Deep learning has emerged as a strong alternative for classical iterative methods for deformable medical image registration, where the goal is to find a mapping between the coordinate systems of two images. Popular classical image registration methods enforce the useful inductive biases of symmetricity, inverse consistency, and topology preservation by construct. However, while many deep learning registration methods encourage these properties via loss functions, none of the methods enforces all of them by construct. Here, we propose a novel registration architecture based on extracting multi-resolution feature representations which is by construct symmetric, inverse consistent, and topology preserving. We also develop an implicit layer for memory efficient inversion of the deformation fields. Our method achieves state-of-the-art registration accuracy on two datasets.