Binding in hippocampal-entorhinal circuits enables compositionality in cognitive maps

Summary

The paper proposes a model for spatial representation in the hippocampal formation using a residue number system (RNS) to encode positions as high-dimensional vectors. These vectors are combined into a single representation through vector binding and maintained by a modular attractor network. The model demonstrates robustness to noise, high-resolution encoding, and effective path integration.

Strengths

- Solid theory behind every addition to the RNS model to capture HF functionality - Testable hypotheses for experiments - Limitation about the bio-plausibility of the proposed model was mentioned in the discussion

Weaknesses

- There were several mention of compositionally as the motivation, but there is no direct analyses to show the effectiveness of model in compositionally - There is virtually no comparison to other models in terms of coding range, robustness to noise and compositionality - Code is not provided

Questions

- How does the time-scale of unit responses compared to actual neurons? Is the attractor model fast enough to track the changes in the environment? - The potential prediction for encoding of episodic memory in this framework is not clear to me.

Rating

7

Confidence

2

Soundness

3

Presentation

3

Contribution

3

Limitations

- Comparison to existing methods, or an ablation study on the proposed method to verify the intended computational role for each component - Test of the cognitive map aspect of HF

Summary

This paper proposes a model for spatial representations in the hippocampal formation. The model relies on a residue number system for encoding spatial positions and uses complex-valued vectors to represent individual residues. These vectors are then combined into a unified vector representing spatial position through a conjunctive vector-binding operation that preserves similarities. The model ensures consistency between individual residues and overall position representation through a modular attractor network, which corresponds to the grid cell modules observed in the entorhinal cortex.

Strengths

While there has been an ample amount of work addressing the computations in hippocampal formation, this paper introduces several interesting ideas and combines them into a comprehensive framework. This model integrates principles of optimal coding, such as maximizing coding range and spatial information per neuron, with an algebraic framework for computation in distributed representation.

Weaknesses

While theoretically valuable, the approach remains relatively high-level without a realistic evaluation and comparison with behavioral or neural data.

Questions

Can you clarify what you mean by "carry-free" hexagonal coding? Can you reflect on scalability in terms of the number of neurons. For example, regarding the statement, "In particular, we require that distinct integer values are represented with nearly orthogonal vectors." how does this requirement affect the scalability of the approach? What is the numerical precision required for numerical stability in terms of the neural activity and the synaptic weights? Can you discuss how realistic this approach is in the context of real neurons with firing raters under 100Hz?

Rating

7

Confidence

2

Soundness

3

Presentation

3

Contribution

3

Limitations

The authors have adequately addressed the limitations.

Summary

The paper proposes a computational model that incorporates a number of properties about encoding of space representation in the system. The mathematical framework appears to be well-justified and carry the desired properties. These properties are related to some of the observations made about the properties of space encoding in hippocampus, however I've found that the paper conflates conceptual similarity (a certain mechanisms seems to have certain properties) and computational/mechanistic similarity (a certain brain mechanisms is _actually_ computing like the model suggest), but more about this later. The way I see this work is that is presents an elegant case for encoding of information in mathematical / algebraic sense, but I struggle to connect these properties and the way the system is evaluated to biology. Put another way - I am not sure *why* this particular computational model is a good model for HC? How do we even evaluate if it's close to what the brain is doing? Or maybe this aspect is actually not important to the authors, and the main contribution on this work lies elsewhere? I must admit I might have misunderstood the motivation and the goal of this work, and I will reflect this in my confidence level. To make a better job in the subsequent round of evaluation I would like the authors to explain how do they understand the importance of this work? What is it that main thing that it bring to the table? Apart from mathematical elegance. The evaluation of the model is based on simulated trajectories, but the comparison is done "within" the proposed model, and does not provide external points of reference to allow the reader to understand if the model is better that some other ones? If what regard? Is it empirically better or worse at explaining known biological quirks of the HF, or the goal was only to model similarity conceptual on an abstract level?

Strengths

* The math is rigorous and there is a clear sense that the constructed mathematical framework is a good match to desired properties.

Weaknesses

* The task on which the model is tested (inputs, output, goals) was not clearly defined in the paper, from Section 4 we know that it is about path integrations and there are simulated trajectories (generated according to behavioural rules of animals) that the model is compared against, but * I think there is a dissonance between the claims of the paper regarding neuroscientific impact of this model and the actual comparisons between the model and biology that are brought forward in the paper. If I am correct that these are actually pretty loose, then from here we logically move onto the next question - if the importance is not in that, then what is it in? * The evaluation of simulated trajectories is not too informative, because it is unclear how trivial or non-trivial it is to show the match between simulated trajectories and the model following them.

