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

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

#machinelearning#memristors#dynamicalsystems

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.

#### Phase transition creates the geometry of the continuum from discrete space

R. Farr, T. Fink

*Physical Review E*

#### The statistical physics of real-world networks

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

*Nature Reviews Physics*

#### On defining the Hamiltonian beyond quantum theory

D. Branford, O. Dahlsten, A. Garner

*Foundations of Physics*

#### Reconstructing grain-shape statistics from electron back-scatter diffraction microscopy

R. Farr, Z. Vukmanovic, M. Holness, E. Griffiths

*Physical Review Materials*

#### Tackling information asymmetry in networks: a new entropy-based ranking index

P. Barucca, G. Caldarelli, T. Squartini

*Journal of Statistical Physics*

#### Eigenvalues of subgraphs of the cube

B. Bollobás, J. Lee, S. Letzter

*European Journal of Combinatorics*

#### Maximum one-shot dissipated work from Rényi divergences

N. Halpern, A. Garner, O. Dahlsten, V. Vedral

*Physical Review E *

123 / 123 papers