[Hans Blom, 970429c]
(Bill Powers (970428.1637 MST))
The evidence is pretty clear that at the lower levels an "inverse
model" is implemented in hardware, not software.
Except that it does not have to be the actual inverse of the
environmental feedback function. In the PCT model it is not. I think
I may have mentioned this one or ten times in the recent past, but
you haven't responded to that observation. Maybe what you mean is
"sort of an inverse," rather than the actual mathematical inverse.
You're so right. It's much better to both put scare quotes around
every word I use _and_ to modify it with "sort of". Let me rephrase
the above:
The "sort of evidence" is pretty "sort of clear" that at the "sort of
lower" "sort of levels" a "sort of inverse" "sort of model" is "sort
of implemented" in "sort of hardware", not "sort of software".
Am I clearer now? 
I hope I don't have to put scare quotes around my formulas :-).
I thought I remembered from an early post that the amount of
correction of parameters made on each iteration had to be adjusted
properly to avoid oscillation in the adaptation.
No, there is no adjustment "to avoid oscillations". That cannot be
done: oscillations would happen _after_ and _because of_ (incorrect)
"correction" of the parameters and thus cannot be used as a source of
information _now_. It is best to think of parameter adjustment as --
in the full scheme -- real-time statistics operations which "consume"
the mutual information (in the form of correlations between the
regressors, e.g. the controller's in- and outputs) inherent in the
controller's "observations" (including its own output). With a
perfect model and perfect control, there is nothing to consume, and
hence no further tuning. As long as the model is imperfect, however,
learning continues.
Anyway, I was reporting only what we observe in the _human_
controller, whatever model you prefer. Try Rick Marken's experiment
-- I think it's the one on "hierarchical control" -- on his Web
page. This lets you control a cursor at a stationary point for a
while, and then the sign of the external connection quietly changes.
It takes about 0.4 second for the human controller to realize that
something is wrong, and make the required internal reversal. This
change is sudden, as is obvious from the plot of the results.
Repeat the experiment, now not changing the sign but changing the
gain by a factor of 2 (or whatever). An MCT controller's behavior --
and human behavior, I expect -- would show sort of the same results.
The other interesting thing about this experiment is that after the
reversal but prior to the human's compensating reversal, the control
system runs away along an exponentially-accelerating curve (the
behavior of a typical PCT model is shown on the same plot). This
shows that the control system retains its characteristics for a
while after the reversal, so the system itself is not detecting it
-- the behavior is exactly what would be expected of a control
system with fixed parameters when the sign of the external
connection is reversed. Clearly, the required change of parameters
is far from immediate.
We would expect the delay to be due to two sources: (1) a pure delay
because of finite nerve conduction velocities, and (2) a delay due to
gathering sufficient information about the change in the environment
function. The latter will be variable, I predict, and based on the
subject's earlier experiences. If the first sign (or gain) change
occurs after having "learned" for a long time that no such thing ever
happens, the delay may be (much?) larger than when, at a later time,
sign (or gain) changes have become sort of normal. Have you ever
observed this? You would, of course, need to start with a naive
subject.
In fact the delay is approximately what I have estimated to be the
delay in the relationship level -- but that probably means nothing.
Would the delay that you predict be constant? If so, we have a Test.
Greetings,
Hans
