Varying the parameters of weight distribution did not account for the observed amount of HD information conveyed by PoSub-FS cells (Fig. 2a). Rather, we found that the number of inputs received by each output unit was a key factor influencing the amount of HD information (Extended Data Fig. 5e). Varying both weight distribution and the number of input units, we obtained a distribution of HD information in output tuning curves that matched the real data (Extended Data Fig. 5f), revealing that the tuning of PoSub-FS cells can be used to estimate both the distribution of weights and the number of input neurons. Notably, under optimal network conditions, Isomap projection of output tuning curve auto-correlograms has a similar geometry to that of real PoSub-FS cells (Extended Data Fig. 5g), confirming similar distribution of tuning shapes.
To further quantify the relative contributions of ADN and local PoSub inputs to PoSub-FS cell tuning, we expanded the simulation to include the following two inputs: one with tuning curve widths corresponding to ADN-HD cells and one with tuning curve widths corresponding to PoSub-HD cells (Fig. 4h, left). We then trained the model using gradient descent to find the variances and means of input weights that result in the best fit between the simulated output and real data. The combination of parameters that best described the real data resulted in ADN inputs distributed in a near Gaussian-like manner but a heavy-tailed distribution of PoSub-HD inputs (Fig. 4h, middle). Using these distribution parameters, we performed simulations to determine the contribution of ADN-HD and PoSub-HD inputs to the output tuning curves and established that PoSub-FS cell-like outputs are best explained by flat, high firing rate inputs from ADN-HD cells and low firing rate, HD-modulated inputs from PoSub-HD cells (Fig. 4h, right).
Our simulations, complemented by direct analytical derivation (detailed in the Supplementary Methods), not only support the hypothesis that the symmetries observed in PoSub-FS cell tuning curves originate from local cortical circuits but also demonstrate that these symmetries emerge from strongly skewed distributions of synaptic weights.
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