TY - JOUR

T1 - Pattern recognition minimizes entropy production in a neural network of electrical oscillators

AU - Hölzel, Robert W.

AU - Krischer, Katharina

N1 - Funding Information:
Financial support through the cluster of excellence “Nanosystems Initiative Munich” ( NIM ) is gratefully acknowledged. We would also like to thank the referees for constructive criticism of the original manuscript.

PY - 2013/11/22

Y1 - 2013/11/22

N2 - We investigate the physical principle driving pattern recognition in a previously introduced Hopfield-like neural network circuit (Hölzel and Krischer, 2011 [13]). Effectively, this system is a network of Kuramoto oscillators with a coupling matrix defined by the Hebbian rule. We calculate the average entropy production 〈dS/dt〉 of all neurons in the network for an arbitrary network state and show that the obtained expression for 〈dS/dt〉 is a potential function for the dynamics of the network. Therefore, pattern recognition in a Hebbian network of Kuramoto oscillators is equivalent to the minimization of entropy production for the implementation at hand. Moreover, it is likely that all Hopfield-like networks implemented as open systems follow this mechanism.

AB - We investigate the physical principle driving pattern recognition in a previously introduced Hopfield-like neural network circuit (Hölzel and Krischer, 2011 [13]). Effectively, this system is a network of Kuramoto oscillators with a coupling matrix defined by the Hebbian rule. We calculate the average entropy production 〈dS/dt〉 of all neurons in the network for an arbitrary network state and show that the obtained expression for 〈dS/dt〉 is a potential function for the dynamics of the network. Therefore, pattern recognition in a Hebbian network of Kuramoto oscillators is equivalent to the minimization of entropy production for the implementation at hand. Moreover, it is likely that all Hopfield-like networks implemented as open systems follow this mechanism.

KW - Global coupling

KW - Oscillatory network

KW - Time-dependent coupling

KW - Weak coupling

UR - http://www.scopus.com/inward/record.url?scp=84884533351&partnerID=8YFLogxK

U2 - 10.1016/j.physleta.2013.08.022

DO - 10.1016/j.physleta.2013.08.022

M3 - Article

AN - SCOPUS:84884533351

SN - 0375-9601

VL - 377

SP - 2766

EP - 2770

JO - Physics Letters, Section A: General, Atomic and Solid State Physics

JF - Physics Letters, Section A: General, Atomic and Solid State Physics

IS - 39

ER -