Minimax and Hamiltonian Dynamics of Excitatory-Inhibitory Networks
Abstract
A Lyapunov function for excitatory-inhibitory networks is constructed. The construction assumes symmetric interactions within excitatory and inhibitory populations of neurons, and antisymmetric interactions be(cid:173) tween populations. The Lyapunov function yields sufficient conditions for the global asymptotic stability of fixed 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.
Cite
Text
Seung et al. "Minimax and Hamiltonian Dynamics of Excitatory-Inhibitory Networks." Neural Information Processing Systems, 1997.Markdown
[Seung et al. "Minimax and Hamiltonian Dynamics of Excitatory-Inhibitory Networks." Neural Information Processing Systems, 1997.](https://mlanthology.org/neurips/1997/seung1997neurips-minimax/)BibTeX
@inproceedings{seung1997neurips-minimax,
title = {{Minimax and Hamiltonian Dynamics of Excitatory-Inhibitory Networks}},
author = {Seung, H. Sebastian and Richardson, Tom J. and Lagarias, J. C. and Hopfield, John J.},
booktitle = {Neural Information Processing Systems},
year = {1997},
pages = {329-335},
url = {https://mlanthology.org/neurips/1997/seung1997neurips-minimax/}
}