Basic questions in dynamical neuroscience and machine learning motivate the study of the stability, robustness, entrainment, and computational efficiency properties of neural network models. The speaker will present some elements of a comprehensive contraction theory for neural networks. Using non-Euclidean norms, the speaker will review recent advances in analyzing and training a class of recurrent/implicit models. It is joint work with Alexander Davydov, Saber Jafarpour, Anton Proskurnikov.