Good paper that introduces an alternative way of parameterizing an invertible linear transformation using the exponential map of an unconstrained matrix. Even though this parameterization has been considered before, the idea of not instantiating the linear transformation but instead computing directly its action on the input vector by Taylor-approximating the exponential map is neat and computationally efficient. The reviewers raised a few concerns, which the rebuttal addresses. I would encourage the authors to take to heart the reviewer's comments and suggestions for improvement when preparing the camera-ready version.