Decoding the Cognitive map: Learning place cells and remapping

Reviewer #1 (Public Review):

Summary:

This work studies representations in a network with one recurrent layer and one output layer that needs to path-integrate so that its position can be accurately decoded from its output. To formalise this problem, the authors define a cost function consisting of the decoding error and a regularisation term. They specify a decoding procedure that at a given time averages the output unit center locations, weighted by the activity of the unit at that time. The network is initialised without position information, and only receives a velocity signal (and a context signal to index the environment) at each timestep, so to achieve low decoding error it needs to infer its position and keep it updated with respect to its velocity by path integration.

The authors take the trained network and let it explore a series of environments with different geometries while collecting unit activities to probe learned representations. They find localised responses in the output units (resembling place fields) and border responses in the recurrent units. Across environments, the output units show global remapping and the recurrent units show rate remapping. Stretching the environment generally produces stretched responses in output and recurrent units. Ratemaps remain stable within environments and stabilise after noise injection. Low-dimensional projections of the recurrent population activity forms environment-specific clusters that reflect the environment's geometry, which suggests independent rather than generalised representations. Finally, the authors discover that the centers of the output unit ratemaps cluster together on a triangular lattice (like the receptive fields of a single grid cell), and find significant clustering of place cell centers in empirical data as well.

The model setup and simulations are clearly described, and are an interesting exploration of the consequences of a particular set of training requirements - here: path integration and decodability. But it is not obvious to what extent the modelling choices are a realistic reflection of how the brain solves navigation. Therefore it is not clear whether the results generalize beyond the specifics of the setup here.

Strengths:

The authors introduce a very minimal set of model requirements, assumptions, and constraints. In that sense, the model can function as a useful 'baseline', that shows how spatial representations and remapping properties can emerge from the requirement of path integration and decodability alone. Moreover, the authors use the same formalism to relate their setup to existing spatial navigation models, which is informative.

The global remapping that the authors show is convincing and well-supported by their analyses. The geometric manipulations and the resulting stretching of place responses, without additional training, are interesting. They seem to suggest that the recurrent network may scale the velocity input by the environment dimensions so that the exact same path integrator-output mappings remain valid (but maybe there are other mechanisms too that achieve the same).

The clustering of place cell peaks on a triangular lattice is intriguing, given there is no grid cell input. It could have something to do with the fact that a triangular lattice provides optimal coverage of 2d space? The included comparison with empirical data is valuable, although the authors only show significant clustering - there is no analysis of its grid-like regularity.

Weaknesses:

The navigation problem that needs to be solved by the model is a bit of an odd one. Without any initial position information, the network needs to figure out where it is, and then path-integrate with respect to a velocity signal. As the authors remark in Methods 4.2, without additional input, the only way to infer location is from border interactions. It is like navigating in absolute darkness. Therefore, it seems likely that the salient wall representations found in the recurrent units are just a consequence of the specific navigation task here; it is unclear if the same would apply in natural navigation. In natural navigation, there are many more sensory cues that help inferring location, most importantly vision, but also smell and whiskers/touch (which provides a more direct wall interaction; here, wall interactions are indirect by constraining velocity vectors). There is a similar but weaker concern about whether the (place cell like) localised firing fields of the output units are a direct consequence of the decoding procedure that only considers activity center locations.

The conclusion that 'contexts are attractive' (heading of section 2) is not well-supported. The authors show 'attractor-like behaviour' within a single context, but there could be alternative explanations for the recovery of stable ratemaps after noise injection. For example, the noise injection could scramble the network's currently inferred position, so that it would need to re-infer its position from boundary interactions along the trajectory. In that case the stabilisation would be driven by the input, not just internal attractor dynamics. Moreover, the authors show that different contexts occupy different regions in the space of low-dimensional projections of recurrent activity, but not that these regions are attractive.

