In this submission, the authors attack the problem of modeling spike trains in neural data using auto-regressive GLM models. The authors recognize a disparity in the set up for training a MLE estimate of the model parameters and a “free running” model used for inference as has been observed in training RNNs. This disparity may lead to unnaturally long sequences and consequently in spike trains, runaway excitation in the spike train history. To address this issue, the authors propose a new method for fitting GLM’s based on maximum mean discrepancy, coupled with spike train kernels. The authors show favorable predictive performance with respect to MLE methods on real and synthetic neural data. All reviewers found the method novel, the experiments appropriate and the presentation of the methods extremely clear. For these reasons, this paper shall be published at NeurIPS.