Roadmap on emerging hardware and technology for machine learning.

Recent progress in artificial intelligence is largely attributed to the rapid development of machine learning, especially in the algorithm and neural network models. However, it is the performance of the hardware, in particular the energy efficiency of a computing system that sets the fundamental limit of the capability of machine learning. Data-centric computing requires a revolution in hardware systems, since traditional digital computers based on transistors and the von Neumann architecture were not purposely designed for neuromorphic computing.

High-Performance Mixed-Signal Neurocomputing With Nanoscale Floating-Gate Memory Cell Arrays.

Potential advantages of analog- and mixed-signal nanoelectronic circuits, based on floating-gate devices with adjustable conductance, for neuromorphic computing had been realized long time ago. However, practical realizations of this approach suffered from using rudimentary floating-gate cells of relatively large area. Here, we report a prototype $28\times28$ binary-input, ten-output, three-layer neuromorphic network based on arrays of highly optimized embedded nonvolatile floating-gate cells, redesigned from a commercial 180-nm nor flash memory.

Capacity, Fidelity, and Noise Tolerance of Associative Spatial-Temporal Memories Based on Memristive Neuromorphic Networks.

We have calculated key characteristics of associative (content-addressable) spatial-temporal memories based on neuromorphic networks with restricted connectivity-"CrossNets." Such networks may be naturally implemented in nanoelectronic hardware using hybrid memristive circuits, which may feature extremely high energy efficiency, approaching that of biological cortical circuits, at much higher operation speed. Our numerical simulations, in some cases confirmed by analytical calculations, show that the characteristics depend substantially on the method of information recording into the memory.

Self-Adaptive Spike-Time-Dependent Plasticity of Metal-Oxide Memristors.

Metal-oxide memristors have emerged as promising candidates for hardware implementation of artificial synapses - the key components of high-performance, analog neuromorphic networks - due to their excellent scaling prospects. Since some advanced cognitive tasks require spiking neuromorphic networks, which explicitly model individual neural pulses ("spikes") in biological neural systems, it is crucial for memristive synapses to support the spike-time-dependent plasticity (STDP). A major challenge for the STDP implementation is that, in contrast to some simplistic models of the plasticity, the elementary change of a synaptic weight in an artificial hardware synapse depends not only on the pre-synaptic and post-synaptic signals, but also on the initial weight (memristor's conductance) value.

Training and operation of an integrated neuromorphic network based on metal-oxide memristors.

Despite much progress in semiconductor integrated circuit technology, the extreme complexity of the human cerebral cortex, with its approximately 10(14) synapses, makes the hardware implementation of neuromorphic networks with a comparable number of devices exceptionally challenging. To provide comparable complexity while operating much faster and with manageable power dissipation, networks based on circuits combining complementary metal-oxide-semiconductors (CMOSs) and adjustable two-terminal resistive devices (memristors) have been developed. In such circuits, the usual CMOS stack is augmented with one or several crossbar layers, with memristors at each crosspoint.

Self-organization in autonomous, recurrent, firing-rate CrossNets with quasi-Hebbian plasticity.

We have performed extensive numerical simulations of the autonomous evolution of memristive neuromorphic networks (CrossNets) with the recurrent InBar topology. The synaptic connections were assumed to have the quasi-Hebbian plasticity that may be naturally implemented using a stochastic multiplication technique. When somatic gain g exceeds its critical value g(t), the trivial fixed point of the system becomes unstable, and it enters a self-excitory transient process that eventually leads to a stable static state with equal magnitudes of all the action potentials x(j) and synaptic weights w(jk).

Negative differential resistance at sequential single-electron tunnelling through atoms and molecules.

We have carried out calculations of electron transport in single-electron transistors using single atoms or small molecules as single-electron islands. The theory is based on a combination of (i) the general theory of the sequential single-electron transport through objects with a quantized energy spectrum, developed by Averin and Korotkov, (ii) the ab initio calculation of molecular orbitals and energy spectra within the density functional theory framework (using the NRLMOL software package), and (iii) Bardeen's approximation for the rate of tunnelling due to wavefunction overlap. The results show, in particular, that dc I-V curves of molecular-scale single-electron transistors typically have extended branches with negative differential resistance.

Defect-tolerant architectures for nanoelectronic crossbar memories.

