Feedforward yet again

from Rick Marken (2010.01.01.1500)]

Bill Powers (2009.12.31.1905 MST)--

No need for embarrassment.

Thanks. And HAPPY NEW YEAR. Here's to 2010 being the final year of
cause-effect psychology... hic...hic

Best

Rick

···

--
Richard S. Marken PhD
rsmarken@gmail.com
www.mindreadings.com

[From Bjorn Simonsen (2010.01.020950 EU ST)]

From Bill Powers (2009.12.25.0430 MDT)

The direction of all signals inside the organism from sensory organs
to muscles is forward, toward the output. Only imagination runs the
other way.

The way I read the last sentence is: “The direction of all signals in imagination mode runs from muscles to sensory organs”. And I don’t understand it.

When I look at Figure 15.3 in B:CP I read that the errorsignal does an adition to the last perceptual signal before the switch close the way for more perceptual signals.

Plese explain me what it means that the imagination signals run the other way.

bjorn

[From Bill Powers (20010.01.02.0755 MST)]

Bjorn Simonsen (2010.01.020950 EU ST

···

From Bill Powers
(2009.12.25.0430 MDT)

The direction of all signals inside the organism from sensory organs

to muscles is forward, toward the output. Only imagination runs the

other way.

The way I read the last sentence is:
“The direction of all signals in imagination mode runs from muscles
to sensory organs”. And I don’t understand it.

When I look at Figure 15.3 in B:CP I read that the errorsignal does an
adition to the last perceptual signal before the switch close the way for
more perceptual signals.

Plese explain me what it means that
the imagination signals run the other
way.

OK, Bjorn, you’re right. Even the imagination loop runs clockwise
in our diagrams. I was thinking that it diverges from the normal path to
the muscles, and so goes “the other way,” but the internal path
runs parallel to the external one. All the connections are therefore in
the forward direction around the loop and the direction is not what makes
the difference between feedforward and feedback.

What feedforward seems to mean is a pathway that carries information to
the output of the control system without depending on feedback effects,
so it doesn’t have to wait for the effect of the output to be sensed. The
only places I can see that happening are the reference-signal path into
the comparator and thence to the output, and from a disturbance directly
to the output without passing through the comparator. I believe Martin
Taylor mentioned these paths.

Of course the path from reference to output isn’t “speeded up”
by feedforward; any change in the way the reference signal behaves
through time just changes the reference condition. However, there is a
natural speeding-up effect that the higher system providing the reference
signal might appreciate. Because there are generally some lags between a
change in the reference signal and the resulting change in the perceptual
signal, the initial change in the reference signal passes through the
comparator to the output function without being diminished, at first, by
negative feedback from the perceptual signal. This has the same effect as
a phase advance in the control loop of the higher system, offsetting some
of the delay in the higher-level loop.

Any speeding-up circuits in the input, comparator, output, or feedback
functions of a control system are simply aspects of the dynamic design of
the system and don’t merit any new terminology. As I pointed out a couple
of days ago, or was it yesterday, rate feedback slows changes in the
controlled variable rather than speeding them up because it introduces
damping into the loop. That can be useful for stabilization – but it
isn’t “feedforward,” a term I now consider totally
useless.

The best way to lay that term to rest would be to trace it back to the
first person who used it – invented it – and see what the context was.
I’ll bet it was someone fighting a rear-guard action to repel the wolves
of feedback from the embattled defenders of S-R theory. Anybody have a
student who needs a topic?

Best,

Bill P.

[Martin Taylor 2010.01.04.17.27]

I've been incommunicado for nearly a week, and have just seen this. So I now can wish everyone a Happy New year a few hours late!

[From Rick Marken (2009.12.29.1705)

Martin Taylor (2009.12.29.16.35)
     

Probably so. But you may have a problem finding conditions that would offer
good discrimination between the two models. As you said in 1995, the
advantage of including prediction shows up mainly when feedback is sluggish.
In my sleep-loss study, the difference between the drug conditions showed up
only after a night of sleep loss, and even then the effect, though clear,
was not very big. As Bill has pointed out, control is pretty good without
prediction under the conditions usually used in tracking studies, so under
those conditions there isn't much room for either prediction or higher-level
sequence generators to show off their advantages. That makes it even harder
to demonstrate the relative benefit of one over the other under the best
discriminative conditions.
     

What is the predictive model?

The one you proposed in 1995, the same one that I used in the sleep deprivation study because it fit human performance better than the "standard" model that was the same except for omitting the predictive component. Both have been several times discussed on CSGnet with diagrams over the last couple of weeks, so I think your question was not really necessary.

Martin

[Martin Taylor 2010.01.04.17.27]

[From Bill Powers (2009.12.30.0745 MST)]

Martin Taylor appears to be proposing that adding a derivative to a perceptual signal amounts to prediction and can be used to speed up control. In fact it will put a lag into the control process, because it makes the error appear to be less than it is and thus reduces the amount of action being used to correct the error.

