Hopfield Network with State-Dependent Threshold

state-dependent threshold strength λ

-0.015

fractional memory load α

0.2308

In a Hopfield network model, the two states of a neuron (firing or at rest) are denoted by the values

±1

. The future state of a neuron is determined by the present state of all the other neurons via the synaptic matrix, but is independent of its own present state. The overlap

m

between the original and the time-evolved state of the network is a measure of "memory recall"; it depends upon the fractional memory load

α

and a state-dependent neuron firing threshold

-1≤λ≤1

. This Demonstration obtains the average time-evolution of

p

patterns stored in a network of

N

neurons (

α=p/N

) with a neuron-state-dependent firing threshold

λ

. The distribution of resulting overlaps between the time-evolved and original states,

P(m)

, shifts from a peak at one to a broad distribution at lower values of

m

as the memory load increases, indicating the threshold memory capacity of the neural network.