The authors report empirical data that shows clustering of place cell centers like they find for their output units. They report that 'there appears to be a tendency for the clusters to arrange in hexagonal fashion, similar to our computational findings'. They only quantify the clustering, but not the arrangement. Moreover, in Figure 7e they only plot data from a single animal, then plot all other animals in the supplementary. Does the analysis of Fig 7f include all animals, or just the one for which the data is plotted in 7e? If so, why that animal? As Appendix C mentions that the ratemap for the plotted animal 'has a hexagonal resemblance' whereas other have 'no clear pattern in their center arrangements', it feels like cherrypicking to only analyse one animal without further justification.

Reviewer #2 (Public Review):

Summary:
The authors proposed a neural network model to explore the spatial representations of the hippocampal CA1 and entorhinal cortex (EC) and the remapping of these representations when multiple environments are learned. The model consists of a recurrent network and output units (a decoder) mimicking the EC and CA1, respectively. The major results of this study are: the EC network generates cells with their receptive fields tuned to a border of the arena; decoder develops neuron clusters arranged in a hexagonal lattice. Thus, the model accounts for entrohinal border cells and CA1 place cells. The authors also suggested the remapping of place cells occurs between different environments through state transitions corresponding to unstable dynamical modes in the recurrent network.

Strengths:
The authors found a spatial arrangement of receptive fields similar to their model's prediction in experimental data recorded from CA1. Thus, the model proposes a plausible mechanisms to generate hippocampal spatial representations without relying on grid cells. This result is consistent with the observation that grid cells are unnecessary to generate CA1 place cells.

The suggestion about the remapping mechanism shows an interesting theoretical possibility.

Weaknesses:
The explicit mechanisms of generating border cells and place cells and those underlying remapping were not clarified at a satisfactory level.

The model cannot generate entorhinal grid cells. Therefore, how the proposed model is integrated into the entire picture of the hippocampal mechanism of meｍory processing remains elusive.

Reviewer #3 (Public Review):

Summary:

The authors used recurrent neural network modelling of spatial navigation tasks to investigate border and place cell behaviour during remapping phenomena.

Strengths:

The neural network training seemed for the most part (see comments later) well-performed, and the analyses used to make the points were thorough.

The paper and ideas were well explained.

Figure 4 contained some interesting and strong evidence for map-like generalisation as environmental geometry was warped.

Figure 7 was striking, and potentially very interesting.

It was impressive that the RNN path-integration error stayed low for so long (Fig A1), given that normally networks that only work with dead-reckoning have errors that compound. I would have loved to know how the network was doing this, given that borders did not provide sensory input to the network. I could not think of many other plausible explanations... It would be even more impressive if it was preserved when the network was slightly noisy.

Weaknesses:

I felt that the stated neuroscience interpretations were not well supported by the presented evidence, for a few reasons I'll now detail.

First, I was unconvinced by the interpretation of the reported recurrent cells as border cells. An equally likely hypothesis seemed to be that they were positions cells that are linearly encoding the x and y position, which when your environment only contains external linear boundaries, look the same. As in figure 4, in environments with internal boundaries the cells do not encode them, they encode (x,y) position. Further, if I'm not misunderstanding, there is, throughout, a confusing case of broken symmetry. The cells appear to code not for any random linear direction, but for either the x or y axis (i.e. there are x cells and y cells). These look like border cells in environments in which the boundaries are external only, and align with the axes (like square and rectangular ones), but the same also appears to be true in the rotationally symmetric circular environment, which strikes me as very odd. I can't think of a good reason why the cells in circular environments should care about the particular choice of (x,y) axes... unless the choice of position encoding scheme is leaking influence throughout. A good test of these would be differently oriented (45 degree rotated square) or more geometrically complicated (two diamonds connected) environments in which the difference between a pure (x,y) code and a border code are more obvious.

Next, the decoding mechanism used seems to have forced the representation to learn place cells (no other cell type is going to be usefully decodable?). That is, in itself, not a problem. It just changes the interpretation of the results. To be a normative interpretation for place cells you need to show some evidence that this decoding mechanism is relevant for the brain, since this seems to be where they are coming from in this model. Instead, this is a model with place cells built into it, which can then be used for studying things like remapping, which is a reasonable stance.