I don't know where you got this idea from. What I pointed out (not proposed) was that in 1995 Rick had shown improved control (by a factor of 2) in conditions of sluggish feedback if the derivative of the perceptual signal was added to the reference input, and that when I used this model in analyzing tracking in conditions of sleep loss, it fitted human performance better than did an equivalent model that lacked the predictive element. Not only that, but including the predictive component made a sufficient difference that one could see that the experimental drugs (modafinil and amphetamine) reduced the degree to which sleepy trackers tended to use prediction as opposed to direct observation, though they did not affect the loop delay detectably.

So, I was not "proposing" anything about the effect of adding in the derivative to the reference signal (equivalent, I guess, to subtracting it from -- not adding it to -- the perceptual signal). I was pointing out that the experiments have been done, and the resulting improvement demonstrated both in respect of the accuracy of control and in respect of the accuracy of fit to human performance.

Martin

[From Rick Marken (2010.01.04.1540)]

Martin Taylor (2010.01.04.17.27)--

Bill Powers (2009.12.30.0745 MST)]

Martin Taylor appears to be proposing that adding a derivative to a
perceptual signal amounts to prediction and can be used to speed up control.

I don't know where you got this idea from. What I pointed out (not proposed)
was that in 1995 Rick had shown improved control (by a factor of 2) in
conditions of sluggish feedback if the derivative of the perceptual signal
was added to the reference input

This was my mistake for not building the whole level 2 system. I was
not demonstrating a predictive control system that improved control
when feedback was "sluggish". I was demonstrating the improved control
that would occur in a pursuit tracking task when the level 2 control
system (which I didn't build, except for the presumed reference output
to the level 1 system) is controlling for matching the cursor to the
sine wave pattern made by the target. The "predictive" reference
signal was just my way of bypassing the need to build the actual level
two "pattern of movement" control system by producing what I would
imagine the reference output of that system would be. What I was
demonstrating (or trying to demonstrate) was hierarchical, not
predictive, control.

Best

Rick

···

--
Richard S. Marken PhD
rsmarken@gmail.com
www.mindreadings.com

[From Bill Powers (2010.01.04.1635 MST)]

Martin Taylor 2010.01.04.17.27 --

So, I was not "proposing" anything about the effect of adding in the derivative to the reference signal (equivalent, I guess, to subtracting it from -- not adding it to -- the perceptual signal).

Ah, I hadn't caught that detail. Yes, subtracting the derivative from the perceptual signal is the opposite of introducing damping. By suppressing changes in the perceptual signal, it makes the initial error after a change in perception larger than it would have been without the derivative, and thus results in more immediate changes in action.

In fact, if you trace events from the output quantity back to the same place, you will find that subtracting the first derivative of the perceptual signal creates a positive feedback loop for derivatives. A transient positive change in output produces a negative change of perception due to the derivative, which produces a positive change in error, which produces a positive change in output -- in the same direction as the original change. When the loop gain for changes approaches unity the system will approach instability.

There are other ways to get the same effect; modeling the input function as a leaky integrator would do it.

I was pointing out that the experiments have been done, and the resulting improvement demonstrated both in respect of the accuracy of control and in respect of the accuracy of fit to human performance.

Could you remind me of how you showed that the accuracy of fit to human performance was increased? I wonder what the relationship of subtracting the derivative is to the trackanalyze program where there is no such subtraction, but there is a transport lag in the input function. There would be some similarity in the effect; the transport lag means there is a delay in rise and fall of the perceptual signal, though not of the same nature as the delay caused by subtracting the derivative.

I'm tempted to try a leaky integrator in place of the transport lag in Demo 4-1. That does seem like a more physiologically likely function - a transport lag of 133 milliseconds is hard to account for in a nervous system where signals travel typically at 50 to several hundred meters per second. The 133 msec number is long enough for a signal to travel 6.6 meters or more, but it's only a tenth of a meter or so from the eye to the visual cortex, in a straight line anyway.

By the way, when you use a model someone else proposed, I view that as joining in the proposal and making you equally responsible for it.

Best,

Bill P.

[From Bill Powers (2010.01.04.1715 MST)]

Martin Taylor 2010.01.04.17.27 --

I forgot to point out that subtracting the derivative from the perceptual signal makes it more sluggish, not less.

Best,

Bill P;

[Martin Taylor 2010.01.04.23.03]

[From Rick Marken (2010.01.04.1540)]

Martin Taylor (2010.01.04.17.27)--
     

  Bill Powers (2009.12.30.0745 MST)]

Martin Taylor appears to be proposing that adding a derivative to a
perceptual signal amounts to prediction and can be used to speed up control.
       

I don't know where you got this idea from. What I pointed out (not proposed)
was that in 1995 Rick had shown improved control (by a factor of 2) in
conditions of sluggish feedback if the derivative of the perceptual signal
was added to the reference input
     

This was my mistake for not building the whole level 2 system. I was
not demonstrating a predictive control system that improved control
when feedback was "sluggish". I was demonstrating the improved control
that would occur in a pursuit tracking task when the level 2 control
system (which I didn't build, except for the presumed reference output
to the level 1 system) is controlling for matching the cursor to the
sine wave pattern made by the target. The "predictive" reference
signal was just my way of bypassing the need to build the actual level
two "pattern of movement" control system by producing what I would
imagine the reference output of that system would be. What I was
demonstrating (or trying to demonstrate) was hierarchical, not
predictive, control.

