Self-mixing interferometry is a well established interferometric measurement technique. In spite of the robustness and simplicity of the concept, interpreting the self-mixing signal is often complicated in practice, which is detrimental to measurement availability. Here we discuss the use of a convolutional neural network to reconstruct the displacement of a target from the self-mixing signal in a semiconductor laser. The network, once trained on periodic displacement patterns, can reconstruct arbitrarily complex displacement in different alignment conditions and setups. The approach validated here is amenable to generalization to modulated schemes or even to totally different self-mixing sensing tasks.