Reviewer #1 (Public Review):
I'll begin by summarizing what I understand from the results presented, and where relevant how my understanding seems to differ from the authors' claims. I'll then make specific comments with respect to points raised in my previous review (below), using the same numbering. Because this is a revision I'll try to restrict comments here to the changes made, which provide some clarification, but leave many issues incompletely addressed.
As I understand it the main new result here is that certain recurrent network architectures promote emergence of coordinated grid firing patterns in a model previously introduced by Kropff and Treves (Hippocampus, 2008). The previous work very nicely showed that single neurons that receive stable spatial input could 'learn' to generate grid representations by combining a plasticity rule with firing rate adaptation. The previous study also showed that when multiple neurons were synaptically connected their grid representations could develop a shared orientation, although with the recurrent connectivity previously used this substantially reduced the grid scores of many of the neurons. The advance here is to show that if the initial recurrent connectivity is consistent with that of a line attractor then the network does a much better job of establishing grid firing patterns with shared orientation.
Beyond this point, things become potentially confusing. As I understand it now, the important influence of the recurrent dynamics is in establishing the shared orientation and not in its online generation. This is clear from Figure S3, but not from an initial read of the abstract or main text. This result is consistent with Kropff and Treves' initial suggestion that 'a strong collateral connection... from neuron A to neuron B... favors the two neurons to have close-by fields... Summing all possible contributions would result in a field for neuron B that is a ring around the field of neuron A.' This should be the case for the recurrent connections now considered, but the evidence provided doesn't convincingly show that attractor dynamics of the circuit are a necessary condition for this to arise. My general suggestion for the authors is to remove these kind of claims and to keep their interpretations more closely aligned with what the results show.
Major (numbered according to previous review)
(1) Does the network maintain attractor dynamics after training? Results now show that 'in a trained network without feedforward Hebbian learning the removal of recurrent collaterals results in a slight increase in gridness and spacing'. This clearly implies that the recurrent collaterals are not required for online generation of the grid patterns. This point needs to be abundantly clear in the abstract and main text so the reader can appreciate that the recurrent dynamics are important specifically during learning.<br /> (2) Additional controls for Figure 2 to test that it is connectivity rather than attractor dynamics (e.g. drawing weights from Gaussian or exponential distributions). The authors provide one additional control based on shuffling weights. However, this is far from exhaustive and it seems difficult on this basis to conclude that it is specifically the attractor dynamics that drive the emergence of coordinated grid firing.<br /> (3) What happens if recurrent connections are turned off? The new data clearly show that the recurrent connections are not required for online grid firing, but this is not clear from the abstract and is hard to appreciate from the main text.<br /> (4) This is addressed, although the legend to Fig. S2D could provide an explanation / definition for the y-axis values.<br /> (5) Given the 2D structure of the network input it perhaps isn't surprising that the network generates 2D representations and this may have little to do with its 1D connectivity. The finding that the networks maintain coordinated grids when recurrent connections are switched off supports my initial concern and the authors explanation, to me at least, remain confusing. I think it would be helpful to consider that the connectivity is specifically important for establishing the coordinated grid firing, but that the online network does not require attractor dynamics to generate coordinated grid firing.<br /> (6) Clarity of the introduction. This is somewhat clearer, but I wonder if it would be hard for someone not familiar with the literature to accurately appreciate the key points.<br /> (7) Remapping. I'm not sure why this is ill posed. It seems the proposed model can not account for remapping results (e.g. Fyhn et al. 2007). Perhaps the authors could just clearly state this as a limitation of the model (or show that it can do this).
Previous review:
This study investigates the impact of recurrent connections on grid fields generated in networks trained by adjusting the strength of feedforward spatial inputs. The main result is that if the recurrent connections in the network are given a 1D continuous attractor architecture, then aligned grid firing patterns emerge in the network following training. Detailed analyses of the low dimensional dynamics of the resulting networks are then presented. The simulations and analyses appear carefully carried out.
The feedforward model investigated by the authors (previously introduced by Kropff & Treves, 2008) is an interesting and important alternative to models that generate grid firing patterns through 2-dimensional continuous attractor network (CAN) dynamics. However, while both classes of model generate grid fields, in making comparisons the manuscript is insufficiently clear about their differences. In particular, in the CAN models grid firing is a direct result of their 2-D architecture, either a torus structure with a single activity bump (e.g. Guanella et al. 2007, Pastoll et al. 2013), or sheet with multiple local activity bumps (Fuhs & Touretzky, Burak & Fiete, 2009). In these models, spatial input can anchor the grid representations but is not necessary for grid firing. By contrast, in the feedforward models neurons transform existing spatial inputs into a grid representation. Thus, the two classes of model implement different computations; CANs path integrate, while the feedforward models transform spatial representations. A demonstration that a 1D CAN generates coordinated 2D grid fields would be surprising and important, but its less clear why coordination between grids generated by the feedforward mechanism would be surprising. As written, it's unclear which of these claims the study is trying to make. If the former, then the conclusion doesn't appear well supported by the data as presented, if the latter then the results are perhaps not so unexpected, and the imposed attractor dynamics may still not be relevant.
Whichever claim is being made, it could be helpful to more carefully evaluate the model dynamics given predictions expected for the different classes of model. Key questions that are not answered by the manuscript include:
- At what point is the 1D attractor architecture playing a role in the models presented here? Is it important specifically for training or is it also contributing to computation in the fully trained network?
- Is an attractor architecture required at all for emergence of population alignment and gridness? Key controls missing from Figure 2 include training on networks with other architectures. For example, one might consider various architectures with randomly structured connectivity (e.g. drawing weights from exponential or Gaussian distributions).
- In the trained models do the recurrent connections substantially influence activity in the test conditions? Or after training are the 1D dynamics drowned out by feedforward inputs?
- What is the low dimensional structure of the input to the network? Can the apparent discrepancy between dimensionality of architecture and representation be resolved by considering structure of the inputs, e.g. if the input is a 2 dimensional representation of location then is it surprising that the output is too?
- What happens to representations in the trained networks presented when place cells remap? Is the 1D manifold maintained as expected for CAN models, or does it reorganise?