Nevertheless, whatever you had in mind when you did it, what you did demonstrate was that adding a predictive component to the reference signal improved control. Sometimes cutting corners in an experiment yields valuable results serendipitously. I guess it was just good fortune for PCT that you didn't do the complete two level system in 1995. If you had done, I might not have had the lead that allowed me to show that sleepy humans seem to use prediction more without the drugs than with them.

This particular phase of the thread came up because you asked me what was the "predictive model" that was to be compared experimentally with your proposed two-level control setup, and I told you that it was the model that you had already presented to us, and that I used to analyze the "sleepy tracking" experiment. How you thought of it at the time or now is irrelevant. It's what you did and what I took you up on that matters.

Martin

[Martin Taylor 2010.01.04.23.14]

[From Bill Powers (2010.01.04.1635 MST)]

Martin Taylor 2010.01.04.17.27 –

I was pointing out that the experiments have

been done, and the resulting improvement demonstrated both in respect
of the accuracy of control and in respect of the accuracy of fit to
human performance.

Could you remind me of how you showed that the accuracy of fit to human
performance was increased?

Modafinil_Model_small1.jpg

I optimized the fit between human and model tracking by varying k, d,
and z in this model. The parameter “z” represents the relative reliance
on prediction as opposed to direct observation of the current position.
If the optimum consistently has z > 0, then the fit is better with
prediction than without. This was the case, and moreover, after a
sleepless night or two the value of z tended to be greater in the
placebo group, but not (or at least not demonstrably) in the
amphetamine or modafinil group. I showed the graph as a Christmas
present to you all [Martin Taylor 2009.12.25.10.46]. The value of d did
not change reliably across drugs or across degree of sleep loss, so the
increased relative reliance on prediction was not a compensation for
increasing loop delay.

I wonder what the relationship of subtracting the
derivative is to the trackanalyze program where there is no such
subtraction, but there is a transport lag in the input function. There
would be some similarity in the effect; the transport lag means there
is a delay in rise and fall of the perceptual signal, though not of the
same nature as the delay caused by subtracting the derivative.

I’m wondering what Rick meant by “sluggishness” when he said
It could have been delay, or it could have been a low-pass filter in
the feedback path. Or maybe something else.
I’m not sure how you mean this. I gave Rick full credit in the
publication, if that’s what you mean. Or maybe you mean that I take
responsibility for demonstrating that it does work as Rick said it did.
To be more precise, Rick said it improved tracking; I generally assume
that simple effective techniques are quite likely to be used by evolved
systems faced frequently with related tasks, and therefore by
implication humans were likely to use Rick’s kind of predictive
technique, or something similar So I took on the responsibility of
testing to see whether this was in fact the case. Is that what you mean?
Martin

···

[From
Rick Marken (950413.1145)]
the level of
improvement depends on the sluggishness of the cursor
control
system.

I’m tempted to try a leaky integrator in place of the
transport lag in Demo 4-1. That does seem like a more physiologically
likely function - a transport lag of 133 milliseconds is hard to
account for in a nervous system where signals travel typically at 50 to
several hundred meters per second. The 133 msec number is long enough
for a signal to travel 6.6 meters or more, but it’s only a tenth of a
meter or so from the eye to the visual cortex, in a straight line
anyway.

By the way, when you use a model someone else proposed, I view that as
joining in the proposal and making you equally responsible for it.

[From Bill Powers (2010.01.05.0905 MST)]

Martin Taylor 2010.01.04.23.14 –

BP: The figures don’t come out very well. Figs 1 and 2 are missing
altogether, with a blank place where they should be, and in the others
all the grey and black rectangles or squares are solidly filled in with
no legends. In Fig. 6, the values on the vertical axis for
“microsleeps per tracking run” are just solid black squares.
This may be a problem in translating from the Apple world to the
Microsoft world, or perhaps these figures were linked rather than
embedded.

BP earlier: Could you remind me
of how you showed that the accuracy of fit to human performance was
increased?

MT:

b7bc31.jpg

I optimized the fit between human and model tracking by varying k, d, and
z in this model. The parameter “z” represents the relative
reliance on prediction as opposed to direct observation of the current
position. If the optimum consistently has z > 0, then the fit is
better with prediction than without. This was the case, and moreover,
after a sleepless night or two the value of z tended to be greater
in the placebo group, but not (or at least not demonstrably) in the
amphetamine or modafinil group. I showed the graph as a Christmas present
to you all [Martin Taylor 2009.12.25.10.46]. The value of d did not
change reliably across drugs or across degree of sleep loss, so the
increased relative reliance on prediction was not a compensation for
increasing loop delay.

BP: I still don’t see any reports on how well the model fit the subjects’
performance. In fact, you say at one point, :

“The mean-square error provides a theory-independent view of the
results, but is of secondary interest for the present report. Of greater
interest is the fitting of the control model to the peculiarities of the
individual tracks, as the sleep deprivation period progressed under the
different drug conditions.”

