Two "correlation games" for a nonlinear network with Hebbian excitatory neurons and anti-Hebbian inhibitory neurons
This work provides a theoretical foundation for neural network models, but it is incremental as it builds on prior work to derive existing network structures from new principles.
The paper tackles the problem of deriving a nonlinear neural network from normative principles by formulating unsupervised learning as a constrained optimization problem and a zero-sum game, resulting in a network where excitatory and inhibitory neurons interact to partially decorrelate excitatory cells.
A companion paper introduces a nonlinear network with Hebbian excitatory (E) neurons that are reciprocally coupled with anti-Hebbian inhibitory (I) neurons and also receive Hebbian feedforward excitation from sensory (S) afferents. The present paper derives the network from two normative principles that are mathematically equivalent but conceptually different. The first principle formulates unsupervised learning as a constrained optimization problem: maximization of S-E correlations subject to a copositivity constraint on E-E correlations. A combination of Legendre and Lagrangian duality yields a zero-sum continuous game between excitatory and inhibitory connections that is solved by the neural network. The second principle defines a zero-sum game between E and I cells. E cells want to maximize S-E correlations and minimize E-I correlations, while I cells want to maximize I-E correlations and minimize power. The conflict between I and E objectives effectively forces the E cells to decorrelate from each other, although only incompletely. Legendre duality yields the neural network.