Fig. 5: The presence of network structure of interaction information in populations projecting to the same target.

a, Schematics of a random network (top), a network with clustered interactions (middle) and a network with modular structure (bottom). b, Sketch of how networks with the identical probability of IE and IL interactions can be organized randomly or in clusters of IE or IL pairs. Red and (+) indicate IE pairs. Blue and (−) indicate IL pairs. c, Relative triplet probability with respect to a random network for nonlabeled and same-target populations during correct (left) and incorrect (right) trials. The random network has the same distribution of pairwise interactions, except that they are shuffled between neurons. d, Global cluster coefficient of IE and IL subnetworks relative to a random network. e, Schematic of a two-pool network model. f, Schematic of the space of two-pool networks is quantified in terms of the probability of IE pairs in pool 1 (x axis) and pool 2 (y axis) minus the probability of these pairs in a random network. Red indicates IE pools and blue indicates IL pools. g, Schematic of some examples of symmetric and asymmetric networks corresponding to different points in the two-pool network space along the diagonal (red dashed line) or antidiagonal (blue dashed line) axes. h, Left: the probabilities of different triplets computed for different two-pool networks minus the triplet probabilities in a random network, computed analytically as derived in Supplementary Note ‘Analytical calculation of triplet probabilities in the two-pool model of network structure’ for two-pool networks. Right: the triplet probabilities for three example model networks sampled from the space of two-pool networks. i, At each point in the 2D space of two-pool networks, comparison of the triplet probabilities for the model network and the empirical data. The similarity index ranges from 1 for similar networks to 0 for completely different networks. Yellow circles correspond to networks that are more similar to data for nonlabeled (left) and same-target projection networks (right). The four dashed contours correspond to two-pool networks with similar value of each of the four triplet probabilities to the one obtained from data (from Fig. 5c for correct trials). j, Using pools of neurons defined based on their choice selectivity to left or right choices, the average interaction information within the pool and between the pools, relative to a random network. Pink indicates same-target projections. Black indicates nonlabeled neurons. Statistical tests are performed over all the pairs of neurons in each pool. k, Similar to j but for the probability of IE pairs within or between pools, relative to a random network. Error bars indicate mean ± s.e.m. estimated using bootstrapping. *P < 0.05, **P < 0.01 and ***P < 0.001, two-sided t test with Holm–Bonferroni correction for statistical multiple comparisons. Nonlabeled, n = 1,080,382 triplets; same projection, n = 30,204 triplets.