I strongly disagree with this choice. By not showing the RMS tracking
errors or differences between model and real behavior, you concealed
information that I consider very important: how poorly most of the
subjects tracked most of the time (though without adequate baseline data
that would be hard to prove). The “microsleeps” were a subject
of contention between us at the time the data were coming in. I felt that
they made the tracking model invalid, since periods of tracking were
being averaged together with periods of no tracking, rendering the model
meaningless. Compounding that error, as I see it, is the averaging of
values of a best-fit parameter over 11 or 12 subjects.

I notice that in figures 3 and 4 you present the best-fit position-gain
and delay parameters normalized to 1, but in the rest of the plots you
present the velocity loop gain normalized to 0 – that is, with the mean
value subtracted instead of computing the ratio. The plot of the velocity
parameter is scaled so that the range of variation in fig. 5 looks about
the same as in fig. 3 – but since there is no indication of what the
actual mean is, it’s impossible to tell whether the variations in
optimized velocity gain are huge or tiny relative to the mean. If the
mean is 1, they are huge. If the mean is 50, they are tiny.

I take it that the figure in your post, reproduced above, is the missing
fig.

2 in the paper.

Assuming that the desired target position is zero, the error signal
appears to be

e = (z/k*(dT/dt) - T) where T is target position and t is time,

and the mouse movements (before delay) are

m = integral[( z*dT/dt) - kT)dt] which is equal to

m = z*T - integral[(-kT)dt] + C, where C is a constant of integration and
can be zero (Richard K - ?)

So your parameter z simply adjusts the amount of target movement that is
added directly to mouse movement before the delay, a simple case of
feedforward since it effectively skips the comparator and output
function. This makes the z-loop a positive feedback loop with a delay in
it. Onlookers, please check if this is right.

Your note at the bottom of the first page, reporting that “Powers
… generously declined participation in the authorship of this
paper” is seriously misleading; my refusal to participate may have
been expressed in a generous way (I don’t remember) but you know that the
reason was my opinion that the study was seriously flawed and I didn’t
want my name attached to it. I realized then, and still do, that the
reasons for the flaws were aspects of the study that were under someone
else’s control, not yours – in part, a schedule that made it impossible
to get good baseline data. But you wanted to use the data anyway, so I
opted out, despite having invested months of programming time in it (in
C, no less).

The lack of practicing to asymptotic performance means that we have no
idea how rapidly the performance declined at the beginning of sleep
deprivation. For all we know, your measures could apply to a performance
that is 90% degraded soon after the start of extended sleeplessness.

We had a number of discussions on the subject of “microsleeps.”
There the problem is that periods of no control behavior at all are being
averaged in with periods when control was happening. The model fits are
very sensitive to periods of bad tracking, because the RMS differences
for subjects with sufficient practice are so small. But there is no
discussion in your paper of this problem, beyond mentioning that
“The more blatant of these instances were removed from the
data.” or any of the others I brought up. Under those
conditions, I didn’t think, to put it mildly, that joint authorship would
be appropriate.

MT: I gave Rick full credit in
the publication, if that’s what you mean. Or maybe you mean that I take
responsibility for demonstrating that it does work as Rick said it did.

BP: Neither one.I meant that no matter whose model you use, your use
implies that you have checked out the model for inconsistencies, errors,
or other problems, so any problems with the model become yours just as
much as the author’s.

MT: To be more precise, Rick
said it improved tracking; I generally assume that simple effective
techniques are quite likely to be used by evolved systems faced
frequently with related tasks, and therefore by implication humans were
likely to use Rick’s kind of predictive technique, or something similar
So I took on the responsibility of testing to see whether this was in
fact the case. Is that what you mean?

BP: No. You are denying responsibility, not taking it (“Rick said
…”). Did you verify that it improved tracking? If it doesn’t
actually improve tracking (and nothing in your paper indicates that it
does), you are leaving the door open for blaming Rick. It would be very
simple to demonstrate an improvement if it occured – why isn’t that in
the paper?

I realize that I’m being somewhat curmudgeonly about this paper and the
study behind it. But I think your paper presents an overly rosy view of
the results and omits information that a reader should be given whether
or not it’s favorable to your conclusions.

Best,

Bill P.

[From Rick Marken (2010.01.05.1100)]

Martin Taylor (2010.01.04.23.14) –

Bill Powers (2010.01.04.1635 MST)]–

Could you remind me of how you showed that the accuracy of fit to human
performance was increased?

I optimized the fit between human and model tracking by varying k, d,
and z in this model. The parameter “z” represents the relative reliance
on prediction as opposed to direct observation of the current position.
If the optimum consistently has z > 0, then the fit is better with
prediction than without. This was the case, and moreover, after a
sleepless night or two the value of z tended to be greater in the
placebo group, but not (or at least not demonstrably) in the
amphetamine or modafinil group. I showed the graph as a Christmas
present to you all [Martin Taylor 2009.12.25.10.46]. The value of d did
not change reliably across drugs or across degree of sleep loss, so the
increased relative reliance on prediction was not a compensation for
increasing loop delay.

