M. K. Ali

Robust chaos in neural networks

Abstract We consider the problem of creating a robust chaotic neural network. Robustness means that chaos cannot be destroyed by arbitrary small change of parameters [Phys. Rev. Lett. 80 (1998) 3049]. We present such networks of neurons with the activation function f ( x )=|tanh s ( x − c )|. We show that in a certain range of s and c the dynamical system x k +1 = f ( x k ) cannot have stable periodic solutions, which proves the robustness. We also prove that chaos remains robust in a network of weakly connected such neurons. In the end, we discuss ways to enhance the statistical properties of data generated by such a map or network.

ASSOCIATIVE MEMORY USING SYNCHRONIZATION IN A CHAOTIC NEURAL NETWORK

Synchronization is introduced into a chaotic neural network model to discuss its associative memory. The relative time of synchronization of trajectories is used as a measure of pattern recognition by chaotic neural networks. The retrievability of memory is shown to be connected to synapses, initial conditions and storage capacity. The technique is simple and easy to apply to neural systems.

PATTERN RECOGNITION WITH STOCHASTIC RESONANCE IN A GENERIC NEURAL NETWORK

We discuss stochastic resonance in associative memory with a canonical neural network model that describes the generic behavior of a large family of dynamical systems near bifurcation. Our result shows that stochastic resonance helps memory association. The relationship between stochastic resonance, associative memory, storage load, history of memory and initial states are studied. In intelligent systems like neural networks, it is likely that stochastic resonance combined with synaptic information enhances memory recalls.

QUANTUM ASSOCIATIVE MEMORY

The unique characteristic of quantum mechanics may be used in the near future to create a quantum associative memory with a capacity exponential in the number of neurons. In this paper we discuss some quantum computational ideas and algorithms necessary to develop a quantum associative memory.

LEARNING, EXPLORATION AND CHAOTIC POLICIES

We consider different versions of exploration in reinforcement learning. For the test problem, we use navigation in a shortcut maze. It is shown that chaotic ∊-greedy policy may be as efficient as a random one. The best results were obtained with a model chaotic neuron. Therefore, exploration strategy can be implemented in a deterministic learning system such as a neural network.

PATTERN RECOGNITION WITH HAMILTONIAN DYNAMICS

We consider pattern recognition schemes that are based upon Hamiltonian dynamical system. Different oscillatory modes are used for storing and encoding patterns, and the effect of resonance is used for determining the most excited mode. We also propose a new technique for pattern orthogonalization resorting to hidden dimensions. Numerical experiments confirm high storage capacity and absence of false memories for the proposed system. Hamiltonian systems may be important as classical analogs of quantum computing systems or quantum neural networks.

Storing Patterns In Hamiltonian Neural Networks

We consider a number of techniques for storing patterns in orthogonal normal modes of a Hamiltonian system. Such techniques, along with the method of selecting the most excited mode, enable us to introduce a new class of pattern recognition systems that we call Hamiltonian neural networks. In contrast to all traditional neural networks, our Hamiltonian neural networks are nondissipative. Quantization of the Hamiltonian of our network is expected to serve as a means for future work on quantum analogs of classical information processing.