[Martin Taylor 941229 18:45]
Bill Powers (941229.1500 MST)
Martin Taylor (941229.1430)
I thought I was trying to solve the problem you pose. Yes, there is a
"goal in the hierarchy." It is to keep the intrinsic variables at
their reference levels.But what system is it that perceives and controls intrinsic variables? A
system that controls the relationship between a target and a cursor
can't ALSO be concerned with controlling intrinsic variables, can it?
No more than a control system that controls for intensities of a stimulus
can ALSO be concerned with the transitions that are controlled at a
higher level. Same deal. Different control systems are concerned with
their own thing. They don't care what inputs they get that they transform
into their perceptual signals. They don't care where their outputs go
or what they do, provided that their perceptual signals come to the
reference level rather than diverging from it or moving erratically.
The systems that perceive and control intrinsic variable are exactly the
same as in the separate reorganizing structure. The ONLY difference between
the two structures is where the outputs of those systems go. In the
localized structure, they contribute to the reference signals of other
ECUs, whereas in the separate structure they affect the parameters of
the main hierarchy. There really isn't any other difference--none, at least,
in how the values of the intrinsic variables are influenced, and none in where
the reference values for those variables come from. The only difference
is in how the outputs of those intrinsic variable control systems act on
the outer world through the main hierarchy. In the localized system,
they act in the same way as any other ECU. In the separate system, they
don't. The reorganization "events" in the localized system are influenced
by local error, which doesn't, in itself, contribute to the values of the
intrinsic variables.
I have been thinking that the only system that can control the states of
intrinsic variables is one that perceives them, compares the perception
with a reference level, and acts on the basis of the difference. What
are you talking about?
The same.
The primary thing that is varied is, in the separate reorganizing
structure, the various signal paths (and the related I/O functions for
the different ECUs). In the localized system, the primary thing that
is varied is the set of reference signal LEVELS. Paths do change, but
as a consequence of failure to control, locally.I must be particularly dense this afternoon. In a localized system,
changing reference _levels_ for lower systems is the normal mode of
operation, isn't it?
Yes, that's one thing I find attractive about the idea.
A reorganizing aspect of a local system in the
hierarchy would have to do things like varying the output gain or the
weightings of signals sent to lower systems -- but the _values_ of the
signals reaching lower systems have to be determined (via the output
function) by the error signal if we're to have a behavioral control
system of the usual sort.
Yes, of course.
Perhaps what didn't come across in any of my last few postings is
that much of what the separate reorganizing system accomplishes by changing
the structure of the main hierarchy, the localized reorganizing system
accomplishes in the "normal mode of operation" without changing the structure
of the hierarchy. When the localized system does reorganize, the things
that are changed are as you say. But it doesn't have to happen as fast
as it does in the separate reorganizing structure, since the "normal mode"
of control of the intrinsic variables is the same as the "normal mode" of
control of any other perceptual signal.
You can't have a higher system learning to
send a particular _value_ of reference signal to lower systems, can you?
Not that I know of!!!
···
================
(I hope this indenting is sufficient to mark off your posts -- I get
tired of deleting hard returns and adding all those ">" marks).
Fine by me. The way I do it, putting in the > marks is easier.
The third (Genetic Algorithm) method will be interesting to see. I've
always wondered how the characteristics of real parents are "combined"
to produce new characteristics in the offspring. If one parent control
system has a gain of 100 and the other a gain of 20, does the child
control system have a gain of 60? Or if one parent perceives a color
that is .3*red + 0.6*green + 0.8*blue, and the other perceives a
different weighting, how do we combine these to create the child's
perceptual function? Or if one parent writes right-handed and the other
writes left-handed, how does the child write?
Well, I don't know how (or whether) it WILL work, but here's how I imagine
it working.
Let's consider an ECU as having four "corners", representing sensory
signals in, perceptual signal out (both upward-going), and reference
signals in, output signal out (both downgoing, and by "reference signals"
I mean the contributions from higher ECSs). Each "corner" has a set of
links to other ECUs. The upgoing and downgoing links may be, but need
not be, to the same set of higher or lower ECUs. The links to the ECUs
at the level below are associated with weights (by convention--it could
be the links to the higher level, or to both; for this discussion it
doesn't matter).
Internal to the ECU are further properties, specifically, the forms of the
perceptual function and the output function (and I often also think of
the incoming contributions to the reference signals as being combined
by some sort of function, but that is optional, and simple addition might
be just fine). And finally, there may be external connections that
affect the gain, or it might be a heritable property or one that evolves
with time according to the success the ECU has in control (increasing
if control is good, decreasing if bad, as one aspect of localized
reorganization).
So, one has a set of preperties, which could be laid out something like this:
Sensory inputs from: (35, 0.3), (2715, -1.2), (4098, 0.1), ....
Perceptual outputs to: 1214, 3067, 24, ...
Reference inputs from: ...
Outputs to: ...
Perceptual input function: (sum of squared inputs + derivative of same)
Output function: (leaky integral, time-constant tau)
Each ECU has such a set. In the "Sensory inputs" line, the bracketed pairs
are supposed to mean the label of the source ECU and the weight it is
given. When combining them using the GA approach, I would take each line
of the above to represent one chromosome, which means that Baby would
not mix up elements from one line of Pop with those of a different line
of Mom, except very rarely (genes do jump chromosomes just occasionally).
