-bravo for detailing computational mechanisms that may link associative processing in hippocampal place cells and metric processing in entorhinal grid cells -it is somewhat unclear what type of analyses and results have actually been aimed at and obtained - page 2: CA3 synapses are mentioned first summary of contributions -discussion: reward, in the eyes of this reviewer, should not be considered a 'sensory stimulus'; rather, reward processing is the result of neural processing of sensory cues in the environment -the figures and their captions are well thought out and effective in communicating their message

I'm mainly going to comment on the execution of the paper since I'm currently not very knowledgeable in the computational neuroscience of navigation in the brain: -Although it is easy to understand the paper content at a high level, I found it quite difficult to understand some important details, requiring multiple passes over the text to make sense of them. Examples: i) There are non-bold letters that denote continuous distributions over space (G, P), and boldfaced versions of them that represent "discretized" vectors that are grid and place cell responses. Is this mapping a simple discretization of the support of the probability functions? If not, what is the mapping? I guess this is a discretization at landmark locations for place cells (one landmark per place cell). Is it the same thing for the grid cells? Suggestion: Why don't you define the mapping in the beginning, and just use the discretized variables using simple matrix algebra? ii) It is a little hard to follow what is a scalar function and what is a vector. I'm assuming bold-faced letters are vectors and others are scalars? On the other hand, for instance T(x_t | x_before, u_t), which is non-bold, is defined as a sum of multivariate normals. iii) Use of \mathcal{N} is confusing. Do you define this to be a symbolic distribution to sample from, or a probability density function? Some mentions of \mathcal{N} have two arguments while some have three (possibly meant as a PDF). Please be consistent in your notation. I'd like to point out a particular use on line 75, because I was not able to understand the representation of a place cell: p_t^p=\mathcal{N}(x_t', \mu_p, variance). Do you define each place cell to represent the PDF of the normal distribution (if so, how)? Or do you mean each place cell is sampled from a normal distribution? Additionally, what does each of the three arguments represent? Is the mean x_t', or \mu_p? iv) I can understand that both the offline and the online update is for ultimately learning the mapping B from place cells to grid cells. However, the information flow is a little convoluted, and makes it a bit unclear what exactly the suggested mechanism is about. I believe that the methods section could be simplified with a more hierarchical organization, e.g. first emphasizing the formation of metric space through path integration (G') and associative map (PB), then combining the two for online localization, and then explaining the realtime and the offline update of B. - The contributions seem to be in the computational neuroscience of navigation; isn't there any related work or prior art that this work shares similarities with / builds on? (Given its popularity, we know that there is substantial work on the topic) For instance, what are some other proposed HPC/MEC related mechanisms that can predict the coordinated HPC-MEC replay? What some other models of combining path integration with place-related sensory signals for navigation? It is difficult to gauge the significance of this work without more context around the current state of knowledge in the field of computational neuroscience. I find this to be an important shortcoming. - The computational models of navigation that I'm familiar with (although admittedly I'm anything but up-to-date on the matter) typically depict HPC as mainly downstream from the cortex, creating the cognitive map through help from MEC. This is based on and corroborated by physiology data (see e.g. [1]). Things might have changed, but what is the biological motivation for proposing your circuit (with HPC->MEC connections most emphasized)? Given that multiple models can be proposed to account for physiologically observed data, it'd be more convincing to provide clear empirical grounds for the proposed model; doing so would strengthen the paper contribution. Minor comment: In eqns. (3) & (4), there is a small-case p_t , I guess this is a typo. [1] Zhang, Sheng-Jia, et al. "Functional connectivity of the entorhinal–hippocampal space circuit." Philosophical Transactions of the Royal Society B: Biological Sciences 369.1635 (2014): 20120516.

The paper tackles a very important problem and bridges two growing fields. The methodology is sound and different observed phenomena are covered to test the feasibility of the framework. The main problem of the paper is that its theoretical contribution is not explicitly specified. Particularly, some ideas in section 2 seems to be borrowed directly from the AI. While the authors have cited the related work in the beginning of the paper, I think it is necessary that they specify the source of each equation (or if it is from themselves).