Questions

(1) The proposed model is based on arithmetic, element-wise operations over vectors, and modulo operations... Is the claim here that computations similar to these ones are happening in HC, or those are just some operations, that satisfy a number of properties? Basically do you want to say that the mechanism of the model is close to HC, or that just some of the observed characteristics of the model are close to HC? (2) Following up on (1) - the closeness between the model and HC is, as far as I can tell, only conceptual, right? There were no comparison made against actual empirical measurements of a biological HC during some task? 122: Could you please elaborate what you mean by "grid modules", I understand that this is different from grid-like spatial activation patterns? Are you referring to grid cells representing different scales, each scale being a "module"? (3) Why the comparison between the trajectories is done using simulated animal trajectories and not actual ones? I understand that it's impossible to model such a chaotic system as a real mouse running in a grid... but if that is the case, what is the benefit of trying to predict trajectories at all, and using simulated trajectories based on some rules of animal behaviour? I guess I am confused about the chosen way to compare the model with biology. Figure 6A (1): What exactly is the baseline model that is marked as "without attractor dynamics"? Figure 6A (2): How come the decoded trajectory matched the true one so closely? Is this result impressive or is it trivial in the context of how the model works and how true trajectories were generated? (4) The predictions listed on lines 316-323 - are they true in biological system? (A) multiplicative interactions between dendritic inputs providing conjunctive binding operation - this one seems to be at the core of potential achievements of the model, but it is very superficially explained, I think it would be great to have a more extensive explanation of what "multiplicative interactions between dendritic inputs providing conjunctive binding operation" actually is, how can we see it manifest in biology, and, after that, how your model achieves it. (B) "Binding between MEC modules" - what is specifically meant by conjunctive composition and binding in neuroscience context as it pertains to your work? Because if we only mean to say that the brain does combines inputs of the modules, then sure, that's trivial and the fact that a model also does that is kind of expected. If you mean some specific mechanism or form of conjunctive composition - then what is it? How does it manifest in biological HF? Does your model do it in the same way? How can we assess that? (C) "relatively fixed attractor weights, plastic HC->sensory weights" - while these are properties of the model, are they properties of the brain?

Rating

5

Confidence

2

Soundness

3

Presentation

3

Contribution

2

Limitations

The authors extensively address the limitation of this work and this provides valuable context to understanding the significance.

Summary

This paper introduces a normative model for spatial representation within the hippocampal formation, integrating optimality principles with an algebraic framework. Spatial positions are encoded using a residue number system (RNS) and represented by high-dimensional, complex-valued vectors. These vectors are combined into a single vector representing position through a similarity-preserving, conjunctive vector-binding operation. The model incorporates a modular attractor network, mirroring the grid cell modules in the entorhinal cortex, to ensure self-consistency among these vectors. The paper showcases the model’s robustness, sub-integer resolution, and path integration capabilities through both theoretical analysis and experimental validation.

Strengths

The use of RNS for spatial representation is a novel approach that maximizes coding range and spatial information per neuron. In addition, the model integrates principles from neuroscience, cognitive science, and artificial intelligence, providing a holistic view of spatial representation in the hippocampal-entorhinal circuits. The authors also provide rigorous theoretical analysis and empirical experiments to support the model’s claims, demonstrating noise robustness and precise spatial representation. The model makes several testable predictions about neural mechanisms, which can guide future experimental research.

Weaknesses

The model’s complexity might pose challenges for practical implementation and experimental validation in biological systems. While the model is comprehensive, it remains a high-level abstraction of spiking neural circuits, potentially overlooking finer neurobiological details.

Questions

1. How biologically plausible is the RNS as a coding mechanism in the hippocampal-entorhinal circuits? Are there any existing biological structures that directly support this model? 2. What specific experiments could be designed to empirically test the predictions made by the model? How feasible are these experiments with current technology? 3. The model suggests encoding contexts as vectors in the entorhinal cortex. How does it manage the vast diversity and complexity of possible contexts in real-world environments? 4. While the model shows robustness to noise in simulations, how would it perform under the more complex and varied types of noise encountered in biological systems?

Rating

7

Confidence

3

Soundness

3

Presentation

3

Contribution

3

Limitations

The model abstracts away many neurobiological details, focusing on high-level representations and processes. This could overlook important aspects of the hippocampal-entorhinal circuitry, such as specific neuronal firing patterns and synaptic plasticity mechanisms. While the modular attractor network is theoretically scalable, it is unclear how well this scalability translates to biological systems. The actual implementation of such a network in the brain might face limitations due to resource constraints and other biological factors.