Huang Wu-qun

Chaotic neural network with nonlinear self-feedback and its application in optimization

Abstract When a special nonlinear self-feedback is introduced into the Hopfield model, the network becomes a chaotic one. Chaotic dynamics of the system can prevent its state from staying at local minima of the energy indefinitely. The system then gets the ability to transfer chaotically among local minima, which can be employed to solve optimization problems. With autonomous adjustment of the parameters, the system can realize the global optimal solution eventually or approximately with transient chaos. Simulations on the Traveling Salesman Problem (TSP) have shown that the proposed chaotic neural network can converge to the global minimum or its approximate solutions more efficiently than the Hopfield network.

Dynamics of Transiently Chaotic Neural Network and Its Application to Optimization

Through adding a nonlinear self-feedback term in the evolution equations of neural network, we introduced a transiently chaotic neural network model. In order to utilize the transiently chaotic dynamics mechanism in optimization problem efficiently, we have analyzed the dynamical procedure of the transiently chaotic neural network model and studied the function of the crucial bifurcation parameter which governs the chaotic behavior of the system. Based on the dynamical analysis of the transiently chaotic neural network model, chaotic annealing algorithm is also examined and improved. As an example, we applied chaotic annealing method to the traveling salesman problem and obtained good results.

Chaotic Dynamics in Weight Space of Neural Networks

When a special nonlinear self-feedback term is introduced into the dynamical equation of the backpropagation training algorithm for networks, the dynamics in weight space of networks can become chaotic. Chaotic dynamics of the system can help it escape from the most commonplace local minima of the energy. Simulation on the XOR problem and the prediction of chaotic time series have shown that the proposed chaotic training algorithm can converge to the global minimum or its approximate solutions efficiently and dramatically faster than the original backpropagation training algorithm.

A cascaded model of neural network for pattern recognition

A cascaded model of neural network and its learning algorithm suitable for optical implementation are proposed. Computer simulations have shown that this model may successfully be applied to an error-tolerance pattern recognitions of multiple 3-D targets with arbitrary spatial orientations.

The Scaling Exponent for 2-Dimensional 6-State Potts Model*

Using an optimal Monte Carlo renormalization group method, the scaling exponent for six-state Potts model on 2-dimensional random triangle lattice is studied. The scaling exponent , is consistent with the expectant value of the scaling theory.

Scaling exponent for 3-state Potts model on 3-dimensional random triangle lattice

An optimal Monte Carlo renormalization group method is applied to 3-state Potts model on 3-dimensional random triangle lattice. The scaling exponent ν of the first order phase transition of this model has been obtained. In the disorder phase ν = 0.369(±0.044), yT = 1/ν = 2.71(±0.32), in the order phase ν = 0.393(±0.048), yT = 2.54(±0.31). They approximate to the prediction of the scaling theory.

Phase Transition and Critical Behavior for XY Model on 2-Dimensional Random Triangle Lattice*

The Monte Carlo renormalization group method is applied to discussing the nature of phase transition of XY model on 2-dimensional random triangle lattices. A line of fixed point and un-universal phase transition are found. The results are in agreement with Kosterlitz-Thouless theory. The susceptibility shows a clear size-dependent low temperature region. This means that it should be divergent in this region.

The phase structure for two parameter actions in SU(2) lattice gauge theory

The variational method has been applied to investigating the phase diagrams of the two parameter actions containing TrU(∂P)3 term in SU(2) lattice gauge theory. The result is in agreement with that obtained by Monte Carlo simulations. This can be helpful to understand the mechanism of the phase transitions.