A network based on the Inverse Function Delayed (ID) model which can recall a temporal sequence of patterns, is proposed. The classical problem that the network is forced to make long distance jumps due to strong attractors that have to be isolated from each other, is solved by the introduction of the ID neuron. The ID neuron has negative resistance in its dynamics which makes a gradual change from one attractor to another possible. It is then shown that a network structure consisting of paired conventional and ID neurons, perfectly can recall a sequence.

In this paper, a simple method to investigate the dynamics of continuous-time neural networks based on the force (kinetic vector) derived from the equation of motion for neural networks instead of the energy function of the system has been described. The number of equilibrium points and limit cycles of one-dimensional neural networks with the asymmetric cyclic connection matrix has been investigated experimently by this method. Some types of equilibrium points and limit cycles have been theoretically analyzed. The relations between the properties of limit cycles and the number of connections also have been discussed.

Self-connection can enlarge the memory capacity of an associative memory based on the neural network. However, the basin size of the embedded memory state shrinks. The problem of basin size is related to undesirable stable states which are spurious. If we can destabilize these spurious states, we expect to improve the basin size. The inverse function delayed (ID) model, which includes the Bonhoeffer-van der Pol (BVP) model, has negative resistance in its dynamics. The negative resistance of the ID model can destabilize the equilibrium states on certain regions of the conventional neural network. Therefore, the associative memory based on the ID model, which has self-connection in order to enlarge the memory capacity, has the possibility to improve the basin size of the network. In this paper, we examine the fundamental characteristics of an associative memory based on the ID model by numerical simulation and show the improvement of performance compared with the conventional neural network.

Many researchers have attempted to solve the combinatorial optimization problems, that are NP-hard or NP-complete problems, by using neural networks. Though the method used in a neural network has some advantages, the local minimum problem is not solved yet. It has been shown that the Inverse Function Delayed (ID) model, which is a neuron model with a negative resistance on its dynamics and can destabilize an intended region, can be used as the powerful tool to avoid the local minima. In our previous paper, we have shown that the ID network can separate local minimum states from global minimum states in case that the energy function of the embed problem is zero. It can achieve 100% success rate in the N-Queen problem with the certain parameter region. However, for a wider parameter region, the ID network cannot reach a global minimum state while all of local minimum states are unstable. In this paper, we show that the ID network falls into a particular permanent oscillating state in this situation. Several neurons in the network keep spiking in the particular permanent oscillating state, and hence the state transition never proceed for global minima. However, we can also clarify that the oscillating state is controlled by the parameter α which affects the negative resistance region and the hysteresis property of the ID model. In consequence, there is a parameter region where combinatorial optimization problems are solved at the 100% success rate.

The visual inspection of defects in products is heavily dependent on human experience and instinct. In this situation, it is difficult to reduce the production costs and to shorten the inspection time and hence the total process time. Consequently people involved in this area desire an automatic inspection system. In this paper, we propose a hardware neural network, which is expected to provide high-speed operation for automatic inspection of products. Since neural networks can learn, this is a suitable method for self-adjustment of criteria for classification. To achieve high-speed operation, we use parallel and pipelining techniques. Furthermore, we use a piecewise linear function instead of a conventional activation function in order to save hardware resources. Consequently, our proposed hardware neural network achieved 6GCPS and 2GCUPS, which in our test sample proved to be sufficiently fast.

In this paper, the authors present a new digital circuit of neuron hardware using a field programmable gate array (FPGA). A new Inverse function Delayed (ID) neuron model is implemented. The Inverse function Delayed model, which includes the BVP model, has superior associative properties thanks to negative resistance. An associative memory based on the ID model with self-connections has possibilities of improving its basin sizes and memory capacity. In order to decrease circuit area, we employ stochastic logic. The proposed neuron circuit completes the stimulus response output, and its retrieval property with negative resistance is superior to a conventional nonlinear model in basin size of an associative memory.

We show that a unit-grup, which represents a group of contiguous units with the same sign of output, is a dominant component for the dynamical behavior of a neural network with anti-symmetrical cyclie connections for the nearest neighbor connections and global connections. In transient state, it is shown that the unit-grup has the dynamics such that the amount n of units which belong to the unit-grup increases with time, and that the increasing rate of n decreases with increasing n. The dynamics cause the large difference of the number of limit-cycles between discrete and continuous time models. Additionally, the period of the limit-cycle depends on the size of the unit-grups. This dependency is obtained from computer simulations and two approximation methods. These approximations provide the lower and the upper bounds of the periods which depend on the gain of an activation function. Using these approximations, we also obtain detailed relations between a period and the other network parameters analytically.

In order to introduce the burst firing, a nerve-cell dynamic feature, we extend the Inverse function Delayed model (ID model), which is the neuron model with ability to oscillate and has powerful ability on the information processing. This dynamics is discussed for the relation with the functional role of the brain and is characterized by repeated patterns of closely spaced action potentials. It is expected that the additional new characteristics add extra functions to neural networks. Using the relation between the ID model and reduced Hodgkin-Huxley model, we propose the neuron model with ability of burst. The proposed model excelled the ID model in solving the N-Queen problem. Additionally, the prototype chip for the burst ID model is implemented and measured.

We have fabricated a new analog memory for integrated artificial neural networks. Several attempts have been made to develop a linear characteristics of floating-gate analog memorys with feedback circuits. The learning chip has to have a large number of learning control circuit. In this paper, we propose a new analog memory SDAM with three cascaded TFTs. The new analog memory has a simple design, a small area occupancy, a fast switching speed and an accurate linearity. To improve accurate linearity, we propose a new chargetransfer process. The device has a tunnel junction (poly-Si/poly-Si oxide/poly-Si sandwich structure), a thin-film transistor, two capacitors, and a floating-gate MOSFET. The diffusion of the charges injected through the tunnel junction are controlled by a source follower operation of a thin film transistor (TFT). The proposed operation is possible that the amounts of transferred charges are constant independent of the charges in storage capacitor.

Further development of a network based on the Inverse Function Delayed (ID) model which can recall temporal sequences of patterns, is proposed. Additional advantage is taken of the negative resistance region of the ID model and its hysteretic properties by widening the negative resistance region and letting the output of the ID neuron be almost instant. Calling this neuron limit ID neuron, a model with limit ID neurons connected pairwise with conventional neurons enlarges the storage capacity and increases it even further by using a weightmatrix that is calculated to guarantee the storage after transforming the sequence of patterns into a linear separation problem. The network's tolerance, or the model's ability to recall a sequence, starting in a pattern with initial distortion is also investigated and by choosing a suitable value for the output delay of the conventional neuron, the distortion is gradually reduced and finally vanishes.