TY - JOUR

T1 - Graph degree sequence solely determines the expected hopfield network pattern stability

AU - Berend, Daniel

AU - Dolev, Shlomi

AU - Hanemann, Ariel

N1 - Publisher Copyright:
© 2014 Massachusetts Institute of Technology.

PY - 2015/1/26

Y1 - 2015/1/26

N2 - We analyze the effect of network topology on the pattern stability of the Hopfield neural network in the case of general graphs. The patterns are randomly selected from a uniform distribution. We start the Hopfield procedure from some pattern v. An error in an entry e of v is the situation where, if the procedure is started at e, the value of e flips. Such an entry is an instability point. Note that we disregard the value at e by the end of the procedure, as well as what happens if we start the procedure from another pattern v v' or another entry e' of v. We measure the instability of the system by the expected total number of instability points of all the patterns. Ourmain result is that the instability of the system does not depend on the exact topology of the underlying graph, but rather only on its degree sequence. Moreover, for a large number of nodes, the instability can be approximated by, where ϕ is the standard normal distribution function and δ1, . . . , δn are the degrees of the nodes.

AB - We analyze the effect of network topology on the pattern stability of the Hopfield neural network in the case of general graphs. The patterns are randomly selected from a uniform distribution. We start the Hopfield procedure from some pattern v. An error in an entry e of v is the situation where, if the procedure is started at e, the value of e flips. Such an entry is an instability point. Note that we disregard the value at e by the end of the procedure, as well as what happens if we start the procedure from another pattern v v' or another entry e' of v. We measure the instability of the system by the expected total number of instability points of all the patterns. Ourmain result is that the instability of the system does not depend on the exact topology of the underlying graph, but rather only on its degree sequence. Moreover, for a large number of nodes, the instability can be approximated by, where ϕ is the standard normal distribution function and δ1, . . . , δn are the degrees of the nodes.

UR - http://www.scopus.com/inward/record.url?scp=84920075170&partnerID=8YFLogxK

U2 - 10.1162/NECO_a_00685

DO - 10.1162/NECO_a_00685

M3 - Letter

C2 - 25380334

AN - SCOPUS:84920075170

SN - 0899-7667

VL - 27

SP - 202

EP - 210

JO - Neural Computation

JF - Neural Computation

IS - 1

ER -