[From Bill Powers (970716.0957 MDT)]
The next version, reorg6.pas, combines the previous two: both the output
and the input functions are reorganized. As it turns out, both
proportionality factors, ki (yellow) and ko (magenta), increase together
(they both start at 0.0). Their proportions seem to depend only on the
relative speeds of reorganization, set by SPEEDKO and SPEEDKI. When these
speeds are the same, the two factors go positive by equal amounts; the
yellow trace for ki is overlaid by the magenta trace for ko.
When the reorganization speeds are different, the final values of ki and ko
are different in what looks like the same ratio. In some cases, both ki and
ko develop in the negative direction, which still preserves negative
feedback. This probably depends on the initialization and which way the
random corrections go in the first couple of iterations. If the signs of ki
and ko became opposite, there would be positive feedback and the system
would start to run away; evidently the reorganizing process never allows
that to happen. In the program as distributed, SPEEDKI is set to 2E-5 and
SPEEDKI is set to 1E-5, so the traces for ki and ko are separated. Both
always seem to go negative with this initialization.
Note that when both ki and ko are negative, the blue trace showing the
controlled input quantity varies in a direction opposite to the variations
in the reference signal. A white "zero" line is plotted in the upper traces
(the lower white trace is the absolute error plotted relative to the bottom
of the screen). Note also that when the red "reference" trace is very close
to the green "perceptual" trace, the result looks yellow.
This kind of reorganization, done with a single isolated control system,
affects the loop gain alone. Both ki and ko are given natural decay rates
so the loop gain will not rise so far as to cause instability.
The simultaneous reorganization of input and output results in partitioning
the loop gain between the output and input functions. If the speed
constants are set so ko increases faster than ki, the input amplification
is diminished and the variations in the input quantity qi (the controlled
variable) are greater with respect to the variations in the reference
signal. So by adjusting the relative speeds of reorganization, it is
possible to arrive at any desired scaling factor between the controlled
variable and the perceptual signal. If other criteria for reorganization
were added, related to absolute amplitude of variation of the input
quantity, they would probably affect this partitioning of gain between
input and output.
···
-----------------------------
A second kind of reorganization would be involved if the output had
multiple effects on the environment and the perception came from multiple
sensors detecting various parts of the environment. This begins to take us
back toward the situation in my initial effort, where I dived into the
middle of the problem without studying it systematically as we're doing here.
If we separate the adjustment of the amount and sign of loop gain from the
distribution of inputs and outputs in the environment, it would seem
necessary to do some kind of normalization (as Hans Blom suggested). The
effect we want is for the sum of the weightings to be constant, so if one
weighting were increased, all the others would have to be decreased
slightly. To do this explicitly would imply that there is something that
can detect the weightings themselves, which is unlikely in a nervous
system. So what we want is a method based on the _signals_ that gives the
same general effect.
One way to do this would be to have each signal coming out of a sensor act
to reduce the gain (the weighting) of all the other sensors. This is
similar to the flip-flop connection that Martin Taylor has been selling,
except that the mutual effects would be multiplicative instead of additive.
The effect of one sensor's output on other sensors would not be to add to
or subtract from the _signal_ of the other sensors, but to affect the
sensitivity of the other sensors. The effective weighting factor for each
sensor would then be given by
we = wr/SUM(other sensor signals)
where we is the effective weight, and
wr is the weight set by reorganization.
This would achieve the desired result of emphasizing the contribution from
the sensors having the largest signals relative to the other sensor
signals, without causing a corresponding change in overall input
sensitivity. And it is at least neurologically plausible.
Well, anyway that's where I'm going next, I think.
Best,
Bill P.