Page 88 - Artificial Intelligence in the Age of Neural Networks and Brain Computing

76 CHAPTER 3 Third Gen AI as Human Experience Based Expert Systems

We can obtain the learning rule observed the cofiring of the presynaptic activity
and the postsynaptic activity by neurophysiologist D.O. Hebb half century ago
.
namely the product between the presynaptic glial input g and the postsynaptic
. 0 j
output firing rate S . We proved it as follows.
i
.
0 1

D W i;j DH brain DDendrite j . . 0
¼ @ . A z g S ; (3.23)
j
i
Dt D W i;j
DDendrite j
Similar to recursive Kalman filter, we obtain BNN learning update rule
(h z Dt):
. . 0

D W i;j ¼ W i;j ðt þ 1Þ W i;j ðtÞ ¼ g S h (3.24)
j
i
If the node j is a hidden node, then the glial cells pass the MFE credit backward
by chain rule
0 1
. 0
. vH brain X B vH brainC v S j
g h . ¼ @ . 0 A$ .
j
vDentrite j k v S vDentrite j
j
. 0 0 1
v S j X vH brain X . 0
v
¼ . @ . A . 0 W k;i S j
vDentrite j k vDentrite k v S i
j

. 0 . 0 X .
¼ S 1 S g k W k;j (3.25)
j j
k
Use is made of the Riccati equation to derive the window function from the slope
. 0
of a logistic map of the output value 0 S 1 :
j
. 0 .
v S j d s j . . . 0 . 0
. ¼ . ¼ s j 1 s j ¼ S j 1 S j (3.26)
vnet j dnet j
.
vnet k
¼ W k;j (3.27)
. 0
v S
j
Consequently, unsupervised learning “Backprop” has BNN passed the “glue
force,” than supervised learning “Backprop” has ANN “passed the “change.” The
former passes the credit, the latter passes the blames:

. . 0 . 0 X .
g ¼ S j 1 S j g W k;j (3.28)
k
j
k