[From Bill Powers (930520.0830 MDT)]
Rick Marken (930519.1400) --
Rick, I think you're coming closer to elucidating an insight
about language.
talking to Bruce Nevin:
I presume you are using the term "reference perception" to
refer to reference signals or to the reference state of a
controlled perception. In either case, these are not set "based
upon experience of trial and error";
Right, reference perceptions are VARIED, not SET. This seems to
be in conflict with the idea that when we want to indicate a
certain kind of fruit, we say "apple." That sounds like a fixed
means of indicating a particular thing -- what has been described
as a fixed reference signal.
I think that there is some confusion (spread around) about when
to speak of signals and when to speak of functions. What is
learned is not a signal, but a function. If, when you look at a
certain arrangement of plastic and glass in front of you, you
think "computer," it is not the signal "computer" (a perception)
that you have learned, but the perceptual function that
translates a set of perceptions of one kind (visual images) into
a set of perceptions of another kind (words). This function can
convert many different input arrangements into the same output
signal; that's the nature of a function.
Whether we imagine the mechanism to involve memory association or
any other principle is irrelevant. What matters is that
reorganization has brought into being a DEVICE, a physical hookup
of neurons, which, when presented with a set of inputs, produces
signals as outputs. If the input signals vary in a particular
way, the output signal will vary. If they vary in an orthogonal
way, the output signal will remain constant.
In our one-signal-one-perception model, this notion causes some
problems, because at a high enough level, signals seem to
indicate categories that are either present or not present. How
does a control system vary a signal that can be only on or off?
This bring to mind something that Marc Olsen brought up some
months ago -- place-coded perceptions. If there are categorical
perceptions associated with distinct words, the only way to vary
such a perception is to vary _which perceptual function_ is
involved. If the higher-order task is to name something, the only
way to vary the name is to scan through different systems of
lower order, each of which is specialized to produce a perception
of a particular name. So instead of varying the _amplitude_ of an
output signal that is sent to a fixed subset of lower-order
comparators, the output function varies the _destination_ of the
output signal.
This implies an output function with a specific property. As the
scalar error signal varies in amplitude, the output function
converts the amplitude not into an amplitude of a fixed output
signal, but into activation of one output signal in an array of
possible output signals. That is, if the error signal is between
e0 and e1, output A is produced; if between e1 and e2, output B
is produced, and so forth: a different output signal for each
subrange of the error signal.
The way in which this conversion takes place creates an ordering
of the output signals; as the error signals rise and fall, the
outputs are selected in a specific order that always remains the
same. Consider selecting a phrase from the set "none, a little,
some, pretty much, a lot, an abundance." This set is ordered in a
way that goes with an analogue amount. If the analogue amount
increases, we move to the right in the list; if it decreases, we
move to the left. Moving right or left corresponds to selecting
different control systems for producing these different phrases
in perception.
We haven't tried to model any control systems that work this way.
But some day I think we'll have to try. One reason is the way the
visual systems seem to be organized. There is preservation of the
mapping of the retina through many layers in the visual system.
Because of this mapping, a variable like position (on the retina)
is represented not by a single signal of variable magnitude, but
by the movement of a locus of activation across the neural maps
of the retina. Retinal position, at least at the level of the
midbrain, is simply preserved as a position in a network. It may
well be that position is being preserved until a level is reached
where it can be converted into a single signal of variable
magnitude. But in visual tracking, which appears to be a rather
low-level process, setting a position reference signal may well
amount to sending a reference signal to a specific place in the
network, with the tracking action then moving the locus of
retinal activation (filtered through an object-recognizer?) to
that place. The error signal is derived from the distance between
two points in the map.
On the other hand, the mapped position could easily be translated
into a single signal if a neuron received inputs from locations
spaced across the map, with the weights increasing with distance
across the map. I don't think we're in a position yet to guess
how it's really done. Our canonical model is at least
functionally equivalent, because it does predict the overall
result properly.
My point is that the functions that are learned may be
accomplished in ways that we haven't discussed much, and that may
have an application to problems of modeling language. But the
fact remains that signals are VARIABLES, and what is learned, as
Rick is pointing out, is not a signal, but a function that
creates relationships between signals.
We have to distinguish between the form of a function that
creates a perceptual signal dependent on other perceptions, and
the value that the signal happens to have at a given time.
···
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Cliff Joslyn (930519) --
Cliff, your dateline is confusing. What I'm used to is an opening
line that says [From <name of the originator of this post>], with
subsequent subheads that say <originator of the post, with date-
time stamp, whose comments I am commenting upon>.
If you think it's worthwhile trying to get any more sense out of
Faisal Kadri, he's your baby. Right now, I don't feel much
motivation to see any more than you reported.
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Best to all,
Bill P.