The mise en scene of memristive networks: effective memory, dynamics and learning

We introduce a Lyapunov function for the dynamics of memristive circuits, and compare the effectiveness of memristors in minimizing the function to widely used optimization software. We study in particular three classes of problems which can be directly embedded in a circuit topology, and show that memristors effectively attempt at (quickly) extremizing these functionals.

An analysis of the literature shows that there are two types of non-memristive models that have been widely used in the modeling of so-called "memristive" neural networks. Here, we demonstrate that such models have nothing in common with the concept of memristive elements: they describe either non-linear resistors or certain bi-state systems, which all are devices without memory. Therefore, the results presented in a significant number of publications are at least questionabl...

Memory effects are ubiquitous in nature and the class of memory circuit elements - which includes memristors, memcapacitors and meminductors - shows great potential to understand and simulate the associated fundamental physical processes. Here, we show that such elements can also be used in electronic schemes mimicking biologically-inspired computer architectures, performing digital logic and arithmetic operations, and can expand the capabilities of certain quantum computatio...

We discuss the physical properties of realistic memristive, memcapacitive and meminductive systems. In particular, by employing the well-known theory of response functions and microscopic derivations, we show that resistors, capacitors and inductors with memory emerge naturally in the response of systems - especially those of nanoscale dimensions - subjected to external perturbations. As a consequence, since memristances, memcapacitances, and meminductances are simply respons...

We construct an exactly solvable circuit of interacting memristors and study its dynamics and fixed points. This simple circuit model interpolates between decoupled circuits of isolated memristors, and memristors in series, for which exact fixed points can be obtained. We introduce a Lyapunov functional that is found to be minimized along the non-equilibrium dynamics and which resembles a long-range Ising Hamiltonian with non-linear self-interactions. We use the Lyapunov func...

Memristors, resistors with memory whose outputs depend on the history of their inputs, have been used with success in neuromorphic architectures, particularly as synapses and non-volatile memories. However, to the best of our knowledge, no model for a network in which both the synapses and the neurons are implemented using memristors has been proposed so far. In the present work we introduce models for single and multilayer perceptrons based exclusively on memristors. We adap...

Biological neuronal networks are characterized by nonlinear interactions and complex connectivity. Given the growing impetus to build neuromorphic computers, understanding physical devices that exhibit structures and functionalities similar to biological neural networks is an important step toward this goal. Self-organizing circuits of nanodevices are at the forefront of the research in neuromorphic computing, as their behavior mimics synaptic plasticity features of biologica...

The development of memristive device technologies has reached a level of maturity to enable the design of complex and large-scale hybrid memristive-CMOS neural processing systems. These systems offer promising solutions for implementing novel in-memory computing architectures for machine learning and data analysis problems. We argue that they are also ideal building blocks for the integration in neuromorphic electronic circuits suitable for ultra-low power brain-inspired sens...

In this paper, we introduce some interesting features of a memristor CNN (Cellular Neural Network). We first show that there is the similarity between the dynamics of memristors and neurons. That is, some kind of flux-controlled memristors can not respond to the sinusoidal voltage source quickly, namely, they can not switch `on' rapidly. Furthermore, these memristors have refractory period after switch `on', which means that it can not respond to further sinusoidal inputs unt...

In this paper, we briefly review the concept of memory circuit elements, namely memristors, memcapacitors and meminductors, and then discuss some applications by focusing mainly on the first class. We present several examples, their modeling and applications ranging from analog programming to biological systems. Since the phenomena associated with memory are ubiquitous at the nanoscale, we expect the interest in these circuit elements to increase in coming years.