text: Summary: The paper propose a method for generating adversarial examples in image recognition problems.  The Adversarial scheme is inspired in the one proposed by Goodgellow  et al 2015 (AT) that introduces small perturbations to the data in the direction that increases the error.  Such a perturbations are random (they have not structure) and lack of interpretation for a human user.  The proposal is to limit the perturbations to just three kind of global motion fields: shift, centered rotation and scale (zoom in/out).  Since the motions are small in scale,  the authors use a first-order Taylor series approximation  (as in classical optical flow).  This approximation allows to obtain close formulas for the perturbed examples; i.e. the correction factor of the Back-propagation computed derivatives w.r.t. original example.  As result, the method is computational efficient respect to the AT and the perturbations are interpretable.  Experiments demonstrate that with the MNIST database is not obtained an improvement in the error reduction but a reduction of the computational time.  However, with ta more general recognition problem conducted with the CIFAR-10 database, the use of the proposed method improves both the error and the computational time, when compared with AT and Virtual Adversarial Train.  Comments:1. The paper presents a series os typos: FILED (title), obouve, freedm, nerual,; please check carfully. 2. The Derivation of eq. (13) should be explained,  It could be said that (12) can be casted as a eigenvalue problem [for example: $ max_{\tilde v} \| \nabla_p L^T \tilde v \|^2 \;\; s.t. \| v\|=1  $] and (13) is the largest eigenvalue of $ \nabla_p L \nabla_p L^T $] 3. The improvement in the error results in the db CIFAR-10 is good enough to see merit in the proposal approach.  Maybe other perturbations with closed formula could be considered and linear combinations of them