The theoretical sections of the paper appear sound, with the Riemannian approaches and their respective invariance properties being properly established. The authors also discuss multiple possible functions that could be applied on the signal powers to obtain the target variable, and prove how using a linear regression model with the Riemannian feature vectors would be optimal for the identity, log and square roots of the signal power. However, they fail to discuss how often these types of scenarios occur in actual MEG/EEG dataset, and also how the performance would deteriorate in case where a different function of the source signals powers is used. The construction of the toy dataset is well thought out to exploit the invariances provided by the Riemannian metrics and demonstrate their performance in the ideal scenario. But as mentioned previously, some additional toy examples that examine the performance of the different models in sub-optimal conditions would also be useful. In addition, it would be interesting to see how the performance of the log-diag model on the toy dataset is affected by the use of supervised spacial filters, or how the geometric distance changes when supervised or unsupervised spacial filters are used.