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 -