Paper:
Training recurrent networks to generate hypotheses about how the brain solves hard navigation problems
Self-localization during navigation with noisy sensors in an ambiguous world is computationally challenging, yet animals and humans excel at it. In robotics, Simultaneous Location and Mapping (SLAM) algorithms solve this problem through joint sequential probabilistic inference of their own coordinates and those of external spatial landmarks. We generate the first neural solution to the SLAM problem by training recurrent LSTM networks to perform a set of hard 2D navigation tasks that require generalization to completely novel trajectories and environments. Our goal is to make sense of how the diverse phenomenology in the brain's spatial navigation circuits is related to their function. We show that the hidden unit representations exhibit several key properties of hippocampal place cells, including stable tuning curves that remap between environments. Our result is also a proof of concept for end-to-end-learning of a SLAM algorithm using recurrent networks, and a demonstration of why this approach may have some advantages for robotic SLAM.

Review:
In this study, the authors trained recurrent neural network models with LSTM units to solve a well studied problem, namely Simultaneous Location and Mapping (SLAM). The authors trained the network to solve several different version of the problems, and made some qualitative comparison to rodent physiology regard spatial navigation behavior. 
In general, I think the authors' approach follows an interesting idea, namely using recurrent network to study the cognitive functions of the brain. This general idea has recently started to attract substantial attentions in computational neuroscience. 
The authors tested several version of the localization tasks, which is extensive. And the attempt to compare the model performance to the neurophysiology should be appreciated. They also attempted to study the inner working of the training network by looking into the dimensionality of the network, which reveals a relatively low dimensional representation, but higher than the dimension of the physical space.
Concerns-
The algorithms used is standard in machine learning, thus my understanding is that the main contribution of the paper presumably should come from either solving the SLAM problem better or shed some light from the neuroscience perspective. However, I am not sure about either of them.
1) For solving the SLAM problem,  I don't see a comparison to the state-of-the-art algorithms in SLAM, so it is unclear where the performance of this algorithm stands. 
After reading through other reviewers' comments and the rebuttal, I share similar concerns with Reviewer 1- it is unclear whether the networks learn to solve the SLAM generically, and whether the network can perform well in completely different environments. The set-up the authors assumed seem to be restrictive, and it is unclear whether it can apply to realist SLAM problem. I agree with Reviewer 1 that this represents one important limitation of this study I initially overlooked, and it was not satisfyingly addressed in the rebuttal. 
2) From the neuroscience perspective, some of the comparison the authors made in Section 3.2 are potentially interesting. However, my main concern is that the "neuron-like representations" shown in Fig.4A,B are not really neuron-like according to the rodent physiology literature. In particular, the place fields shown in Fig4A and 4B do not resemble the place fields reported in rodent physiology, which typically have roughly circular symmetric shape. I'd certainly appreciate these results better if these spatial tuning resembles more to the known rodent physiology.  Can the authors show the place fields of all the neurons in the trained network, something like Fig 1 in Wilson & McNaughton (1993, Science)? That'd be helpful in judging the similarity of the representation in the trained network and the neural representation of location in rodents.
Also, in the rodent literature, the global remapping and rate remapping are often distinguished and the cause for these two types of remapping are not well-understood at this point. Here the authors only focus on global remapping. One potentially interesting question is whether the rate remapping also exist in the trained network. The paper would be stronger if the authors could shed some light on the mechanisms for these two types of remapping from their model. Just finding global remapping across different environment isn't that surprising in my view.
Related to Fig4E, it is known that neurons in hippocampus CA1 exhibit a heavy tail in their firing rate (e.g, discussed in ref[20]). Do the authors see similar distributions of the activity levels in the trained network?
3) The manuscript is likely to be stronger if the authors could emphasize either the performance of the network in performing SLAM or  explaining the neurophysiology. Right now, it feels that the paper puts about equal weights on both, but neither part is strong enough.
According to the introduction and abstract, it seems that the authors want to emphasize the similarity to the rodent physiology. In that regard, Fig. 2 and Fig. 3 are thus not particularly informative, unless the authors show the performance from the recurrent network is similar to the rodent (or maybe even humans, if possible) behavior in some interesting ways. To emphasize the relevance to neuroscience, it is useful to have a more extended and more thorough comparison to the hippocampus neurophysiology, though I am not sure if that's possible given the place fields of the trained network units do not resemble the neurophysiology that well, as I discussed earlier.
Alternatively, to emphasize the computational power of the RNN model in solving SLAM, it would be desirable to compare the RNN to some state-of-the-art algorithms. I don't think the particle filtering approach the authors implemented represents the state-of-the-art in solving SLAM. But I could be wrong on this, as I am not very familiar with that literature.
Finally, a somewhat minor point- 
the authors make the comparison on the capacity of the network to the multi-chart attractor model in the Discussion, but I am not sure how that represents a fair comparison. I'd think one LSTM unit is computational more powerful than a model neuron in a multi-chart attractor model. I'd like to understand why the authors think a comparison can be drawn here.