Hierarchical Neural Circuit Theory of Normalization and Inter-areal Communication

Reviewer #1 (Public review):

In this paper, Pal and colleagues propose a mechanistic unification of two influential accounts of inter-areal communication: communication through coherence and communication subspaces. A major strength of the paper is that it does not treat coherence and communication subspaces as independent phenomena, as typically done, but instead derives both from the same circuit with divisive normalization. In this framework, noise-driven fluctuations around the normalized fixed point determine covariance and cross-power structure (which, in retrospect, makes so much sense to be related). Then, they show how these determine linear prediction performance and the effective dimensionality of the communication subspace. They also show (however not very visually, see recommendation below for a figure) how divisive normalization is crucial to shape inter-areal coherence and the dimensionality of communication.

I found this conceptual contribution potentially very influential, but somewhat obscured by the technical complexity of the model. The central intuition (I think) is that recurrent normalization can organize cross-area fluctuations, both frequency-specific correlations and cross-covariances. Took me a while to grasp this insight, mostly because I was stuck with the model details. Note that I have some experience with network dynamics, but not with this particular model.

Reviewer #2 (Public review):

Summary:

The authors extend the ORGaNICs framework (a recurrent circuit that dynamically implements divisive normalization) to connected cortical areas with explicit top-down feedback. Because the network has a known analytical fixed point that coincides with (or closely approximates) the normalization equation, the authors can linearize about that fixed point and derive closed-form expressions for the power spectral density, inter-areal coherence, and communication subspaces. Using a two-area instantiation (V1 & V2) with a single fixed parameter set and no data fitting, they show the model reproduces: (i) contrast-response functions with steeper slope V2; (ii) gamma-band power and coherence peaks that shift to higher frequency with contrast; and (iii) a low-dimensional inter-areal communication subspace that is lower-dimensional than the within-area subspace. They derive parallel predictions of what happens by changing model parameters: feedback gain enhances inter-areal and suppresses within-area communication, and normalization is necessary for both the oscillatory dynamics and the reduced subspace dimensionality. A three-area extension (V1&V4, V1&V5/MT) is used to argue that differential top-down feedback can dynamically route functional connectivity.

Strengths:

(1) Analytical tractability: Deriving power spectra, coherence, and communication-subspace structure in closed form from a known fixed point is genuinely valuable.

(2) Conceptual unification: Framing coherence and communication subspaces as arising from the same normalization-driven dynamics is an elegant and useful contribution.

(3) Breadth from few assumptions: A large range of phenomena (contrast gain, gamma dynamics) emerges from normalization-based model assumptions.

(4) Biological grounding: The mapping of model variables onto identified cell types connects the abstract computation to known cortical microcircuitry.

(5) The prediction that input-gain versus feedback-gain modulation produce distinct spectral signatures gives experimentalists a clear way to test the framework.

Weaknesses:

(1) Comparisons are qualitative, not quantitative: The theory/experiment panels are visual side-by-side comparisons. There is no quantitative goodness-of-fit for any predictions.

(2) The simulations use τ ≈ 1 ms for all cell types, which the authors acknowledge is unrealistically short; realistic values would shift the gamma peaks to lower frequencies.

(3) Divisive normalization is a special case and is recovered exactly only for the identity recurrent matrix (self-normalization). Some statements that the circuit implements divisive normalization exactly need softening.

(4) The element-wise (multiplicative) interaction in the modulator dynamics is not tied to a specific cellular mechanism.

Reviewer #3 (Public review):

Summary

The work of Pal and colleagues considers a hierarchical and multi-population version of the "oscillatory recurrent gated neural integrator circuits" (ORGaNICs) model, showing through analytics that the model captures multiple relevant experimental results: first of all, its oscillatory dynamics produce a profile with high resemblance to experimental results, both in terms of decay of power at high frequency and in terms of shifting peak as a function of stimulus contrast. Second, inter-areal communication subspace dimensionality is lower than within-area dimensionality. The authors then proceed to further characterize the model's response properties as a function of input and feedback gain. In particular, they find that frequencies transmitted with higher strength also carry more information, that changing gain modifies the dimensionality of communication subspaces, and that these properties can be used in a three-layer model, where an upstream area can select which downstream area to communicate to, based on the strength of feedback gain.

Strengths

This work demonstrates that a single-circuit model with normalization properties can capture both the oscillatory dynamics and the inter-areal communication properties measured in cortical circuits, matching multiple experimental results. The full analytical tractability of the model is highly advantageous, allowing for easier exploration of parameters, replicability, and effective interpretations of results compared to purely numerical approaches.

The work also makes a useful conceptual link between normalization, coherence-based communication, and subspace-based communication. In particular, it shows how both phenomena can emerge from the same circuit dynamics, where normalization is a key factor.

Interestingly, the model is also extended to multiple areas, showing how attention (in the form of changes in feedback gain) can synchronize the activity of a downstream area with one of two upstream areas, thus effectively selecting which area to communicate with.

In general, this is an interesting computational framework and a useful starting point for future modeling work. A particular strength is that it connects normalization, oscillatory dynamics, coherence, and communication subspaces within one analytically tractable model, making it possible to generate mechanistic hypotheses about when inter-areal communication should be stronger, lower-dimensional, or preferentially routed through feedback.

Weaknesses

Although I see the analytic approach as a strength, at the same time I regard the lack of any numerical comparison as a big weakness. Circuit simulations would not only confirm the correctness of the analytics, but also offer further insights on the error margins and on the regimes where the analytics are valid. This is because, to my understanding, the analytics are based on a linear approximation around the operating regime, which means deviations might be expected, especially for high gain levels in the input, or in the feedforward and feedback pathways.

Another problem is that the analytically tractable model seems to rely on effective connectivity weights that break Dale's law. Numerical simulations with explicitly modeled excitatory and inhibitory units might give insights into effects due, e.g., to the additional transmission delays mentioned in the Discussion.

Another weakness is the use of the term "predictions" to indicate features of the model dynamics that are purely described in the context of the model parameters. Although the model's response properties may certainly lead to predictions, I think the term requires a better contextualization in terms of neurophysiology and experimental neuroscience. The Discussion draws very interesting and valuable bridges between neuron morphology, interneuron types, and model parameters. But it seems it's left to the reader to backtrack and figure out which biological mechanisms or experimental manipulations should correspond to changes in input or feedback gain, and how these should be distinguished from possible changes in feedforward gain.

Relatedly, the manuscript places substantial emphasis on modulation of feedback gain, but does not comparably explore modulation of the feedforward gain, β2, which regulates the V1-to-V2 drive. This seems important because changes in feedforward gain could also influence communication subspace dimensionality and oscillatory dynamics. Therefore, predictions related to top-down feedback modulations should be taken with a grain of salt.

Last but not least, the model dynamics are split among multiple elements and nonlinear interactions, reaching a level of complexity far higher than the other ORGaNICs formulations present in the literature. The authors derive these dynamics in the supplementary material, as a dynamical system that converges to a fixed-point solution that includes "exact divisive normalization". I wonder, however, if there could be simpler solutions that also produce normalization, either approximate or in a different form than the one proposed by the authors. Note also that the designation of "excitatory neurons" is misleading: despite the presence of two explicitly inhibitory populations, the "excitatory" units also interact with negative effective weights both recurrently and in the inter-areal interactions, thus breaking Dale's law.