Sparse balance: excitatory-inhibitory networks with small bias currents and broadly distributed synaptic weights

Abstract

Cortical circuits generate excitatory currents that must be cancelled by strong inhibition to assure stability. The resulting excitatory-inhibitory (E-I) balance can generate spontaneous irregular activity but, in standard balanced E-I models, this requires that an extremely strong feedforward bias current be included along with the recurrent excitation and inhibition. The absence of experimental evidence for such large bias currents inspired us to examine an alternative regime that exhibits asynchronous activity without requiring unrealistically large feedforward input. In these networks, irregular spontaneous activity is supported by a continually changing sparse set of neurons. To support this activity, synaptic strengths must be drawn from high-variance distributions. Unlike standard balanced networks, these sparse balance networks exhibit robust nonlinear responses to uniform inputs and non-Gaussian statistics. In addition to simulations, we present a mean-field analysis to illustrate the properties of these networks.

Input correlations impede suppression of chaos and learning in balanced rate networks

“…Our study is relevant in light of recent advances in optogenetics that allow for time-dependent stimulation of a selected population of neurons. Theoretical models that distinguish between different network dynamic regimes are of interest for this purpose [9,16,17]. Our work addresses this question through the spatiotemporal structure of the feedforward input.…”

“…Chaos in balanced firing-rate networks was studied previously [4,13,14,22], but the dynamic cancellation of correlated input and its implications on chaos suppression in rate networks were not investigated, nor were the implications for learning. It would be interesting to investigate the influence of input correlations on chaos in alternative models of the balanced state [9,17] and rate networks with low-rank structure [24][25][26][27].…”

Targeting diverse operational regimes in recurrent spiking networks

“…Some features predicted by the balanced state, such as high correlations between excitatory and inhibitory currents within neurons, have been observed experimentally [62, 63]. However, other features, such as strong feedforward inputs, have not been experimentally reported, and some experiments argue against it [22, 64–67]. Unlike the balanced state framework, which assumes a tight E/I input balance, alternative models such as the SSN only assume loose E/I balance to achieve inhibitory stabilization [20, 29, 48, 57, 58].…”

“…2 ). Moreover, the distribution of synaptic weights has been shown to play a significant role in the overall activity regime of spiking networks [22, 74], suggesting that heterogeneity in the properties of neuronal populations could be an important feature of spiking networks which future works could include in the SSN prediction. Finally, our study of medium-sized spiking networks (∼ 10 3 neurons) lays the groundwork for the analysis of much larger networks, such as a whole functional area (∼ 10 5 neurons [75]).…”

“…However, the computational hallmarks of the balanced network limit, including response linearity and strong feedforward connections, are not consistent with the diversity of experimentally reported non-linear responses across cortical areas [19] and reports of weak feedforward inputs [20]. Therefore, experimental observations deviating from the balanced state predictions have been often addressed by keeping the core excitatory/inhibitory (E/I) balance framework while adding specific synaptic plasticity rules [21], more complex synaptic strength distributions [22], or a semi-balance condition which allows for excess inhibition [23]. Further-more, the existence and stability of the balanced state limit come with strict conditions on the feedforward and recurrent connection strengths (see [16, 24], Appendix), which exclude many network connectivity configurations.…”