Minimax Dynamics of Optimally Balanced Spiking Networks of Excitatory and Inhibitory Neurons

Excitation-inhibition balance is ubiquitously observed in the cortex. Recent studies suggest an intriguing link between balance on fast timescales, tight balance, and efficient information coding with spikes. We further this connection by taking a principled approach to optimal balanced networks of excitatory (E) and inhibitory(I) neurons. By deriving E-I spiking neural networks from greedy spike-based optimizations of constrained minimax objectives, we show that tight balance arises from correcting for deviations from the minimax optimum. We predict specific neuron firing rates in the networks by solving the minimax problems, going beyond statistical theories of balanced networks.