Figure 1

Correlations in the DG. (a) The correlation coefficient $\rho$ increases with firing probability $\mu$ for constant input correlation $\lambda$. (b) The KL divergence ${\Delta }_h$ between the DG and its second-order approximation is modulated by the mean firing rate $\mu$ and the correlation $\rho$ in a population of size $n=5$. (c) In small populations ($n=5$), the multi-information explained ($I_2$) by a DG is close to 1. (d) The strain of the homogeneous DG is negative and correlation dependent. (e) For large populations, $I_2$ between the models is close to 0 for small correlations, i.e., the models are very dissimilar. (f) Scaling of the entropy rate (i.e., entropy per neuron) of the Ising and DG model for mean $\mu =0.1$, and comparison with asymptotic values (labeled $\infty$). The entropy rate drops initially before settling to the asymptotic value. For weak correlations, differences between models only become apparent for large $n$.Reuse & Permissions

Figure 2

Population spike-count distributions and sparsity: (a),(b) The spike-count distributions for the DG (a) and Ising model (b) for population size $n=100$ and $\mu =0.1$ are substantially different. (Large-$n$ approximation, dashed grey lines). Note that $\rho =0.25$ is the critical correlation, and that the Ising model is bimodal, despite the absence of higher-order interactions. (c),(d) Population sparsities for the DG (c) and the corresponding Ising model (d), (parameters as above, sparsity normalized by population size). The DG is much sparser than the Ising model for large population sizes.Reuse & Permissions

Figure 3

Scaling of specific heat: Specific heat of the DG with mean $\mu =0.1$ and correlation $\rho =0.1$ diverges at $T=1$. Inset: The specific heat of the DG at $T=1$ grows linearly with population size, whereas it saturates for the Ising model.Reuse & Permissions