Paradoxical self-sustained dynamics emerge from orchestrated excitatory and inhibitory homeostatic plasticity rules

Cortical networks have the remarkable ability to self-assemble into dynamic regimes in which excitatory positive feedback is balanced by recurrent inhibition. This inhibition-stabilized regime is increasingly viewed as the default dynamic regime of the cortex but how it emerges in an unsupervised manner remains an open question. Theoretical work has established that four sets of weights (WE←E, WE←I, WI←E, WI←I) must obey specific relationships to produce inhibition-stabilized dynamics, but it is not known how the brain autonomously sets the values of all four weight classes to be in the suitable regime. We prove that classic forms of homeostatic plasticity are unable to generate inhibition-stabilized dynamics and that their instability is caused by a signature property of inhibition-stabilized networks: the paradoxical effect. We next derive a novel family of cross-homeostatic rules for the four weight classes that overcome the paradoxical effect and robustly lead to the emerge of stable dynamics. These local rules shed new light on how the brain may reach its default dynamic state and provide a valuable tool to self-assemble artificial neural networks into ideal computational regimes.