It would be nice to know how much improvement in prediction was produced by including the “z” value. I presume that you were using a pursuit tracking task? I’ll try this in my program but I believe that the benefits of inserting the predictive component into the reference (or perception) could only accrue in the pursuit case.

I’m wondering what Rick meant by “sluggishness” when he said
[From
Rick Marken (950413.1145)]
the level of
improvement depends on the sluggishness of the cursor
control
system.

I’m wondering too. I guess I should go back and re-read that whole 1995 exchange. As I remember it, it was all about understanding why pursuit tracking is typically better than compensatory tracking. Maybe you could bundle up the relevant 1995 posts from this discussion and post them? Or maybe just mail them to me and I’ll look them over to see what I’ve already done.

Right now I think I’ll compare putting prediction into the compensatory and pursuit model that I have finally gotten to work right.

Best

Rick

···


Richard S. Marken PhD
rsmarken@gmail.com

www.mindreadings.com

[Martin Taylor 2010.01.05.14.39]

[From Rick Marken (2010.01.05.1100)]

I’m wondering what Rick meant
by “sluggishness” when he said
[From
Rick Marken (950413.1145)]
the level of
improvement depends on the sluggishness of the cursor
control
system.

I’m wondering too. I guess I should go back and re-read that whole 1995
exchange. As I remember it, it was all about understanding why pursuit
tracking is typically better than compensatory tracking. Maybe you
could bundle up the relevant 1995 posts from this discussion and post
them? Or maybe just mail them to me and I’ll look them over to see what
I’ve already done.

I got it from Dag’s archives, so you probably would be better going
there rather than getting them from me.

Right now I think I’ll compare putting prediction into the compensatory
and pursuit model that I have finally gotten to work right.

That’s undoubtedly the best approach, especially since Bill would like
me to provide results from the sleepy tracking study that I would be
surprised if I could resurrect (I’ll look, but have no great hopes).
Even if I did find them, Bill has a kind of Catch-22 comment, that the
experiment was bad because tracking was bad, but then if tracking were
good, adding a predictive component couldn’t be of much help.

It might be important to consider different kinds of “sluggishness”
when you redo the experiments according to acceptable criteria. Then
again, it might not. Only experimentation will tell.

You asked whether the tracking was pursuit or compensatory. There were
several different tracking tasks, apparently at different perceptual
levels. Here’s the description from the paper at
. Bill says
he has trouble seeing the figures. I had that trouble using either
NeoOffice 3 or Nisus Writer Pro, both of which ae supposed to read
Microsoft Word “.doc” files. But I could read it fine using Word 2008
or Word X on the Mac, and Word 2007 on the PC ought to work, too.

Martin

···

http://www.mmtaylor.net/PCT/modafinil.tracking.doc

There were six different
tasks, only
five of which are included in the results described here; the sixth
task was
characteristically different in that it employed two markers and two
cursors.

In two of the tasks, the
marker and
the cursor were vertical lines approximately 3 cm long.
In one, the disturbance affected the
marker, and the subject used the mouse to keep the cursor aligned with
it
vertically (pursuit tracking); in the other, both the disturbance and
the
marker affected only the cursor, and the subject was required to
compensate for
the disturbance in order to keep the cursor vertically under the marker
(compensatory tracking).

The third task presented
the subject
with a circle of about 10 cm diameter, and a small disk of about 0.5 cm
diameter that progressed slowly counterclockwise around the perimeter
of the
circle. The disturbance moved the small disk radially, and the subject
used the
mouse to compensate so as to keep the disk on the circle perimeter. The
mouse
affected the radial position of the disk, which meant that as the disk
moved
around the circle a left-right mouse movement might make the disk move
left,
right, up or down.

The fourth task presented
what
looked like a pendulum swinging from a point near the top-middle of the
screen. Outside the arc of the
pendulum bob, a disk moved in an arc at a speed that was affected by
the
disturbance. The mouse also
affected that speed, and the subject’s task was to keep the disk
aligned with
the shaft of the pendulum as the pendulum swung back and forth.

The fifth task was
visually quite
different, in that the display consisted only of a two-digit (or
three-digit)
number with digits about 2 cm tall.
The disturbance added a positive or negative increment to the
number, as
did the mouse movement, and the subject used the mouse to keep the
number as
close to “50” as possible. In this task, both cursor and marker are
conceptual
numeric values, rather than being physical locations. The cursor is the
value
of the number represented by the digits on the screen, and the marker a
memory
for the value “50.”

Each
task was run with three different kinds of disturbance, two of which
varied
smoothly, and the third in jumps. Each kind was run at two difficulty
levels.
With six tasks and six combinations of disturbance type and difficulty,
there
were 36 distinct task-disturbance combinations, 6 of which were run
during each
individual hour of the experiment, in two group of three.
Each group of three had one of each
kind of disturbance, and each group of six had one of each task type
and one of
each disturbance-difficulty combination. Over each 6-hour experimental
block,
all 36 task-disturbance combinations were run once.

