[Martin Taylor 931016 17:30]
(Bill Powers 931006.1230 to Avery Andrews 931006.1711)

Second, I don't buy the idea of a "template" which implies a
reference pattern with which a perceptual pattern is directly
compared (as a cutout template is compared with an object to see
if the object's shape is right). The PCT model represents all
perceptions as single unidimensional signals, meaning that
reference signals are also single unidimensional signals. In PCT,
an object would be a collection of attribute-signals that enters
an object-detector, with the state of the object in some respect
being represented by the magnitude of the resulting perceptual
signal. All that remains to match is one magnitude for each
degree of freedom (one control system per d.f).

As I understand it, PCT or HPCT make no committment to the form of a
Perceptual Input Function. It is easiest to contemplate ECSs in which
the PIF is a monotonic function of some space defined by "attribute
signals" (sensory signals or lower-level perceptual signals); but there
is no requirement that a PIF have this characteristic, and indeed in
some of his tutorial discussions recently (to Hal?) Bill has been dealing
with control in a world in which the perceptual function is non-monotonic.
The perceptual signal is single-valued, but its value changes non-
monotonically as a function of any path within the space of attribute

OK. The "classic" PIF that is usually used in discussion is a linear
discriminator that divides the attribute space into two contiguous regions,
in one of which the perceptual value is greater than some specified
value and in the other of which it is less. Through any point in the
attribute space there is a non-zero gradient; there are no points in the
attribute space that form a local maximum or minimum. This is the form
usually used in a node of a multilayer perceptron, and is at the base of
my repeated claim that a four-layer HPCT structure could control any
temporal-spatial configuration whatever.

In the non-HPCT world, multilayer perceptrons are used to classify complex
patterns such as handwritten or spoken words. But it is often found that
networks can be more efficient using nodes with a different perceptual
function, called a "radial basis function." Such a function is not a
discriminator. Each radial basis function provides a single-valued
perceptual signal, as the discriminator does. But the function is not
monotonic in the attribute space. It represents a single-peaked mountain
whose value is maximum at some point and grades down to zero at infinity
in every direction in the attribute space. Such a function can be a
"template" in a control system.

A radial basis function cannot be a PIF in a single ECS that controls
its perceptual signal, because there is no direction in the attribute
space that is more likely than another to increase the value of the
perceptual signal. But it could be an element in a more complex kind
of control system that incorporated an e-coli kind of local reorganization
to direct the momentary direction of output effect in the attribute space
(rather like a multidimensional version of Rick's experiment in changing
the direction of linkage between joystick and cursor).

Overall, I see no theoretical objection to the use of radial basis functions
("templates") as PIFs or parts of PIFs in a control hierarchy. The
perceptual signal of such a PIF is the degree to which an input pattern
is like some standard pattern. The pattern could be at any level of
abstraction. Since radial basis functions have proved very effective
in speech recognition experiments--sometimes far more so than discriminant
functions--I would think it not unlikely that they occur in control