Strong and localized recurrence controls dimensionality of neural activity across brain areas

The brain contains an astronomical number of neurons, but it is their collective activity that underlies brain function. The number of degrees of freedom that this collective activity explores – its dimensionality – is therefore a fundamental signature of neural dynamics and computation (1–7). However, it is not known what controls this dimensionality in the biological brain – and in particular whether and how recurrent synaptic networks play a role (8–10). Through analysis of high-density Neuropixels recordings (11), we argue that areas across the mouse cortex operate in a sensitive regime that gives these synaptic networks a very strong role in controlling dimensionality. We show that this control is expressed across time, as cortical activity transitions among states with different dimensionalities. Moreover, we show that the control is mediated through highly tractable features of synaptic networks. We then analyze these key features via a massive synaptic physiology dataset (12). Quantifying these features in terms of cell-type specific network motifs, we find that the synaptic patterns that impact dimensionality are prevalent in both mouse and human brains. Thus local circuitry scales up systematically to help control the degrees of freedom that brain networks may explore and exploit.


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The complexity of a neural network's activity can be 24 measured by its dimensionality -that is, the number of 25 collective degrees of freedom that its neurons explore. Di-26 mensionality is closely linked to neural computation. Signal 27 classification, for example, benefits from network activities 28 that increase the dimensionality of the incoming signals to 29 be classified (2-4, 13, 14). However, compressing inputs 30 into lower-dimensional activity patterns helps generalization 31 to novel signals (1,15,16). Studies have emphasized the     averaged across neurons and across the entire experimental session (orange), averaged within each neural state (red) and after performing LFA for each state (bordeaux). j) Same as i but for the normalized standard deviation of cross-covariances s = δc a . k) Same as i for the relative ratio (s/(s + m)). l) Same as i for the dimensionality measured by the participation ratio (PR), Eq. (1). Left scale (y-axis) extrapolated dimensionality to 10 5 neurons, right scale (y-axis) in percentage normalized to the number of neurons. This suggests that dimensionality should be quantified within 88 and across states, rather than as a single all-encompassing 89 number. 90 We identified states using a Hidden Markov Model (HMM).

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Here, transitions among states are assumed to occur dis-92 cretely via a Markov chain; within each state (colored in-93 tervals in Fig. 1c and Fig. 1f), neurons fire spikes as Poisson  In each session the number of states was set via an unsu-100 pervised cross-validation procedure (7.4 ± 1.7 across 26 ses-101 sions, which ranged from 5 to 11 patterns, see Methods and 102 Fig. S1). Neural states appeared separated in the space of 103 population responses (Fig. 1h), and were influenced by ani-104 mal behavior (e.g. running, Fig. 1d). 105 We computed the widely used participation ratio D PR (17, (1) Here, v, m and s are respectively the ratios between 115 the standard deviation of variances (δa), the average of     (Fig. 2b top), there is a direct relationship between di-182 mensionality and recurrency R: (2) novel compact analytical quantity that shows how recurrency 258 is modulated by local structure: R = σ · R motifs .

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The first term, σ, stems from the strength and number of con-260 nections and has been studied before (56) (see Suppl. Mat.

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S4.7). The second: compactly describes the influence of connectivity motifs, in a 263 form that is novel here. In this equation τ rec , τ chn , τ div , τ con visual cortex (out of more than 32, 000 potential connections 294 that were tested) and 363 synapses from human cortex.

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Recall that the recurrency R as defined above has an over-296 all scaling term, σ, and a motif contribution term given by than those of layer 5 (Fig. 4b). This predicts a higher σ and 304 hence R in layer 2 (Fig. 4d), consistent with the lower dimen-305 sionality found there (Fig. 2e right). Second, as in (12), we 306 noted that PV cells are more connected to pyramidal cells, 307 compared with SST and VIP cells (Fig. 4c). This predicts 308 that changes in PV activity will have a greater effect on re-309 currency and hence dimensionality (Fig. 4e, consistent with 310 Fig. 2f). teract the influence of EE and II motifs and lead to the overall 343 decrease in recurrency R motifs < 1 (Fig. 4h, Fig. S9).

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The distinct roles of E and I motifs in regulating R motifs point 345 to additional ways that recurrency, and hence dimensionality, 346 may be controlled dynamically in neural circuits. As noted 347 above, one pathway for this control is via a differential acti-348 vation of cell types (Fig. 4e), engaging different overall con-349 nection strengths σ in the network. Here, we explore how 350 motifs may play an additional role in this process.

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First, we separately quantified cell-type specific motifs in 352 the synaptic physiology dataset and found strong differences 353 across the analyzed cell types (Fig. S10)   and VIP (Fig. 4j). This was true across all choices of parame-362 ters (Fig. 4k). This result shows an additional mechanism by 363 which an increased activity of PV interneurons may reduce 364 the overall dimensionality, as found in our analysis (Fig. 2f), Next, we asked whether cross-layer differences in connec-370 tivity motifs could likewise affect the recurrency, and hence 371 dimensionality and its modulation across states. We found 372 that the corresponding motif contribution R motifs for exci-373 tatory synapses was significantly stronger for layer 2 and 5 374 than for layer 6 (Fig. 4l). However, when combined with II 375 and EI effects, the overall difference in R motifs across layers 376 2 and 5 reversed (Fig. 4l left) for our default parameters. We 377 conclude that we have evidence that differences in connection 2/3 of the mouse cortex (Fig. 4m).

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Summary and discussion 390 We showed that neural networks across the mouse cortex op-391 erate in a strongly recurrent regime, in which the dimension-392 ality of their activity is strongly constrained. A feature of cir-393 cuits in this regime is the ability to sensitively modulate the 394 relative dimensionality of their activity patterns via their recurrency R, a unifying measure of a network's overall recur-396 rent coupling strength. We note that related concepts of activ-397 ity sensitivity have been studied in other close-to-critical dy-398 namical regimes, such as the reverberating regime controlled 399 by E-I balance rather than recurrency and hypothesized to 400 have important consequences for computation (57).

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Our theoretical work links observations on dimensionality to 402 predictions for network recurrency R: a higher dimensional-403 ity suggests a lower recurrency and vice-versa. Moreover, 404 we showed that the critical circuit features that determine 405 a circuit's recurrency R are not just its overall connection 406 strength, but also a tractable set of local synaptic motifs. We 407 use theoretical tools to quantify the effect of these motifs via a 408 compact index R motifs . This provides a concrete target quan-