First, a number of issues pertaining to analog VLSI implementation of Backpropagation (BP) and Deterministic Boltzmann Machine (DBM) learning algorithms are clarified. According to the results from software simulation, a mismatch between the activation function and derivative generated by independent circuits degrades the BP learning performance. The perfomance can be improved, however, by adjusting the gain of the activation function used to obtain the derivative, irrespective of the original activation function. Calculation errors embedded in the circuits also degrade the learning preformance. BP learning is sensitive to offset errors in multiplication in the learning process, and DBM learning is sensitive to asymmetry between the weight increment and decrement processes. Next, an analog VLSI architecture for implementing the algorithms using common building block circuits is proposed. The evaluation results of test chips confirm that synaptic weights can be updated up to 1 MHz and that a resolution exceeding 14 bits can be attained. The test chips successfully perform XOR learning using each algorithm.

We propose a CMOS circuit that can be used as an equivalent to resistors. This circuit uses a simple differential pair with diode-connected MOSFETs and operates as a high-resistance resistor when driven in the subthreshold region of MOSFETs. Its resistance can be controlled in a range of 1-1000 MΩ by adjusting a tail current for the differential pair. The results of device fabrication with a 0.35-µm 2P-4M CMOS process technology is described. The resistance was 13 MΩ for a tail current of 10 nA and 135 MΩ for 1 nA. The chip area was 105 µm110 µm. Our resistor circuit is useful to construct many high-resistance resistors in a small chip area.

Analog computation is a processing method that solves problems utilizing an analogy of a physical system to the problem. As it is based on actual physical effects and not on symbolic operations, it is therefore a promising architecture for quantum processors. This paper presents an idea for relating quantum structures with analog computation. As an instance, a method is proposed for solving an NP-complete (nondeterminis-tic polynomial time complete) problem, the three-color-map problem, by using a quantum-cell circuit. The computing process is parallel and instantaneous, so making it possible to obtain the solution in a short time regardless of the size of the problem.

A threshold-logic gate device consisting of subthreshold MOSFET circuits is proposed. The gate device performs threshold-logic operation, using the technique of current-mode addition and subtraction. Sample digital subsystems, i.e., adders and morphological operation cells based on threshold logic, are designed using the gate devices, and their operations are confirmed by computer simulation. The device has a simple structure and operates at low power dissipation, so it is suitable for constructing cell-based, parallel processing LSIs such as cellular-automaton and neural-network LSIs.

This paper describes the learning performance of the deterministic Boltzmann machine (DBM), which is a promising neural network model suitable for analog LSI implementation. (i) A new learning procedure suitable for LSI implementation is proposed. This is fully-on-line learning in which different sample patterns are presented in consecutive clamped and free phases and the weights are modified in each phase. This procedure is implemented without extra memories for learning operation, and reduces the chip area and power consumption for learning by 50 percent. (ii) Learning in a layer-type DBM with one output unit has characteristic local minima which reduce the effective number of available hidden units. Effective methods to avoid reaching these local minima are proposed. (iii) Although DBM learning is not suitable for mapping problems with analog target values, it is useful for analog data discrimination problems.

We designed subthreshold analog MOS circuits implementing an inhibitory network model that performs noise-shaping pulse-density modulation (PDM) with noisy neural elements, with the aim of developing a possible ultralow-power one-bit analog-to-digital converter. The static and dynamic noises given to the proposed circuits were obtained from device mismatches of current sources (transistors) and externally applied random spike currents, respectively. Through circuit simulations we confirmed that the circuit exhibited noise-shaping properties, and signal-to-noise ratio (SNR) of the network was improved by 7.9 dB compared with that of the uncoupled network as a result of noise shaping.

