to justify theoretically and the models are often difficult to calibrate, relying on customized optimization schemes. Based on the paradigm of representation learning, we extend the Lee-Carter model to multiple populations using deep neural networks, which automatically select an optimal model structure. We fit this model to mortality rates since 1950 for all countries in the Human Mortality Database and observe that the out-of-sample forecasting performance of the model is highly competitive.