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 input statistics. Interestingly, the speed, not the size, of synaptic fluctuations dictates the degree of sparsity in the model. In addition to simulations, we provide a mean-field analysis to illustrate the properties of these networks.

Targeting operational regimes of interest in recurrent neural networks

“…Bistability and persistent activity can be obtained in the SSN model [ 30 ] without the need for synaptic plasticity [ 66 ] or complex synaptic weight distributions [ 67 ]. Unlike supersaturation and inhibition stabilization, bistability cannot be delimited by a simple tractable condition on network parameters ( S1 Text ).…”

A Universal Description of Stochastic Oscillators

“…An exciting challenge is to extend our analysis of two coupled oscillators to the general case of N weakly coupled oscillators with its obvious applications to neural [86][87][88], mechano-sensory [89][90][91], genetic [1,92], metabolic [93], and energy supply networks [94], to name but a few examples. Because our analytical approach can be generalized to this case, different scenarios of connectivity (sparse, random or structured) and heterogenity (in the single oscillator properties or in the connections) can be studied analytically.…”

Input correlations impede suppression of chaos and learning in balanced firing-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 [ 10 , 19 , 21 ]. Our work addresses this question through the spatiotemporal structure of the feedforward input.…”

“…between different network dynamic regimes are of interest for this purpose [10,19,21]. Our work addresses this question through the spatiotemporal structure of the feedforward input.…”

“…Chaos in balanced firing-rate networks was studied previously [4,15,16,20], 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 [10,21] and recurrent networks with low-rank structure [26][27][28][29].…”