[From Rick Marken (2010.01.05.1310)]

Bill Powers (2010.01.05.0905 MST) to Martin Taylor –

BP: I still don’t see any reports on how well the model fit the subjects’
performance. In fact, you say at one point, :

“The mean-square error provides a theory-independent view of the
results, but is of secondary interest for the present report. Of greater
interest is the fitting of the control model to the peculiarities of the
individual tracks, as the sleep deprivation period progressed under the
different drug conditions.”

Are you reading this in a published paper, Bill? If so, where was it published? When?

I strongly disagree with this choice. By not showing the RMS tracking
errors or differences between model and real behavior, you concealed
information that I consider very important:

If this is a published paper did the reviewers catch this? Martin?

Your note at the bottom of the first page, reporting that “Powers
… generously declined participation in the authorship of this
paper” is seriously misleading; my refusal to participate may have
been expressed in a generous way (I don’t remember) but you know that the
reason was my opinion that the study was seriously flawed and I didn’t
want my name attached to it.

Then it is published? What journal?

Best

Rick

···


Richard S. Marken PhD
rsmarken@gmail.com
www.mindreadings.com

[From Bill Powers (2010.01.05.1820 MST)]

Rick Marken (2010.01.05.1310) --

Are you reading this in a published paper, Bill? If so, where was it
published? When?

Martin attached it to a post. Here it is again.

Best,

Bill P.

modafinil.tracking.doc (74.5 KB)

[From Rick Marken (2010.01.05.1745)]

Bill Powers (2010.01.05.1820 MST)--

Rick Marken (2010.01.05.1310) --

Are you reading this in a published paper, Bill? If so, where was it
published? When?

Martin attached it to a post. Here it is again.

Thanks. Was this ever published, Martin?

Best

Rick

···

--
Richard S. Marken PhD
rsmarken@gmail.com
www.mindreadings.com

[Martin Taylor 2010.01.05.23.59]

[From Rick Marken (2010.01.05.1745)]

Bill Powers (2010.01.05.1820 MST)--

Rick Marken (2010.01.05.1310) --

Are you reading this in a published paper, Bill? If so, where was it
published? When?
       

Martin attached it to a post. Here it is again.
     

Thanks. Was this ever published, Martin?

Yes, what you see is what you get (if you can see the figures, that is).

It wasn't in a general circulation journal, but in the proceedings of a
workshop. One afternoon was devoted to the Modafinil study, of which my
study was a small add-on. It was the 1995 meeting of the Military
Testing Association (if I got the name right -- the initials are MTA,
and that's my memory of what they meant). I looked up the reference in
my publication list, and found I had not included it -- perhaps because
that was when I retired -- so I can't give you a more precise reference.
Maybe a little Googling might find it. I don't know.

In case you can't see the figures, I've made a PDF of it, which I
attach. I'll upload it to my web site so people can have the option of
which version to download.

Martin

modafinil.tracking.pdf (259 KB)

[Martin Taylor 2010.01.06.00.16]

[From Bill Powers (2010.01.05.0905 MST)]

Martin Taylor 2010.01.04.23.14 –

BP: The figures don’t come out very well. F

I hope the PDF I attached to a message to Rick a few minutes ago comes
out better.

BP earlier: Could you
remind me
of how you showed that the accuracy of fit to human performance was
increased?

MT:

![b7bc31.jpg|291x268](upload://lffbtAcfv9DDt11FraAVdFCuTec.jpeg)

I optimized the fit between human and model tracking by varying k, d,
and
z in this model. The parameter “z” represents the relative
reliance on prediction as opposed to direct observation of the current
position. If the optimum consistently has z > 0, then the fit is
better with prediction than without. This was the case, and moreover,
after a sleepless night or two the value of z tended to be greater
in the placebo group, but not (or at least not demonstrably) in the
amphetamine or modafinil group. I showed the graph as a Christmas
present
to you all [Martin Taylor 2009.12.25.10.46]. The value of d did not
change reliably across drugs or across degree of sleep loss, so the
increased relative reliance on prediction was not a compensation for
increasing loop delay.

BP: I still don’t see any reports on how well the model fit the
subjects’
performance. In fact, you say at one point, :

“The mean-square error provides a theory-independent view of the
results, but is of secondary interest for the present report. Of
greater
interest is the fitting of the control model to the peculiarities of
the
individual tracks, as the sleep deprivation period progressed under the
different drug conditions.”

I strongly disagree with this choice. By not showing the RMS tracking
errors or differences between model and real behavior, you concealed
information that I consider very important: how poorly most of the
subjects tracked most of the time (though without adequate baseline
data
that would be hard to prove).

I know where you are coming from, but I disagree with you. I’ll tell
you why, and perhaps you will agree with me. But before doing so, I
will say that had this been done in the last few years, the data would
properly have been deposited in an on-line “supporting material”
repository. In 1995, such things did not exist, so far as I know. I
strongly believe that the actual tracking errors would not have been
appropriate for inclusion in the actual paper, no matter how much space
I had been allowed.

