To tackle important combinatorial optimization problems, a variety of annealing-inspired computing accelerators, based on several different technology platforms, have been proposed, including quantum-, optical- and electronics-based approaches. However, to be of use in industrial applications, further improvements in speed and energy efficiency are necessary. Here, we report a memristor-based annealing system that uses an energy-efficient neuromorphic architecture based on a Hopfield neural network. Our analogue–digital computing approach creates an optimization solver in which massively parallel operations are performed in a dense crossbar array that can inject the needed computational noise through the analogue array and device errors, amplified or dampened by using a novel feedback algorithm. We experimentally show that the approach can solve non-deterministic polynomial-time (NP)-hard max-cut problems by harnessing the intrinsic hardware noise. We also use experimentally grounded simulations to explore scalability with problem size, which suggest that our memristor-based approach can offer a solution throughput over four orders of magnitude higher per power consumption relative to current quantum, optical and fully digital approaches. A memristor-based annealing system that uses an analogue neuromorphic architecture based on a Hopfield neural network can solve non-deterministic polynomial (NP)-hard max-cut problems in an approach that is potentially more efficient than current quantum, optical and digital approaches.

Power-efficient combinatorial optimization using intrinsic noise in memristor Hopfield neural networks

The Future of Memristors: Materials Engineering and Neural Networks

When possessing a potential difference between two neurons, an electromagnetic induction current appears in the Hopfield neural network (HNN), which can be emulated by a flux-controlled memristor synapse. Thus, a three-order two-neuron-based autonomous memristive HNN is presented in this paper, which is the lowest order and has not been reported in the previous studies. With the mathematical model, the detailed stability analyses for the line equilibrium are executed, so that the fold and Hopf bifurcation sets and stability region distributions in the parameter plane are obtained. Furthermore, numerical results of coexisting bifurcation patterns are investigated, which are confirmed effectively by local basins of attraction and phase plane plots. The numerical results demonstrate coexisting multi-stable patterns of the spiral chaotic patterns with different dynamic amplitudes, periodic patterns with different periodicities, and stable resting patterns with different positions in the memristive HNN. Besides, the circuit synthesis and breadboard experiments are performed to well validate the numerical simulations.

Coexisting multi-stable patterns in memristor synapse-coupled Hopfield neural network with two neurons

A new hyperbolic-type memristor emulator is presented and its frequency-dependent pinched hysteresis loops are analyzed by numerical simulations and confirmed by hardware experiments. Based on the emulator, a novel hyperbolic-type memristor based 3-neuron Hopfield neural network (HNN) is proposed, which is achieved through substituting one coupling-connection weight with a memristive synaptic weight. It is numerically shown that the memristive HNN has a dynamical transition from chaotic, to periodic, and further to stable point behaviors with the variations of the memristor inner parameter, implying the stabilization effect of the hyperbolic-type memristor on the chaotic HNN. Of particular interest, it should be highly stressed that for different memristor inner parameters, different coexisting behaviors of asymmetric attractors are emerged under different initial conditions, leading to the existence of multistable oscillation states in the memristive HNN. Furthermore, by using commercial discrete components, a nonlinear circuit is designed and PSPICE circuit simulations and hardware experiments are performed. The results simulated and captured from the realization circuit are consistent with numerical simulations, which well verify the facticity of coexisting asymmetric attractors' behaviors.

/pdf/coexisting-behaviors-of-asymmetric-attractors-in-hyperbolic-ik3hsgi9q2.pdf

Coexisting Behaviors of Asymmetric Attractors in Hyperbolic-Type Memristor based Hopfield Neural Network.

The ability to store and manipulate information is a hallmark of computational systems. Whereas computers are carefully engineered to represent and perform mathematical operations on structured data, neurobiological systems adapt to perform analogous functions without needing to be explicitly engineered. Recent efforts have made progress in modelling the representation and recall of information in neural systems. However, precisely how neural systems learn to modify these representations remains far from understood. Here, we demonstrate that a recurrent neural network (RNN) can learn to modify its representation of complex information using only examples, and we explain the associated learning mechanism with new theory. Specifically, we drive an RNN with examples of translated, linearly transformed or pre-bifurcated time series from a chaotic Lorenz system, alongside an additional control signal that changes value for each example. By training the network to replicate the Lorenz inputs, it learns to autonomously evolve about a Lorenz-shaped manifold. Additionally, it learns to continuously interpolate and extrapolate the translation, transformation and bifurcation of this representation far beyond the training data by changing the control signal. Furthermore, we demonstrate that RNNs can infer the bifurcation structure of normal forms and period doubling routes to chaos, and extrapolate non-dynamical, kinematic trajectories. Finally, we provide a mechanism for how these computations are learned, and replicate our main results using a Wilson–Cowan reservoir. Together, our results provide a simple but powerful mechanism by which an RNN can learn to manipulate internal representations of complex information, enabling the principled study and precise design of RNNs. Recurrent neural networks (RNNs) can learn to process temporal information, such as speech or movement. New work makes such approaches more powerful and flexible by describing theory and experiments demonstrating that RNNs can learn from a few examples to generalize and predict complex dynamics including chaotic behaviour.

Teaching recurrent neural networks to infer global temporal structure from local examples

With the discovery of the memristor devices, most researchers have focused on the simulation and application of memristive characteristics, especially the nonvolatile storage potential of the memristor. However, the fusion of image storage and operation is seldom discussed. Therefore, this paper focuses on the electrical characterization of silver chalcogenide based on memristor devices, which can be used as a synapse to mimic the STDP and SRDP learning rules in neuromorphic systems. Then on this basis, a improved memristive cross array structure is designed, whose storage and operation are set in a single unit. Furthermore, this improved memristive cross array and image processing are combined with adjusting the memristor resistance by synaptic plasticity to achieve the integration of storage and processing. Finally, the effectiveness of the design is verified by the LTSPICE experiments of the nonlinear grayscale transformation and logic operation of the image. The design breaks the gap between the processing and storage in the Von Neumann architecture, which will be helpful to the development of the parallel computing in the future.

Fusion of Image Storage and Operation Based on Ag-Chalcogenide Memristor with Synaptic Plasticity

A novel memristive Hopfield neural network with application in associative memory

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Fusion of Image Storage and Operation Based on Ag-Chalcogenide Memristor with Synaptic Plasticity

A novel memristive Hopfield neural network with application in associative memory