Baby would get a set of elements from Pop and a set from Mom of each
line. In the case of the functions, Baby might just take either Mom's
or Pop's. But there are recombinable elements of functions that make
sense sometimes, and Baby might get some kind of composite function, or
perhaps occasionally the sum of both functions--that's how new kinds
of functions might come to exist.
if one parent perceives a color
that is .3*red + 0.6*green + 0.8*blue, and the other perceives a
different weighting, how do we combine these to create the child's
perceptual function?
As I conceive it, if one has 0.3R+0.6G+0.8B and the other has 0.7R+0.2G+0.4B,
the child might have 0.7R+0.6G+0.8B, or 0.3R+0.6G+0.4B, but it would
never have 0.5R+0.4G+0.6B. Similarly with the "right-handed v left-handed"
question. The child would be one or the other.
But there can be functions affected by multiple genes, and then one can
get averaging. Let's suppose that the colour weighting of 0.3R in Mom
was generated NOT by one link of weight 0.3, but by summing four links
of weight 0.1 and one of weight -0.1, and that 0.7R (in Pop) was generated
by 9 links of weight 0.1 and two of weight -0.1. Then Baby could have
any weight for R between -0.3 and +1.3, with the most probable weight
being around 0.5.
If Mom and Pop are on the same level of the hierarchy, so is Baby. But if
Mom and Pop are on neighbour levels, Baby is a bastard! Baby has some
inputs from and outputs to different levels. If this turns out to be good,
in that Baby can control without screwing up neighbour ECUs (including
Mom and Pop as probably the closest neighbours), there's no problem. But
much more probably, there will be conflict, and local relinking and
reorganization by changing functions and weights will go on. I suspect
what will happen is that the level-jumping links will tend to vanish
more readily than the ones that leave Baby on an identifiable level,
with connections going one-up and one-down. That level may not be the
level of either Mom or Pop, but might be between them. Usually not, I
suspect, but occasionally so.
Even more interesting will be to see how levels of control are handled.
It seems to me that to speak of inheritability of control
characteristics, it's necessary to assume that the hierarchy itself is
inherited in complete form rather than learned through experience with
the world.
I don't think my approach would require this. It's quite a bit of
speculation, but I'm hazarding a guess that the result of this mechanism
for building new ECU Babies would be an irregular structure of levels,
rather than a haphazard network. We'll have to see.
Without having worked out the detail, my assumption is that the
initial stage is that the ECUs whose perceptual signals correspond
to the intrinsic variables exist initially, together with some
means of affecting the outer world. That, and the reorganizing
mechanism, is all.Right, that's my supposition about my reoreganizing system, too --
except that the initial control systems don't affect the outside world
at all. They affect only the mass of neurons that is going to become the
hierarchy of control that DOES interact with the outside world. This
_is_ the reorganizing mechanism as I see it. If you're proposing some
other reorganizing mechanism, how about describing it?
That's what I thought I had done over the last flurry of postings! What
did I really do? Actually, neither you nore I have described a MECHANISM.
What we have described is what happens when some kind of signal is at
a high level; in your case the signal is an output signal from the
control system for an intrinsic variable, caused by the existence of
a non-zero error for that variable, and the signal is applied somewhere
in the main hierarchy. In the localized system, the signal is the
existence of sustained and especially increasing error in any ECU. But
what happens in the presence of high values of the signal is the same
in both systems. (I have an imaginary--well, even more imaginary--variant:
the error induces some kind of chemical change which can diffuse into the
neighbourhood of the ECU in which the error occurs, and this change is
such as to induce weight changes not only in the ECU experiencing the
error, but also in the physical neighbours. Or perhaps it could be through
the glial cells, which apparently have some as yet undeciphered role in
communication among neurons. Well, mmm, forget about this bracket until
a few decades have passed!).
===================
On when another reorganization occurs:
I thought "immediately" was sufficiently vague. If the direction is
wrong, another reorganization occurs as soon as the wrongness can be
detected and another change can be made. OK now?
Yes, but a problem remains. When the "first" reorganization occurred,
"wrongness" was there, and will remain at least until the effect of that
reorganization has begun to show in the correspondign transient. But
disturbances also cause transients, as do changes in reference signals.
And if the "first" reorganization was unhelpful, "wrongness" will remain.
What is it that determines how long to tolerate "wrongness" before trying
a new reorganization? It will be different at different levels of the
hierarchy.
The same problem exists in both the separate and the localized reorganization
structures. I don't have a good answer. A hardware control engineer
would probably use induced noisy jitter to determine the effective loop
delay, and adjust the reorganization interval appropriately. Or perhaps
the small, discrete steps we have been talking about are actually a
continuous process with a bandwidth low compared to that of the control
loop being affected by the reorganization (making Baby ECUs can't be, so
far as I can see). Or maybe something else. Why, after all, should the
reorganization loop be a Test-Operate-Test-Operate (Toto Totes no baggage)
system, when all the other control systems are working simultaneously at
all points in the loop?
Enough for today. I see less of my desk than before, but there's more
shelf space onto which the desk crud can be loaded tomorrow.
Martin