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A companion paper introduces a nonlinear network with Hebbian excitatory (E)neurons that are reciprocally coupled with anti-Hebbian inhibitory (I) neuronsand also receive Hebbian feedforward excitation from sensory (S) afferents. Thepresent paper derives the network from two normative principles that aremathematically equivalent but conceptually different. The first principleformulates unsupervised learning as a constrained optimization problem:maximization of S-E correlations subject to a copositivity constraint on E-Ecorrelations. A combination of Legendre and Lagrangian duality yields azero-sum continuous game between excitatory and inhibitory connections that issolved by the neural network. The second principle defines a zero-sum gamebetween E and I cells. E cells want to maximize S-E correlations and minimizeE-I correlations, while I cells want to maximize I-E correlations and minimizepower. The conflict between I and E objectives effectively forces the E cellsto decorrelate from each other, although only incompletely. Legendre dualityyields the neural network.

Two "correlation games" for a nonlinear network with Hebbian excitatory neurons and anti-Hebbian inhibitory neurons