Elucidating the Selection Mechanisms in Context-Dependent Computation through Low-Rank Neural Network Modeling

Reviewer #1 (Public review):

Summary:

This paper investigates how recurrent neural networks (RNNs) can perform context-dependent decision-making (CDM). The authors use low-rank RNN modeling and focus on a CDM task where subjects are presented with sequences of auditory pulses that vary in location and frequency, and they must determine either the prevalent location or frequency based on an external context signal. In particular, the authors focus on the problem of differentiating between two distinct selection mechanisms: input modulation, which involves altering the stimulus input representation, and selection vector modulation, which involves altering the "selection vector" of the dynamical system.

First, the authors show that rank-one networks can only implement input modulation and that higher-rank networks are required for selection vector modulation. Then, the authors use pathway-based information flow analysis to understand how information is routed to the accumulator based on context. This analysis allows the authors to introduce a novel definition of selection vector modulation that explicitly links it to changes in the effective coupling along specific pathways within the network.

The study further generates testable predictions for differentiating selection vector modulation from input modulation based on neural dynamics. In particular, the authors find that:
(1) A larger proportion of selection vector modulation is expected in networks with high-dimensional connectivity.
(2) Single-neuron response kernels exhibiting specific profiles (peaking between stimulus onset and choice onset) are indicative of neural dynamics in extra dimensions, supporting the presence of selection vector modulation.
(3) The percentage of explained variance (PEV) of extra dynamical modes extracted from response kernels at the population level can serve as an index to quantify the amount of selection vector modulation.

Strengths:

The paper is clear and well-written, and it draws bridges between two recent important approaches in the study of CDM: circuit-level descriptions of low-rank RNNs, and differentiation across alternative mechanisms in terms of neural dynamics. The most interesting aspect of the study involves establishing a link between selection vector modulation, network dimensionality, and dimensionality of neural dynamics. The high correlation between the networks' mechanisms and their dimensionality (Figure 7d) is surprising since differentiating between selection mechanisms is generally a difficult task, and the strength of this result is further corroborated by its consistency across multiple RNN hyperparameters (Figure 7-Figure Supplement 1 and Figure 7-figure supplement 2). Interestingly, the correlation between the selection mechanism and the dimensionality of neural dynamics is also high (Figure 7g), potentially providing a promising future avenue for the study of neural recordings in this task.

Weaknesses:

The first part of the manuscript is not particularly novel, and it would be beneficial to clearly state which aspects of the analyses and derivations are different from previous literature. For example, the derivation that rank-1 RNNs cannot implement selection vector modulation is already present in the Extended Discussion of Pagan et al., 2022 (Equations 42-43). Similarly, it would be helpful to more clearly explain how the proposed pathway-based information flow analysis differs from the circuit diagram of latent dynamics in Dubreuil et al., 2022.

With regard to the results linking selection vector modulation and dimensionality, more work is required to understand the generality of these results, and how practical it would be to apply this type of analysis to neural recordings. For example, it is possible to build a network that uses input modulation and to greatly increase the dimensionality of the network simply by adding additional dimensions that do not directly contribute to the computation. Similarly, neural responses might have additional high-dimensional activity unrelated to the task. My understanding is that the currently proposed method would classify such networks incorrectly, and it is reasonable to imagine that the dimensionality of activity in high-order brain regions will be strongly dependent on activity that does not relate to this task.

Finally, a number of aspects of the analysis are not clear. The most important element to clarify is how the authors quantify the "proportion of selection vector modulation" in vanilla RNNs (Figures 7d and 7g). I could not find information about this in the Methods, yet this is a critical element of the study results. In Mante et al., 2013 and in Pagan et al., 2022 this was done by analyzing the RNN linearized dynamics around fixed points: is this the approach used also in this study? Also, how are the authors producing the trial-averaged analyses shown in Figures 2f and 3f? The methods used to produce this type of plot differ in Mante et al., 2013 and Pagan et al., 2022, and it is necessary for the authors to explain how this was computed in this case.

I am also confused by a number of analyses done to verify mathematical derivations, which seem to suggest that the results are close to identical, but not exactly identical. For example, in the histogram in Figure 6b, or the histogram in Figure 7-figure supplement 3d: what is the source of the small variability leading to some of the indices being less than 1?

Reviewer #2 (Public review):

This manuscript examines network mechanisms that allow networks of neurons to perform context-dependent decision-making.

In a recent study, Pagan and colleagues identified two distinct mechanisms by which recurrent neural networks can perform such computations. They termed these two mechanisms input-modulation and selection-vector modulation. Pagan and colleagues demonstrated that recurrent neural networks can be trained to implement combinations of these two mechanisms, and related this range of computational strategies with inter-individual variability in rats performing the same task. What type of structure in the recurrent connectivity favors one or the other mechanism however remained an open question.

The present manuscript addresses this specific question by using a class of mechanistically interpretable recurrent neural networks, low-rank RNNs.

The manuscript starts by demonstrating that unit-rank RNNs can only implement the input-modulation mechanism, but not the selection-vector modulation. The authors then build rank three networks that implement selection-vector modulation and show how the two mechanisms can be combined. Finally, they relate the amount of selection-vector modulation with the effective rank, ie the dimensionality of activity, of a trained full-rank RNN.

Strengths:

(1) The manuscript is written in a straightforward manner.
(2) The analytic approach adopted in the manuscript is impressive.
(3) Very clear identification of the mechanisms leading to the two types of context-dependent modulation.
(4) Altogether this manuscript reports remarkable insights into a very timely question.

Weaknesses:

- The introduction could have been written in a more accessible manner for any non-expert readers.