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

TL;DR

This paper derives a nonlinear neural network model with Hebbian excitatory and anti-Hebbian inhibitory neurons from two normative principles, framing it as a zero-sum game that promotes decorrelation and correlation optimization.

Contribution

It introduces two equivalent normative principles leading to a neural network model based on zero-sum games between neuron types, providing a new theoretical foundation.

Findings

The network maximizes S-E correlations under a copositivity constraint.

The E-I conflict encourages decorrelation among E neurons.

The duality approach yields a novel neural network formulation.

Abstract

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.