After a decade of research, we developed a prototype device and experimentally demonstrated that the direct phi q interaction could be memristive, as predicted by Chua in 1971. With a constant input current to avoid any parasitic inductor effect, our device meets three criteria for an ideal memristor: a single valued, nonlinear, continuously differentiable, and strictly monotonically increasing constitutive phi q curve, a pinched v i hysteresis loop, and a charge only dependent resistance. Our work represents a step forward in terms of experimentally verifying the memristive flux charge interaction but we have not reached the final because this prototype still suffers from two serious limitations: 1, a superficial but dominant inductor effect (behind which the above memristive fingerprints hide) due to its inductor-like core structure, and 2. bistability and dynamic sweep of a continuous resistance range. In this article, we also discuss how to make a fully functioning ideal memristor with multiple or an infinite number of stable states and no parasitic inductance, and give a number of suggestions, such as open structure, nanoscale size, magnetic materials with cubic anisotropy (or even isotropy), and sequential switching of the magnetic domains. Additionally, we respond to a recent challenge from arXiv.org that claims that our device is simply an inductor with memory since our device did not pass their designed capacitor-memristor circuit test. Contrary to their conjecture that an ideal memristor may not exist or may be a purely mathematical concept, we remain optimistic that researchers will discover an ideal memristor in nature or make one in the laboratory based on our current work.

Restricted Boltzmann machines (RBMs) and their extensions, called 'deep-belief networks', are powerful neural networks that have found applications in the fields of machine learning and artificial intelligence. The standard way to training these models resorts to an iterative unsupervised procedure based on Gibbs sampling, called 'contrastive divergence' (CD), and additional supervised tuning via back-propagation. However, this procedure has been shown not to follow any gradient and can lead to suboptimal solutions. In this paper, we show an efficient alternative to CD by means of simulations of digital memcomputing machines (DMMs). We test our approach on pattern recognition using a modified version of the MNIST data set. DMMs sample effectively the vast phase space given by the model distribution of the RBM, and provide a very good approximation close to the optimum. This efficient search significantly reduces the number of pretraining iterations necessary to achieve a given level of accuracy, as well as a total performance gain over CD. In fact, the acceleration of pretraining achieved by simulating DMMs is comparable to, in number of iterations, the recently reported hardware application of the quantum annealing method on the same network and data set. Notably, however, DMMs perform far better than the reported quantum annealing results in terms of quality of the training. We also compare our method to advances in supervised training, like batch-normalization and rectifiers, that work to reduce the advantage of pretraining. We find that the memcomputing method still maintains a quality advantage ($>1\%$ in accuracy, and a $20\%$ reduction in error rate) over these approaches. Furthermore, our method is agnostic about the connectivity of the network. Therefore, it can be extended to train full Boltzmann machines, and even deep networks at once.

A new computer prototype called a "memcomputer" works by mimicking the human brain, and could one day perform notoriously complex tasks like breaking codes, scientists say. These new, brain-inspired computing devices also could help neuroscientists better understand the workings of the human brain, researchers say. In a conventional microchip, the processor, which executes computations, and the memory, which stores data, are separate components. In contrast, Massimiliano Di Ventra, a theoretical physicist at the University of California, San Diego, and his colleagues are building "memcomputers," made up of "memprocessors," that both process and store data. This setup mimics the neurons that make up the human brain, with each neuron serving as both the processor and the memory. The building blocks of memcomputers were first theoretically predicted in the 1970s, but they were manufactured for the first time in 2008.

We suggest an approach to use memristors (resistors with memory) in programmable analog circuits. Our idea consists in a circuit design in which low voltages are applied to memristors during their operation as analog circuit elements and high voltages are used to program the memristor's states. This way, as it was demonstrated in recent experiments, the state of memristors does not essentially change during analog mode operation. As an example of our approach, we have built several programmable analog circuits demonstrating memristor-based programming of threshold, gain and frequency.