Title :
Lyapunov functions for rotor neural networks
Author_Institution :
Res. Lab. of Electron., MIT, Cambridge, MA, USA
fDate :
29 June-1 July 1994
Abstract :
The state of a rotor neuron is constrained to live on the surface of a sphere in ℜn. A rotor neural network is used to minimize an arbitrary cost function with respect to these "spherical" states. One practical example of such a situation is optimal charge distribution on a sphere in electromagnetism. In this paper, I show that if the cost function is quadratic in the neuron states, the synchronous, iterated-map algorithm used to find the fixed-points of the network has a Lyapunov function. I also propose a continuous-time dynamical system for finding the fixed-points, that is valid for any cost function. Moreover, I show that this continuous-time dynamics has a Lyapunov function. Finally, I show that a similar continuous-time algorithm and a similar Lyapunov function can be used for solving fixed-point equations more general than those of rotor neural networks.
Keywords :
Lyapunov methods; iterative methods; neural nets; Lyapunov functions; arbitrary cost function minimization; continuous-time dynamical system; fixed-points; optimal charge distribution; quadratic cost function; rotor neural networks; spherical states; synchronous iterated-map algorithm; Contracts; Cost function; Covariance matrix; Equations; Laboratories; Lyapunov method; Neural networks; Neurons; Physics; Tin;
Conference_Titel :
American Control Conference, 1994
Print_ISBN :
0-7803-1783-1
DOI :
10.1109/ACC.1994.735196