We present on-chip oscillator arrays synchronized by random noises, aiming at skew-free clock distribution on synchronous digital systems. Nakao et al. recently reported that independent neural oscillators can be synchronized by applying temporal random impulses to the oscillators [1],[2]. We regard neural oscillators as independent clock sources on LSIs; i.e., clock sources are distributed on LSIs, and they are forced to synchronize through the use of random noises. We designed neuron-based clock generators operating at sub-RF region (< 1 GHz) by modifying the original neuron model to a new model that is suitable for CMOS implementation with 0.25-µm CMOS parameters. Through circuit simulations, we demonstrate that i) the clock generators are certainly synchronized by pseudo-random noises and ii) clock generators exhibited phase-locked oscillations even if they had small device mismatches.

This paper outlines the method of constructing single-electron logic circuits based on the binary decision diagram (BDD), a graphical representation of digital functions. The circuit consists of many unit devices, BDD devices, cascaded to build the tree of a BDD graph. Each BDD device corresponds to a node of the BDD graph and operates as a two-way switch for the transport of a single electron. Any combinatorial logic can be implemented using BDD circuits. Several subsystems for a single-electron processor have been constructed using semiconductor nano-process technology.

This paper describes a guiding principle for designing functional single-electron tunneling (SET) circuitsthat is a way to elicit the potential functions of a given SET circuit by using as a guiding tool the SET circuit stability diagram. A stability diagram is a map that depicts the stable regions of a SET circuit based on the circuit's variable coordinates. By scrutinizing the diagram, we can infer all the potential functions that can be obtained from a circuit configuration. As an example, we take up a well-known SET-inverter circuit and uncover its latent functions by studying the circuit configuration, based on its stability diagram. We can produce various functions, e.g., step-inverter, Schmidt-trigger, memory cell, literal, and stochastic-neuron functions. The last function makes good use of the inherent stochastic nature of single-electron tunneling, and can be applied to Boltzmann-machine neural network systems.

We developed a CMOS watchdog sensor that simulates the changes in quality of perishables such as farm and marine products. The sensor can imitate a chemical reaction that causes the changes in the quality of perishables, with a wide range of activation energy from 0.1 eV to 0.7 eV. Attached to perishable goods, the sensor simulates the deterioration of the goods caused by surrounding temperatures. By reading the output of the sensor, consumers can determine whether the goods are fresh or not. This sensor consists of subthreshold CMOS circuits with a low-power consumption of 5 µW or less.

This paper proposes an architecture for circuit construction for developing single-electron integrated circuits based on majority logic. The majority logic gate circuit proposed consists of a capacitor array for input summation and a single-electron inverter for threshold operation. It accepts an odd number of inputs and produces the corresponding output on the basis of the principle of majority decision; it produces an output of logic "1" if the majority of the inputs is 1, and an output of "0" if the majority is 0. By combining the proposed majority gate circuits, various subsystems can be constructed with a smaller number of devices than that of Boolean-based construction. An adder and a parity generator are designed as examples. It is shown by computer simulation that the designed subsystems produce the correct logic operations. The operation error induced by thermal agitation is also estimated.

This paper proposes a method of constructing single-electron logic subsystems on the basis of the binary decision diagram (BDD). Sample subsystems, an adder and a comparator, are designed by combining single-electron BDD devices. It is demonstrated by computer simulation that the designed subsystems successfully produce, through pipelined processing, an output data flow in response to the input data flow. The operation error caused by thermal agitation is estimated. An output interface for converting single-electron transport into binary-voltage signals is also designed.

We developd a method of implementing a multiple-valued Hopfield network on electronic circuits by using single-electron circuit technology. The single-electron circuit shows quantized behavior in its operation because of the discrete tunnel transport of electrons. It can therefore be successfully used for implementing neuron operation of the multiple-valued Hopfield network. The authors developed a single-electron neuron circuit that can produce the staircase transfer function required for the multiple-valued neuron. A method for constructing a multiple-valued Hopfield network by combining the neuron circuits was also developed. A sample network was designed that solves an example of the quadratic integer-programming problem. And a computer simulation demonstrated that the sample network can converge to its optimal state that represents the correct solution to the problem.

