Balanced networks under spike-time dependent plasticity

Abstract

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.

Contributions and synaptic basis of diverse cortical neuron responses to task performance

“…Given the instability of pairwise Hebbian excitatory plasticity 32,55 , we included two forms of heterosynaptic plasticity on excitatory-to-excitatory and inhibitory-to-excitatory synapses based on previous spiking RNN studies 33 which would (1) systematically weaken all presynaptic weights to prevent any one presynaptic connection from dominating (heterosynaptic balancing) and (2) systematically strengthen postsynaptic weights to prevent a weakened synapse from dropping out entirely (heterosynaptic balancing) …”

Evaluating the extent to which homeostatic plasticity learns to compute prediction errors in unstructured neuronal networks

“…Initial connectivity in the model is random (connection probability p = 0.1) with initial weights, J ab jk , determined only by pre-and post-synaptic neuron type (J ab jk = j ab for connected neurons). Excitatory connectivity, J ae jk , remained fixed, but inhibitory connectivity evolves according to a homeostatic, inhibitory spike-timing-dependent plasticity (iSTDP) rule [17,19,20,24]. Specifically, each time that neuron j in population a = e, i spikes (which occurs at times t a n,j ), the inhibitory synaptic weights targeting that neuron are updated according to…”

“…As a result, x a j (t) estimates the firing rate of neuron j in population a by performing an exponentiallyweighted sliding average of the spike density. This plasticity rule tends to push excitatory and inhibitory firing rates toward their target rates, r e 0 and r i 0 , respectively (see [17,19,20,22,24] and the mean-field theory presented below).…”

“…While this assumption is strong, it should be satisfied when dX(t) is sufficiently small. In addition, balanced excitation and inhibition linearize the firing rate responses of networks to external input [30,40,41,42,36,43], so this assumption should hold in networks with balanced excitation and inhibition, which is encouraged by inhibitory synaptic plasticity [17,20,22,24].…”

“…Homeostatic inhibitory synaptic plasticity is a widely observed and widely studied type of synaptic plasticity [16,17,18,19,20,15,21] in which the strength of inhibitory synapses are adjusted in an activity-dependent manner that tends to push the postsynaptic neurons' firing rates toward a homeostatic baseline targets. Simulations and theoretical analyses of mathematical models of homeostatic inhibitory plasticity show that, while firing rates are near their targets in response to stimuli on which the network has been trained, firing rates deviate from their targets in response to unfamiliar stimuli in these models [17,22,14,23,15,24].…”