We have calculated the maximum useful bit density that may be achieved by the synergy of bad bit exclusion and advanced (BCH) error correcting codes in prospective crossbar nanoelectronic memories, as a function of defective memory cell fraction. While our calculations are based on a particular ("CMOL") memory topology, with naturally segmented nanowires and an area-distributed nano/CMOS interface, for realistic parameters our results are also applicable to "global" crossbar memories with peripheral interfaces. The results indicate that the crossbar memories with a nano/CMOS pitch ratio close to 1/3 (which is typical for the current, initial stage of the nanoelectronics development) may overcome purely semiconductor memories in useful bit density if the fraction of nanodevice defects (stuck-on-faults) is below approximately 15%, even under rather tough, 30 ns upper bound on the total access time.

Global reinforcement learning in neural networks.

In this letter, we have found a more general formulation of the REward Increment = Nonnegative Factor x Offset Reinforcement x Characteristic Eligibility (REINFORCE) learning principle first suggested by Williams. The new formulation has enabled us to apply the principle to global reinforcement learning in networks with various sources of randomness, and to suggest several simple local rules for such networks. Numerical simulations have shown that for simple classification and reinforcement learning tasks, at least one family of the new learning rules gives results comparable to those provided by the famous Rules A(r-i) and A(r-p) for the Boltzmann machines.

A numerical study of Coulomb interaction effects on 2D hopping transport.

We have extended our supercomputer-enabled Monte Carlo simulations of hopping transport in completely disordered 2D conductors to the case of substantial electron-electron Coulomb interaction. Such interaction may not only suppress the average value of hopping current, but also affect its fluctuations rather substantially. In particular, the spectral density S(I)(f) of current fluctuations exhibits, at sufficiently low frequencies, a 1/f-like increase which approximately follows the Hooge scaling, even at vanishing temperature.

A numerical study of transport and shot noise in 2D hopping.

We have used modern supercomputer facilities to carry out extensive Monte Carlo simulations of 2D hopping (at negligible Coulomb interaction) in conductors with a completely random distribution of localized sites in both space and energy, within a broad range of the applied electric field E and temperature T, both within and beyond the variable-range hopping region. The calculated properties include not only dc current and statistics of localized site occupation and hop lengths, but also the current fluctuation spectrum. Within the calculation accuracy, the model does not exhibit 1/f noise, so that the low-frequency noise at low temperatures may be characterized by the Fano factor F.

CrossNets: high-performance neuromorphic architectures for CMOL circuits.

The exponential, Moore's Law, progress of electronics may be continued beyond the 10-nm frontier if the currently dominant CMOS technology is replaced by hybrid CMOL circuits combining a silicon MOSFET stack and a few layers of parallel nanowires connected by self-assembled molecular electronic devices. Such hybrids promise unparalleled performance for advanced information processing, but require special architectures to compensate for specific features of the molecular devices, including low voltage gain and possible high fraction of faulty components. Neuromorphic networks with their defect tolerance seem the most natural way to address these problems.

Quantum fluctuations in Josephson junction comparators.

We have developed a method for calculation of quantum fluctuation effects, in particular, of the uncertainty zone developing at the potential curvature sign inversion, for a damped harmonic oscillator with arbitrary time dependence of frequency and for arbitrary temperature, within the Caldeira-Leggett model. The method has been applied to the calculation of the gray zone width Delta Ix of Josephson-junction balanced comparators. The calculated temperature dependence of Delta Ix in the range 1.

Universal distribution of transparencies in highly conductive Nb/AlO(x)/Nb junctions.

We report the observation of the universal distribution of transparencies, predicted by Schep and Bauer [Phys. Rev. Lett.

"Single-Electron Parametron": Reversible Computation in a Discrete-State System.

The energy dissipation in a proposed digital device in which discrete degrees of freedom are used to represent digital information (a "single-electron parametron") was analyzed. If the switching speed is not too high, the device may operate reversibly (adiabatically), and the energy dissipation ℰ per bit may be much less than the thermal energy scale kBT (where kB is Boltzmann's constant and T is temperature). The energy-time product ℰtau is, however, much greater than Planck's constant Planck's over 2pi, at least in the standard "orthodox" model of single-electron tunneling that was used in these calculations.