Masa-aki Sato
The Asynchronous MFT Equation
Converges Faster Than the Hopfield Network
Abstract:The analog Hopfield network has been applied for a variety of optimization problems. Peterson and Anderson (Peterson and Anderson 1987, 1988) have shown that the Liapunov function of the Hopfield network corresponds to the free energy function in the mean field theory (MFT）of the Boltzmann machine. They proposed an asynchronous MFT equation to find local minima of the free energy function. However, convergence of the asynchronous MFT equation has not been analyzed theoretically. This article gives proof that the asynchronous MFT equation decreases the free energy by a finite amount at each time step, and converges to a local minimum of the free energy function. It is also shown that the asynchronous MFT equation converges faster than the Hopfield network.
Good solutions for large size TSP can be obtained by using a MFT for a Potts spin model. This article also provides proof that the asynchronous MFT equation for a Potts spin model converges to a local minimum of the model's free energy.