Nobuyuki Matsui

Qubit neural network and its learning efficiency

Neural networks have attracted much interest in the last two decades for their potential to realistically describe brain functions, but so far they have failed to provide models that can be simulated in a reasonable time on computers; rather they have been limited to toy models. Quantum computing is a possible candidate for improving the computational efficiency of neural networks. In this framework of quantum computing, the Qubit neuron model, proposed by Matsui and Nishimura, has shown a high efficiency in solving problems such as data compression. Simulations have shown that the Qubit model solves learning problems with significantly improved efficiency as compared to the classical model. In this paper, we confirm our previous results in further detail and investigate what contributes to the efficiency of our model through 4-bit and 6-bit parity check problems, which are known as basic benchmark tests. Our simulations suggest that the improved performance is due to the use of superposition of neural states and the use of probability interpretation in the observation of the output states of the model.

Fault-tolerance in nanocomputers: a cellular array approach

Asynchronous cellular arrays have gained attention as promising architectures for nanocomputers, because of their lack of a clock, which facilitates low power designs, and their regular structure, which potentially allows manufacturing techniques based on molecular self-organization. With the increase in integration density comes a decrease in the reliability of the components from which computers are built, and implementations based on cellular arrays are no exception to this. This paper advances asynchronous cellular arrays that are tolerant to transient errors in up to one third of the information stored by its cells. The cellular arrays require six rules to describe the interactions between the cells, implying less complexity of the cells as compared to a previously proposed (nonfault-tolerant) asynchronous cellular array that employs nine rules.

ASSOCIATIVE MEMORY IN QUATERNIONIC HOPFIELD NEURAL NETWORK

Associative memory networks based on quaternionic Hopfield neural network are investigated in this paper. These networks are composed of quaternionic neurons, and input, output, threshold, and connection weights are represented in quaternions, which is a class of hypercomplex number systems. The energy function of the network and the Hebbian rule for embedding patterns are introduced. The stable states and their basins are explored for the networks with three neurons and four neurons. It is clarified that there exist at most 16 stable states, called multiplet components, as the degenerated stored patterns, and each of these states has its basin in the quaternionic networks.

Discrete stochastic process underlying perceptual rivalry

&NA; In perceptual rivalry such as ambiguous figure perception and binocular rivalry, the conscious percept spontaneously alternates between two stable interpretations of an unchanging stimulus. It is well known that the time intervals of the perceptual alternation follow a gamma distribution (GD), but its implication for the alternation mechanism has not been clarified. We examined quantitatively GDs fitted to alternation intervals, and found that the shape‐determining parameter a of the GDs took natural numbers. Because a GD determined by a natural number &agr; is mathematically obtained from a discrete stochastic process (Poisson process), our result indicates that such a stochastic process underlies perceptual rivalry and that the &agr;‐time accumulation of the discrete events causes a perceptual alternation.

An Examination of Qubit Neural Network in Controlling an Inverted Pendulum

The Qubit neuron model is a new non-standard computing scheme that has been found by simulations to have efficient processing abilities. In this paper we investigate the usefulness of the model for a non linear kinetic control application of an inverted pendulum on a cart. Simulations show that a neural network based on Qubit neurons would swing up and stabilize the pendulum, yet it also requires a shorter range over which the cart moves as compared to a conventional neural network model.

Image Compression by Layered Quantum Neural Networks

We have proposed the qubit neuron model as a new scheme in non-standard computing. Identification problems have been investigated on neural networks constructed by this qubit neuron model, and we have found high processing abilities of them. In this paper, we evaluate the performance of the quantum neural network of large size in image compression problems to estimate the utility for the practical applications comparing with the conventional network consists of formal neuron model.

Quaternion Neural Network and Its Application

Quaternion neural networks are models of which computations in the neurons is based on quaternions, the four-dimensional equivalents of imaginary numbers. This paper shows by experiments that the quaternion-version of the Back Propagation (BP) algorithm achieves correct geometrical transformations in color space for an image compression problem, whereas real-valued BP algorithms fail.

A network model based on qubitlike neuron corresponding to quantum circuit

Investigations into quantum computations have begun from the pioneering theoretical studies of Feynman, Deutsch, and others, and detailed studies have been done since the discovery of a quantum algorithm which can solve the problem of factorizing a large integer in polynomial time by Shor in 1994. Recently, the existence of nonalgorithmic quantum computations in microtubules inside a neural circuit has been debated, resulting in the proposal of the concept of the quantum neural computation theory, although detailed studies have not as yet been made. In this paper, in order to construct a new framework for describing the cohesiveness of the distribution and synthesis inherent in a neural network, a neural state is described quantum dynamically and a qubitlike neural network corresponding to the quantum circuit of quantum computations is studied. Specifically, a qubitlike neural network is constructed for a 3-bit quantum circuit, which is the minimum quantum logical gate describing all basic logical operations, and in this model we investigate how to determine circuit parameters by learning.

A Neural Chaos Model of Multistable Perception

We present a perception model of ambiguous patterns based on the chaotic neural network and investigate the characteristics through computer simulations. The results induced by the chaotic activity are similar to those of psychophysical experiments and it is difficult for the stochastic activity to reproduce them in the same simple framework. Our demonstration suggests functional usefulness of the chaotic activity in perceptual systems even at higher cognitive levels. The perceptual alternation may be an inherent feature built in the chaotic neuron assembly.

Fundamental Properties of Quaternionic Hopfield Neural Network

Associative memory by Hopfleld-type recurrent neural networks with quaternionic algebra, called quaternionic Hopfield neural network, is proposed in this paper. The variables in the network are represented by quaternions of four dimensional hypercomplex numbers. The neuron model, the energy function, and the Hebbian rule for embedding patterns into the network are introduced. The properties of this network are analyzed concretely through examples of the network with 3 and 4 quaternion neurons. It is demonstrated that there exist fixed attractors in the network, i.e., the pattern association from test pattern close to a stored pattern is possible in the quaternionic network, as in real-valued Hopfleld networks.