591 research outputs found
Asymptotic behavior of memristive circuits
The interest in memristors has risen due to their possible application both
as memory units and as computational devices in combination with CMOS. This is
in part due to their nonlinear dynamics, and a strong dependence on the circuit
topology. We provide evidence that also purely memristive circuits can be
employed for computational purposes. In the present paper we show that a
polynomial Lyapunov function in the memory parameters exists for the case of DC
controlled memristors. Such Lyapunov function can be asymptotically
approximated with binary variables, and mapped to quadratic combinatorial
optimization problems. This also shows a direct parallel between memristive
circuits and the Hopfield-Little model. In the case of Erdos-Renyi random
circuits, we show numerically that the distribution of the matrix elements of
the projectors can be roughly approximated with a Gaussian distribution, and
that it scales with the inverse square root of the number of elements. This
provides an approximated but direct connection with the physics of disordered
system and, in particular, of mean field spin glasses. Using this and the fact
that the interaction is controlled by a projector operator on the loop space of
the circuit. We estimate the number of stationary points of the approximate
Lyapunov function and provide a scaling formula as an upper bound in terms of
the circuit topology only.Comment: 20 pages, 8 figures; proofs corrected, figures changed; results
substantially unchanged; to appear in Entrop
Toward bio-inspired information processing with networks of nano-scale switching elements
Unconventional computing explores multi-scale platforms connecting
molecular-scale devices into networks for the development of scalable
neuromorphic architectures, often based on new materials and components with
new functionalities. We review some work investigating the functionalities of
locally connected networks of different types of switching elements as
computational substrates. In particular, we discuss reservoir computing with
networks of nonlinear nanoscale components. In usual neuromorphic paradigms,
the network synaptic weights are adjusted as a result of a training/learning
process. In reservoir computing, the non-linear network acts as a dynamical
system mixing and spreading the input signals over a large state space, and
only a readout layer is trained. We illustrate the most important concepts with
a few examples, featuring memristor networks with time-dependent and history
dependent resistances
Spiking Neural Networks for Inference and Learning: A Memristor-based Design Perspective
On metrics of density and power efficiency, neuromorphic technologies have
the potential to surpass mainstream computing technologies in tasks where
real-time functionality, adaptability, and autonomy are essential. While
algorithmic advances in neuromorphic computing are proceeding successfully, the
potential of memristors to improve neuromorphic computing have not yet born
fruit, primarily because they are often used as a drop-in replacement to
conventional memory. However, interdisciplinary approaches anchored in machine
learning theory suggest that multifactor plasticity rules matching neural and
synaptic dynamics to the device capabilities can take better advantage of
memristor dynamics and its stochasticity. Furthermore, such plasticity rules
generally show much higher performance than that of classical Spike Time
Dependent Plasticity (STDP) rules. This chapter reviews the recent development
in learning with spiking neural network models and their possible
implementation with memristor-based hardware
Neuro-Fuzzy Computing System with the Capacity of Implementation on Memristor-Crossbar and Optimization-Free Hardware Training
In this paper, first we present a new explanation for the relation between
logical circuits and artificial neural networks, logical circuits and fuzzy
logic, and artificial neural networks and fuzzy inference systems. Then, based
on these results, we propose a new neuro-fuzzy computing system which can
effectively be implemented on the memristor-crossbar structure. One important
feature of the proposed system is that its hardware can directly be trained
using the Hebbian learning rule and without the need to any optimization. The
system also has a very good capability to deal with huge number of input-out
training data without facing problems like overtraining.Comment: 16 pages, 11 images, submitted to IEEE Trans. on Fuzzy system
Reliable Modeling of Ideal Generic Memristors via State-Space Transformation
The paper refers to problems of modeling and computer simulation of generic memristors caused by the so-called window functions, namely the stick effect, nonconvergence, and finding fundamentally incorrect solutions. A profoundly different modeling approach is proposed, which is mathematically equivalent to window-based modeling. However, due to its numerical stability, it definitely smoothes the above problems away
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