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

F. Caravelli

International Journal of Parallel, Emergent and Distributed Systems 33, 350 (2017)

#machinelearning#memristors#dynamicalsystems

Download the PDF

LQ placeholderThe internal memory dynamics of memristors can be interpreted as a learning process following a constrained gradient descent.

The internal memory dynamics of memristors can be interpreted as a learning process following a constrained gradient descent.

We discuss the properties of the dynamics of purely memristive circuits using a recently derived consistent equation for the internal memory variables of the involved memristors. In particular, we show that the number of independent memory states in a memristive circuit is constrained by the circuit conservation laws, and that the dynamics preserves these symmetries by means of a projection on the physical subspace. Moreover, we discuss other symmetries of the dynamics under various transformations of the internal memory, and study the linearized and strongly non-linear regimes of the dynamics. In the strongly non-linear regime, we derive a conservation law for the internal memory variables. We also provide a condition on the reality of the eigenvalues of Lyapunov matrices describing the linearized dynamics close to a fixed point. We show that the eigenvalues ca be imaginary only for mixtures of passive and active components. Our last result concerns the weak non-linear regime. We show that the internal memory dynamics can be interpreted as a constrained gradient descent, and provide the functional being minimized. This latter result provides another direct connection between memristors and learning.

LQ placeholder

Degree-correlations in a bursting dynamic network model

F. Vanni, P. Barucca

Journal of Economic Interaction and Coordination

LQ placeholder

Scale of non-locality for a system of n particles

S. Talaganis, I. Teimouri

Sub. to Physical Review D

LQ placeholder

Changes to Gate Closure and its impact on wholesale electricity prices: The case of the UK

A. Facchini, A. Rubino, G. Caldarelli, G. Liddo

Energy Policy

LQ placeholder

How much can we influence the rate of innovation?

T. Fink, M. Reeves

Science Advances

LQ placeholder

The statistical physics of real-world networks

G. Cimini, T. Squartini, F. Saracco, D. Garlaschelli, A. Gabrielli, G. Caldarelli

Nature Reviews Physics

LQ placeholder

PopRank: Ranking pages’ impact and users’ engagement on Facebook

A. Zaccaria, M. Vicario, W. Quattrociocchi, A. Scala, L. Pietronero

PLoS ONE

128 / 128 papers