Remember that there were six very different tasks, so right from the
start the RMS errors were not commensurate. Of course, that would not
affect the relative fit of the model to the human as opposed to the
target, but at the time I had not developed the triangulation approach
we discussed last winter (was it so long ago?). Compounding that issue
was the fact that there were three different difficulty levels for each
of two kinds of disturbance (smoothly varying and stepped), so the
quality of the tracking varied all over the place. The actual quality
of the track was not of interest to the study, which was related to the
relative effects of the drugs on different aspects of performance. (I
was involved in a quite distinct experiment in the same study, which
dealt with the performance of subjects who could not see one another,
one trying to guide the other to draw a route on a map containing
landmarks when the guide’s map differed in some landmark details from
the student’s map – for example, the guide’s map might have two
“watertower” landmarks when the student’s had only one.)

Since the tracking error was both incommensurate across tasks and
appreciably different across task difficulty levels, the actual RMS
values would have no meaning in respect of the objectives of the study.
But changes in the model-fitting parameters would do, and those were
most reasonably fitted by normalizing out intersubject differences and
differences due to tracking difficulty and task type.

The “microsleeps” were a subject
of contention between us at the time the data were coming in. I felt
that
they made the tracking model invalid, since periods of tracking were
being averaged together with periods of no tracking, rendering the
model
meaningless.

No, they were not. At least they were not if the criterion for asessing
a period of time as a microsleep was anywhere close to being
reasonable. Periods judged to be microsleep were omitted from the model
fit assessment, along with (as I remember) a short “guard” interval
around the microsleep period.

Compounding that error, as I see it, is the averaging of
values of a best-fit parameter over 11 or 12 subjects.

I didn’t do that, so far as I remember. I think I averaged after
normalization. It wouldn’t make a lot of difference either way, if the
parameter values were not too widely different or if their
distributions were reasonably symmetric about their means.

I notice that in figures 3 and 4 you present the best-fit position-gain
and delay parameters normalized to 1, but in the rest of the plots you
present the velocity loop gain normalized to 0 – that is, with the
mean
value subtracted instead of computing the ratio.

The gain and delay values are necessarily positive, and the relevant
feature is their scale as a multiplier. The velocity parameter is a
ratio which can be positive or negative. It also is scaled, but there
is a definite neutral point at zero, as opposed to the arbitrary choice
of 1.0 as the neutral point in normalizing the gain and delay
parameters. The relative scale in the picture doesn’t signify anything.
What does signify is that before the first sleepless night the ratios
are scattered around zero (no consistent use of prediction) whereas
later they are all positive, slightly so for the two drug conditions,
but much more so in the placebo condition, and more after the second
sleepless night than after the first. You can get an idea of the
reliability of the measures by comparing the successive points along
each curve, though I admit that you can’t see whether one task or
another is more conducive to the use of prediction.

The plot of the velocity
parameter is scaled so that the range of variation in fig. 5 looks
about
the same as in fig. 3 – but since there is no indication of what the
actual mean is, it’s impossible to tell whether the variations in
optimized velocity gain are huge or tiny relative to the mean. If the
mean is 1, they are huge. If the mean is 50, they are tiny.

Those numbers are rally meaningless, I think. The important point is
that after the end of the first sleepless night, 17 of 18 cases show a
positive value, and the 18th is zero.

I take it that the figure in your post, reproduced above, is the
missing
fig.

2 in the paper.

Yes, it’s that figure, but why do you say Figure 2 is missing? It’s
labelled in the figure caption, in my copy.

So your parameter z simply adjusts the amount of target movement that
is
added directly to mouse movement before the delay, a simple case of
feedforward since it effectively skips the comparator and output
function.

It doesn’t actually skip the comparator function. It enters the
comparator through its addition to the reference. That agrees with my
subjective impression of what is going on. One deliberately targets the
cursor to a point further along the track than the current target
position. It simply feels the way the diagram is drawn.
Mathematically, of course, the result is the same as adding to the
target movement.

This makes the z-loop a positive feedback loop with a
delay in
it. Onlookers, please check if this is right.

Yes, it’s obviously right, since the velocity component is entered into
the positive side of the comparator, and there’s no sign inversion
anywhere else in the loop. I hadn’t noted that before. I wonder how the
90 degree phase shifts involved in taking the derivative affect the
stability of this? I imagine you have analyzed it or simulated it?

Your note at the bottom of the first page, reporting that “Powers
… generously declined participation in the authorship of this
paper” is seriously misleading; my refusal to participate may have
been expressed in a generous way (I don’t remember) but you know that
the
reason was my opinion that the study was seriously flawed and I didn’t
want my name attached to it.

Well, our memories do differ. I remember your declining authorship as a
very generous gesture. You had indeed raised objections of the kind you
raise here, but I don’t remeber them as being anywhere near as
definitive as you now make them out to be.

The lack of practicing to asymptotic performance means that we have no
idea how rapidly the performance declined at the beginning of sleep
deprivation. For all we know, your measures could apply to a
performance
that is 90% degraded soon after the start of extended sleeplessness.