A novel analog-computation system using quantum-dot spin glass is proposed. Analog computation is a processing method that solves a mathematical problem by applying an analogy of a physical system to the problem. A 2D array of quantum dots is constructed by mixing two-dot (antiferromagnetic interaction) and three-dot (ferromagnetic interaction) systems. The simulation results show that the array shows spin-glass-like behavior. We then mapped two combinatorial optimization problems onto the quantum-dot spin glasses, and found their optimal solutions. The results demonstrate that quantum-dot spin glass can perform analog computation and solve a complex mathematical problem.

The Belousov-Zhabotinsky (BZ) reaction provides us important clues in controlling 2D phase-lagged stable synchronous patterns in an excitable medium. Because of the difficulty in computing reaction-diffusion systems in large systems using conventional digital processors, we here propose a cellular-automaton (CA) circuit that emulates the BZ reaction. In the circuit, a two-dimensional array of parallel processing cells is responsible for fast emulation, and its operation rate is independent of the system size. The operations of the proposed CA circuit were demonstrated by using a simulation program with integrated circuit emphasis (SPICE).

Area-restricted illumination of light onto a voltage-biased single-electron tunnel junction array is modeled by reduced resistance of junctions, and its effects on current-voltage characteristics, charge distributions and potential profiles are calculated by a Monte Carlo method. The results show that photocurrent nearly proportional to the applied voltage is generated above a threshold voltage determined by Coulomb blockade effect. The photocurrent increases with increasing irradiated area, which is ascribed to reduction in total resistance of the circuit. Under irradiation, a characteristic charge distribution is formed, i. e. , negative and positive charge bumps are formed in the nodes at the dark and bright boundaries. The charge bumps serve to screen the electric field formed by the bias voltage and create almost a flat potential in the irradiated area. Furthermore, time-response of the charge distribution to a pulse irradiation is also studied. For high dark resistance, the charge bumps are sustained for a long period working as a memory of light. These results suggest feasibility of single-electron photonic devices such as photodetectors and photomemories.

A multiple-valued logic inverter is proposed that uses single-electron-tunneling (SET) circuits in which the discreteness of the electron charge is utilized. The inverter circuit, which is composed of only two SET transistors, has a memory function as well as an inverter function for multiple-valued logic. A quantizing circuit and a D flip-flop circuit for multiple-valued logic can be compactly constructed by combining two inverters. A threshold device can be compactly constructed by attaching more than one input capacitor to the inverter circuit. A quaternary full adder circuit can be constructed by using two threshold devices. Implementation issues are also discussed.

We found a new class of stochastic resonance (SR) in a simple neural network that consists of i) photoreceptors generating nonuniform outputs for common inputs with random offsets, ii) an ensemble of noisy McCulloch-Pitts (MP) neurons each of which has random threshold values in the temporal domain, iii) local coupling connections between the photoreceptors and the MP neurons with variable receptive fields (RFs), iv) output cells, and v) local coupling connections between the MP neurons and the output cells. We calculated correlation values between the inputs and the outputs as a function of the RF size and intensities of the random components in photoreceptors and the MP neurons. We show the existence of "optimal noise intensities" of the MP neurons under the nonidentical photoreceptors and "nonzero optimal RF sizes," which indicated that optimal correlation values of this SR model were determined by two critical parameters; noise intensities (well-known) and RF sizes as a new parameter.

An on-chip process, supply voltage, and temperature (PVT) compensation technique for low-voltage CMOS digital circuits was proposed. Because the degradation of circuit performance originates from the variation of the saturation current in transistors, we developed a compensation circuit consisting of a reference current that is independent of PVT variations. The circuit is operated so that the saturation current in digital circuits is equal to the reference current. The operations of the circuit were confirmed by SPICE simulation with a set of 0.35-µm standard CMOS parameters. Monte Carlo simulations showed that the proposed technique effectively improves circuit performance by 71%. The circuit is useful for on-chip compensation to mitigate the degradation of circuit performance with PVT variation in low-voltage digital circuits.