Minimax and Hamiltonian Dynamics of Excitatory-Inhibitory Networks

A Lyapunov function for excitatory-inhibitory networks is constructed. The construction assumes symmetric interactions within excitatory and inhibitory populations of neurons, and antisymmetric interactions between populations. The Lyapunov function yields su cient conditions for the global asymptotic stability of xed points. If these conditions are violated, limit cycles may be stable. The relations of the Lyapunov function to optimization theory and classical mechanics are revealed by minimax and dissipative Hamiltonian forms of the network dynamics. The dynamics of a neural networkwith symmetric interactionsprovablyconvergesto xed points under very general assumptions 1, 2 . This mathematical result helped to establish the paradigm of neural computation with xed point attractors 3 . But in reality, interactions between neurons in the brain are asymmetric. Furthermore, the dynamical behaviors seen in the brain are not con ned to xed point attractors, but also include oscillations an...

• Type: Conference
• Year: 1997
• Where: NIPS
• Authors: H. Sebastian Seung, Tom J. Richardson, J. C. Lagarias, John J. Hopfield
• Keywords: Lyapunov Function, NIPS 1997, NIPS 2007, Xed Point, Xed Point Attractors