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. A hardware platform based on emerging devices and new architecture is the hope for future computing with dramatically improved throughput and energy efficiency. Building such a system, nevertheless, faces a number of challenges, ranging from materials selection, device optimization, circuit fabrication and system integration, to name a few. The aim of this Roadmap is to present a snapshot of emerging hardware technologies that are potentially beneficial for machine learning, providing the Nanotechnology readers with a perspective of challenges and opportunities in this burgeoning field.

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. All active blocks of the circuit, including 101 780 floating-gate cells, have a total area below 1 mm2. The network has shown a 94.7% classification fidelity on the common Modified National Institute of Standards and Technology benchmark, close to the 96.2% obtained in simulation. The classification of one pattern takes a sub-1- $\mu \text{s}$ time and a sub-20-nJ energy-both numbers much better than in the best reported digital implementations of the same task. Estimates show that a straightforward optimization of the hardware and its transfer to the already available 55-nm technology may increase this advantage to more than $10^{2}\times $ in speed and $10^{4}\times $ in energy efficiency.

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. Of the four methods we have explored, two methods look especially promising-one based on the quadratic programming, and the other one being a specific discrete version of the gradient descent. The latter method provides a slightly lower memory capacity (at the same fidelity) then the former one, but it allows local recording, which may be more readily implemented in nanoelectronic hardware. Most importantly, at the synchronous retrieval, both methods provide a capacity higher than that of the well-known Ternary Content-Addressable Memories with the same number of nonvolatile memory cells (e.g., memristors), though the input noise immunity of the CrossNet memories is lower.

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). However, even in the static state, the spatial distribution of the action potential signs and their correlation with the distribution of initial values x(j)(0) may be rather complicated because of the activation function's nonlinearity. We have quantified such correlation as a function of g, cell connectivity M, and plasticity rate η, for a random distribution of initial values of x(j) and w(jk), by numerical simulation of network dynamics, using a high-performance graphical processing unit system. Most interestingly, the autocorrelation function of action potentials is a nonmonotonic function of g because of a specific competition between self-excitation of the potentials and self-adaptation of synaptic weights.

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. Moreover, as the technology matures, and the pitch ratio approaches an order of magnitude, the crossbar memories may be far superior to the densest semiconductor memories by providing, e.g., a 1 Tbit/cm2 density even for a plausible defect fraction of 2%. These highly encouraging results are much better than those reported in literature earlier, including our own early work, mostly due to more advanced error correcting codes.

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 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. For sufficiently large samples, F scales with conductor length L as (L(c)/L)(α), where α = 0.76 ± 0.08<1, and parameter L(c) is interpreted as the average percolation cluster length. At relatively low E, the electric field dependence of parameter L(c) is compatible with the law [Formula: see text] which follows from directed percolation theory arguments.

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. At higher f, there is a crossover to a broad range of frequencies in which S(I)(f) is nearly constant, hence allowing characterization of the current noise by the effective Fano factor [Formula: see text]. For sufficiently large conductor samples and low temperatures, the Fano factor is suppressed below the Schottky value (F = 1), scaling with the length L of the conductor as F = (L(c)/L)(α). The exponent α is significantly affected by the Coulomb interaction effects, changing from α = 0.76 ± 0.08 when such effects are negligible to virtually unity when they are substantial. The scaling parameter L(c), interpreted as the average percolation cluster length along the electric field direction, scales as [Formula: see text] when Coulomb interaction effects are negligible and [Formula: see text] when such effects are substantial, in good agreement with estimates based on the theory of directed percolation.

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 1.5 to 4.2 K is in virtually perfect agreement with experimental data for Nb-trilayer comparators with critical current densities of 1.0 and 5.5 kA/cm2, without any fitting parameters.