The dynamics of local cortical networks are irregular, but correlated. Dynamic excitatory–inhibitory balance is a plausible mechanism that generates such irregular activity, but it remains unclear how balance is achieved and maintained in plastic neural networks. In particular, it is not fully understood how plasticity induced changes in the network affect balance, and in turn, how correlated, balanced activity impacts learning. How do the dynamics of balanced networks change under different plasticity rules? How does correlated spiking activity in recurrent networks change the evolution of weights, their eventual magnitude, and structure across the network? To address these questions, we develop a theory of spike–timing dependent plasticity in balanced networks. We show that balance can be attained and maintained under plasticity–induced weight changes. We find that correlations in the input mildly affect the evolution of synaptic weights. Under certain plasticity rules, we find an emergence of correlations between firing rates and synaptic weights. Under these rules, synaptic weights converge to a stable manifold in weight space with their final configuration dependent on the initial state of the network. Lastly, we show that our framework can also describe the dynamics of plastic balanced networks when subsets of neurons receive targeted optogenetic input.
The dynamics of local cortical networks are irregular, but correlated. Dynamic excitatoryinhibitory balance is a plausible mechanism that generates such irregular activity, but it remains unclear how balance is achieved and maintained in plastic neural networks. In particular, it is not fully understood how plasticity induced changes in the network affect balance, and in turn, how correlated, balanced activity impacts learning. How does the dynamics of balanced networks change under different plasticity rules? How does correlated spiking activity in recurrent networks change the evolution of weights, their eventual magnitude, and structure across the network? To address these questions, we develop a general theory of plasticity in balanced networks. We show that balance can be attained and maintained under plasticity induced weight changes. We find that correlations in the input mildly, but significantly affect the evolution of synaptic weights. Under certain plasticity rules, we find an emergence of correlations between firing rates and synaptic weights. Under these rules, synaptic weights converge to a stable manifold in weight space with their final configuration dependent on the initial state of the network. Lastly, we show that our framework can also describe the dynamics of plastic balanced networks when subsets of neurons receive targeted optogenetic input. I. INTRODUCTIONNeuronal activity in the cortex is irregular, correlated, and frequently dominated by a low dimensional component [1][2][3][4][5][6]. Many early models designed to explain the mechanisms that drive irregular neural activity also resulted in asynchronous states [7,8]. However, more recent extensions have shown how correlated states can be generated both internally and exogenously, while preserving irregular single cell activity [9][10][11][12][13].Correlated activity can also drive synaptic plasticity [14,15]. It is thus important to understand how irregular, correlated cortical activity shapes the synaptic architecture of the network, and in turn, how changes in synaptic weights affect network dynamics and correlations. Neural activity is also characterized by a balance between excitation and inhibition [1,[16][17][18][19][20][21]. We therefore ask how weights and population dynamics evolve in such states, and whether different types of synaptic plasticity drive a network out of balance, or help maintain balance in the presence of correlations?To address these questions, we develop a general theory that relates firing rates, spike count covariances, and changes in synaptic weights in balanced spiking networks. Our framework allows us to analyze the effect of general pairwise spike-timing dependent plasticity (STDP) rules. We show how the weights and the network's dynamics evolve under different classical rules, such as Hebbian plasticity, Kohonen's rule, and a form of inhibitory plasticity [22][23][24][25][26]. In general, the predictions of our theory agree well with empirical simulations. We also explain when and how mean field theory d...
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