Page 84 - Artificial Intelligence in the Age of Neural Networks and Brain Computing

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

FIGURE 3.6
The utility of FMF logic is Boolean Logic of Union W & Intersection X of open set Fuzzy
Membership Functions (FMF) which cannot be normalized as the probability. The
Boolean logic is sharp, not fuzzy. Unfortunately, the shortened “Fuzzy (membership function)
Logic”as “Fuzzy Logic” is a misnomer. Logic cannot be fuzzy, but the set can be open set as
all possibilities. Szu has advocated a bifurcation of chaos (advocated first by Walter
Freeman in human brains with Bob Kozma) as a learnable FMF, making the deterministic
chaos as the learnable dynamics of FMF (cf. Max Planck: ResearcGate.net).

top-down and bottom-up for local concurrency. Richard Lipmann of MITRE has
given a succinct introduction of neural networks in IEEE ASSP Magazine (1984),
where he proved that a single layer can do a linear classifier, and multiple layers
give convex hull classifier to maximize the PD, and minimize the FAR. Stanford
Bernie Widrow; Harvard Paul Werbos, UCSD David Rumelhart, Carnegie-Mellon
James McClelland, U. Torrente Geoffrey Hinton, UCSD Terence Sejnowski, have
pioneered the Deep Learning multiple layer models, Backward Error Propagation
computational (backprop) model. The Output Performance could efficiently be
the supervised learning at Least Mean Square (LMS) error cost function of the
desired outputs versus the actual outputs. The performance model could be more
flexible by the relaxation process as unsupervised learning at Minimum Herman
Helmholtz Free Energy: Brain Neural Networks (BNN) evolves from the Charles
Darwinian fittest survival viewpoint; the breakthrough came when he noted Lyell’s
suggestion that fossils found in rocks at the Galapagos Islands each supported its
own variety of finch bird, a theory of evolution occurring by the process of Natural
Selection or Natural Intelligence at the isothermal equilibrium thermodynamics due

to Ref. [10] a constant temperature brain (Homo sapiens 37 C; Chicken 40 C)
operated at a minimum isothermal Helmholtz free energy when the input power
of pairs transient random disturbance of b brainwaves may be represented by the
degree of uniformity called the entropy S, as indicated by the random pixel
histogram are relaxed to do the common sense work for the survival.
Healthy brain memory may be modeled as BNN serving MPD commutation
computing, and learning at synaptic weight junction level between j-th and i-th neu-
rons that Donald Hebb introduced in a learning model [W j,i ] five decades ago. The
mathematical definition as given by McCullough-Pitts and Von Neumann introduced
the concept of neurons as binary logic element as follows (Fig. 3.7):

.
1
.
.
.
0 a ¼ s X h 1; dsðxÞ ¼ a 1 a ; (3.15a)
. dx
1 þ exp X