FIG. 3.

Parametrizing correlations via exchangeability. The activity of $K_e=100$ exchangeable synaptic inputs collected over $N$ consecutive time bins can be represented as {0, 1}-valued array ${\left\{X_{k,i}\right\}}_{1\le k\le K_e,1\le i\le N}$, where $X_{k,i}=1$ if input $k$ activates in time bin $i$. Under assumptions of exchangeability, the input spiking correlation is entirely captured by the count statistics of how many inputs coactivate within a given time bin. In the limit $K_e\to \mathrm{\infty }$, the distribution of the fraction of coactivating inputs coincides with the directing de Finetti measure, which we consider as a parametric choice in our approach. In the absence of correlation, synapses tend to activate in isolation: ${\rho }_e=0$ in (a). In the presence of correlation, synapses tend to coactivate, yielding a disproportionately large synaptic activation event: ${\rho }_e=0.1$ in (b). Considering the associated cumulative counts specifies discrete-time jump processes that can be generalized to the continuous-time limit, i.e., for time bins of vanishing duration $\Delta t\to 0^{+}$.