However, the remapping results were also puzzling. The authors present convincing evidence that the recurrent units effectively form 6 different maps of the 6 different environments (e.g. the sparsity of the cod, or fig 6a), with the place cells remapping between environments. Yet, as the authors point out, in neural data the finding is that some cells generalise their co-firing patterns across environments (e.g. grid cells, border cells), while place cells remap, making it unclear what correspondence to make between the authors network and the brain. There are existing normative models that capture both entorhinal's consistent and hippocampus' less consistent neural remapping behaviour (Whittington et al. and probably others), what have we then learnt from this exercise?

One striking result was figure 7, the hexagonal arrangement of place cell centres. I had one question that I couldn't find the answer to in the paper, which would change my interpretation. Are place cell centres within a single clusters of points in figure 7a, for example, from one cell across the 100 trajectories, or from many? If each cluster belongs to a different place cell then the interpretation seems like some kind of optimal packing/coding of 2D space by a set of place cells, an interesting prediction. If multiple place cells fall within a single cluster then that's a very puzzling suggestion about the grouping of place cells into these discrete clusters. From figure 7c I guess that the former is the likely interpretation, from the fact that clusters appear to maintain the same colour, and are unlikely to be co-remapping place cells, but I would like to know for sure!

I felt that the neural data analysis was unconvincing. Most notably, the statistical effect was found in only one of seven animals. Random noise is likely to pass statistical tests 1 in 20 times (at 0.05 p value), this seems like it could have been something similar? Further, the data was compared to a null model in which place cell fields were randomly distributed. The authors claim place cell fields have two properties that the random model doesn't (1) clustering to edges (as experimentally reported) and (2) much more provocatively, a hexagonal lattice arrangement. The test seems to collude the two; I think that nearby ball radii could be overrepresented, as in figure 7f, due to either effect. I would have liked to see a computation of the statistic for a null model in which place cells were random but with a bias towards to boundaries of the environment that matches the observed changing density, to distinguish these two hypotheses.

Some smaller weaknesses:
- Had the models trained to convergence? From the loss plot it seemed like not, and when including regularisors recent work (grokking phenomena, e.g. Nanda et al. 2023) has shown the importance of letting the regularisor minimise completely to see the resulting effect. Else you are interpreting representations that are likely still being learnt, a dangerous business.
- Since RNNs are nonlinear it seems that eigenvalues larger than 1 doesn't necessarily mean unstable?
- Why do you not include a bias in the networks? ReLU networks without bias are not universal function approximators, so it is a real change in architecture that doesn't seem to have any positives?
- The claim that this work provided a mathematical formalism of the intuitive idea of a cognitive map seems strange, given that upwards of 10 of the works this paper cite also mathematically formalise a cognitive map into a similar integration loss for a neural network.

Aim Achieved? Impact/Utility/Context of Work

Given the listed weaknesses, I think this was a thorough exploration of how this network with these losses is able to path-integrate its position and remap. This is useful, it is good to know how another neural network with slightly different constraints learns to perform these behaviours. That said, I do not think the link to neuroscience was convincing, and as such, it has not achieved its stated aim of explaining these phenomena in biology. The mechanism for remapping in the entorhinal module seemed fundamentally different to the brain's, instead using completely disjoint maps; the recurrent cell types described seemed to match no described cell type (no bad thing in itself, but it does limit the permissible neuroscience claims) either in tuning or remapping properties, with a potentially worrying link between an arbitrary encoding choice and the responses; and the striking place cell prediction was unconvincingly matched by neural data. Further, this is a busy field in which many remapping results have been shown before by similar models, limiting the impact of this work. For example, George et al. and Whittington et al. show remapping of place cells across environments; Whittington et al. study remapping of entorhinal codes; and Rajkumar Vasudeva et al. 2022 show similar place cell stretching results under environmental shifts. As such, this papers contribution is muddied significantly.