Homeostatic Plasticity Enables Stable yet Tunable Neuronal Assemblies

Strongly interconnected neuronal populations, called assemblies, dynamically form through synaptic plasticity mechanisms and are thought to be a substrate for memories in the brain. Many assembly formation models use Hebbian excitatory-to-excitatory plasticity, where coordinated activity strengthens recurrent structure. However, these models typically yield binary assembly outcomes: networks with either weak (no assembly) or maximally strong (assembly) connectivity. We consider networks with a combination of Hebbian excitatory-to-excitatory plasticity and inhibitory-to-excitatory synapses with plasticity that homeostatically stabilizes excitatory neuron firing at a target value. When we set excitatory-to-excitatory plasticity to be homeostatically compliant, in that potentiation and depression are balanced at the homeostatic target firing rate, we find a stable continuum of synaptic strengths, and assembly structure is no longer binary. We use a recurrent network of spiking neuron models and an associated mean-field theory to identify this continuum as a line attractor in synaptic weight space. While along the attractor, homeostasis ensures that neuronal firing rates are invariant, the dynamical response properties of the network are quite malleable, with strongly coupled networks having high gain and longer timescale responses. Using our mean-field theory we show how correlated stochastic spiking activity among the excitatory neurons can destroy the line attractor, yet this can be mitigated when correlated inputs are shared across the excitatory and inhibitory neurons. Altogether, we provide a learning framework based on homeostasis, where a tunable and flexible assembly structure is possible.