Trading Place for Space: Increasing Location Resolution Reduces Contextual Capacity in Hippocampal Codes

We are grateful for the positive response, as well as the valuable suggestions and pointers to existing literature.

In the initial submission, there was a typo that propagated throughout our text, exchanging dorsal and ventral, and hence also the predicted scaling along the dorso-ventral axis. We thank the reviewer for pointing this out! In fact the ventral cells have wider tuning then the dorsal cells, and we will fix this typo in the final paper, and include citations to the Kjelstrup et al. and the Komorowski et al papers. Note that our predictions are based more on the relative firing field sizes of place cells, and not on where these cells are located, so the key results of our paper remain unchanged. In particular, we predict that cells with wider tunings are better tuned for contextual separation but are worse at fine tuned spatial tasks, while those with narrower tunings are better tuned for tasks associated with fine-grained memory, but worse at contextual separation (though both are still able to contribute to both tasks). Correcting our dorso-ventral typo, our suggestions about experiments involving the dorsal hippocampus should be replaced with experiments involving the ventral hippocampus, and vice-versa. In particular, as the ventral cells are those with wider tuning, the corrected prediction is that selective inhibition of ventral cells should lead to worse contextual performance. Conversely, the fact that the more dorsal cells have narrower tuning suggests that selective inhibition of the dorsal hippocampus should lead to worse performance in fine grained memory tasks under our model. After this correction, our model is in line with the experimental papers you mention. In particular, our theory is supported by the result that lesions of the dorsal hippocampus impair spatial tasks (Moser et. al. 1995, Hock and Bunsey 1998) while lesions of the ventral hippocampus do not meaningfully affect performance on spatial tasks, and we will cite these experiments in the final paper. Likewise, the fact that conditioned contextual fear responses, like those described in Richmond et. al. (1999) and Bannerman et. al. (2003), are impaired after ventral lesions also supports our hypothesis that the more widely tuned neurons are better for context separation.

As for the predictions involving clustering near boundaries, we will likewise cite the relevant experimental work in the final paper. In particular, the increased incidence of place cells near boundaries in Wiener et al. (1989) is in line with the predictions made by our model. As for noise variability experiments, one could inject white noise into hippocampal neurons through electrical input, or pharmacologically increase firing variability, which under our model should reduce both spatial and contextual specificity. In particular, there is a noise threshold above which the ability to separate context disappears in our geometric model. However our condition for contextual separability is likely stricter than one implemented by the hippocampus of a realistic animal, so contextual separation should persist to some extent past this noise threshold – i.e., we expect the threshold to be more of a smooth crossover than a sharp transition.

Finally we will address the minor edits suggested by the reviewer.

We appreciate the time taken by the reviewer to review our submission, and the suggestions provided.

We believe that our submission is relevant to the NeurIPS community, and in particular, to the neural coding section of the Neuroscience topic, which is listed in the call for submissions. As contextual discriminability and spatial memory are both implicated by hippocampal function, approaching both through the geometry of the underlying hippocampal codes will be of interest to this community. Although the work presented here does not directly touch on the applications or theory of artificial networks, we believe that a better understanding of biological neural networks will lead to a better understanding of artificial networks, and give insights into how to design them for certain tasks. For instance, research at DeepMind (Banino et. al, 2018, Nature), by Cueva and Wei (ICLR 2018) and by Sorscher et al (NeurIPS 2019) has found that grid-like representations, similar to those found in the Medial Entorhinal Cortex, emerge naturally for networks trained on spatial navigation, leading to deep learning agents with mammal-like navigational abilities. Likewise, place cells in the hippocampus are implicated in general short term memory (Benna and Fusi, 2020, PNAS). So a better theoretical understanding of hippocampal function will be of interest to the wider NeurIPS community when it comes to designing networks capable of flexible memory storage and retrieval.

The reviewer asked if we could have used alternate criteria for separation of neural manifolds. Indeed, there are some options. For example, the work of SueYeon Chung involves a linear separation criterion for perceptual manifolds in deep neural networks (Chung et. al., 2018 APS, Chung et. al, 2020, Nature Communications). Pursuing a simpler separability criteria between activity manifolds, like the linear separation of point-cloud manifolds used in the above work, but in the context of hippocampal coding, is a possible direction we would like to explore in future research.

As for selective inhibition experiments, these are possible via induced lesions to various regions of the hippocampus in rodents. Lesions in the dorsal region of the hippocampus should lead to impairment on tasks in which high spatial resolution is crucial, such as during maze navigation, while lesions to the ventral hippocampus should lead to greater impairment in contextual tasks. (A typo in our text that inverted dorsal and ventral, but we will correct this in the final version. Also see comments and responses to reviewer Dte5.) Some of these experiments have already been performed (again see comments to Dte5), and are in agreement with our (typo-corrected) predictions. We will also expand on the possible confusion experiments that could be run to test our hypothesis, and include the relevant citations. With regard to explicit descriptions for variable names and references to the supplemental material, we will make these both more clear in the final submission as well.

Thank you for the comments and for taking the time to review our paper. Indeed, we chose to focus our paper on global remapping, with only brief discussion of rate and partial remapping. This is because global remapping has a more dramatic and constraining effect than rate/partial remapping in our analysis: in terms of our manifold picture, partial and rate remapping alter or deform the existing manifolds, while global remapping involves “jumping” from one manifold to another. Global remapping often occurs in situations where context shifts dramatically, which for example can occur when animals move, or are moved, from one environment to another, even if the environments are superficially similar (Leutgeb et. al., 2005 Science, Alme et. al. 2014, PNAS). Partial and rate remapping often occur when an environment is modified, such as via slight changes to wall geometry, introduction of olfactory cues, or movement of cue cards within the same environment (Leutgeb et. al. 2005 Science, Bostock et. al. 1991 Hippocampus, Anderson and Jeffrey, 2003 JNeurosci). In our view, these experiments demonstrate that partial and rate remapping involve a “deformation” of existing memory tasks, while global remapping occurs and is required when completely new memory tasks arise – such as entering a new environment or changing the animal’s goals – so that the animal is required to remember both the current task and the past ones separately, as opposed to slightly modifying the old task. In the context of our manifold picture, partial and rate remapping involve the deformation/refinement of the neural manifolds we are considering, while global remapping involves switching from one manifold to another. Our results about the capacity for storing context follow from estimating the number of such manifolds that can be packed into the activity space in the presence of noise. We can account for partial and rate remapping also in our framework by giving each manifold an additional width due to variations in the encoded structures that are not due to neural noise, but rather due to variations that arise from partial remapping. Thus, the qualitative structure of our results will remain unchanged by including the effects of partial remapping. We will discuss this extension in the revised submission – thank you for encouraging us to do so. Note that, mechanistically, in the context of a network implementation, partial/rate remapping might involve the alteration of some continuous attractor implemented by the hippocampus, while global remapping would involve jumping from one continuous attractor to another.