Isn’t it a lot more probable that the subjects continued to learn
during the course of the study, and that this learning would act in
opposition to the observed performance deterioration?

MT: I gave Rick full
credit in
the publication, if that’s what you mean. Or maybe you mean that I take
responsibility for demonstrating that it does work as Rick said it did.

BP: Neither one.I meant that no matter whose model you use, your use
implies that you have checked out the model for inconsistencies,
errors,
or other problems, so any problems with the model become yours just as
much as the author’s.

Fine, I agree with that, but it makes me even more puzzled as to why
you brought this up in the first place.

I realize that I’m being somewhat curmudgeonly about this paper and the
study behind it. But I think your paper presents an overly rosy view of
the results and omits information that a reader should be given whether
or not it’s favorable to your conclusions.

I don’t think it omits anything relevant to the conclusions I drew.
What it omits are data that might be of interest for other reasons,
such as for what tasks and difficulty levels might prediction be more
likely to be used. The results of the study are concerned with whether
the two drugs (the then standard amphetamine and the experimental
modafinil, which was in regular use by the French army) have similar or
different effects on reducing the ill effects of sleep loss. From my
two little studies, it seems that there isn’t much difference between
the drugs in tracking, but both differ from the placebo in that under
the drugs people are more attentive to the actual target position
relative to their expectation of its position, and that in the dialogue
study subjects tended to what one might call “risky” behaviour
(accepting their prior assumptions about things and not asking for
corroboration) under modafinil, but not under amphetamine.

Indeed, after this study, all the experimenters agreed that we would
not want to fly or drive with someone who was being kept awake by
modafinil. As I can personally attest, it makes one feel alive and
alert despite sleep loss, but I can give a real-world example of why
it’s not a good idea to use it when you have to make decisions. I was
at a meeting in Paris, having flown two days previously to avoid jet
lag. One of my colleagues flew (sleepless) overnight, and arrived at
the meeting direct from the airport. He was falling asleep at the
meeting table, and I happened to have a modafinil tablet which I gave
him. He woke up and felt fine, and he became alert and coherent, but
whenever a volunteer was needed for a job, he volunteered. It took him
a little while to realize how much extra work he had let himself in
for, and let the other members of the group avoid!

Martin

[From Bill Powers (2010.01.06.0100 MSTG)]

Martin Taylor 2010.01.06.00.16 --

I feel a lot of empathy for your position, Martin, and I don't want to be cruel about this. When we started that sleep-deprivation project we had big plans. I cooked up six control tasks which were supposed to involve different levels of control, and we were going to see how sleep deprivation and the other treatments would affect the parameters of control, found by matching model behavior to real behaviors in each task. It looked like a sure thing, since we knew we could get very good and consistent results in experiments we had done ourselves. A great opportunity, it seemed.

But it turned out that the other people involved in the experiment had their own ideas of how to use the subjects' time, and the subjects didn't take the tasks as seriously as we hoped, so the result was a lot of very disappointing data. It would have been much better to use one or two tasks and give enough practice so the subjects were controlling very well, so we could see any changes of parameters very clearly. But we didn't know that ahead of time and there was no way to do that once the experiment got under way. It was a mess. You may recall that I laid out of lot of conditions we wanted to establish to get the most consistent data possible, including the physical arrangement of the apparatus, ways of assuring constant viewing distance, and other stuff I've mostly forgotten. Fat chance! None of that was done, as far as I remember. I got a definite impression that the other investigators didn't give much weight to your part of the project, or think it very important.

When I saw the results that started coming in, I knew that our ambitions were doomed. The "microsleep" phenomenon finished it off for me. The integrators in the models went right on integrating while the subject held the mouse motionless or moved it randomly and the error signal zoomed upward, and there was no way to just cut out the bad part and stitch the before and after parts together and still get a good match of model to data, at least not a match that meant anything. You were convinced there had to be a way to salvage something, and I was convinced that the experiment was dead. That's when I opted out. You kept on looking for a way to get some result of value, and I wished you could just let it go.

I think we're now stumbled onto the last fatal flaw, the fact that the derivative you added and called "prediction" actually introduced positive feedback into the loop. If you and Rick haven't already seen the implication of this, allow me, belatedly, to point it out: positive feedback does not reduce error, it increases error. If the disturbance goes positive and causes the target to depart from its reference position in the positive direction, the derivative will make the reference signal go positive, and as I showed earler will cause the mouse to move in the direction that makes the target move more in the direction of the initial disturbance. Trace the effects around the loop, you'll see.

I can now almost see what happened. The clue is the fact that you had to divide the multiplier for the derivative, z, by the gain of the output integrator, k. If you didn't do that, any loop gain greater than 1 would produce instant oscillations or runaway for z greater than 1. That's probably what happened at first (Rick, how did you handle this?). So either you had to make z very small, which would reduce its effects relative to the target position changes, or you would have to make the integrator gain very small, which would give poor control. Your solution was to divide z by k so no matter what k was, z would have the same effect on the derivative component of the loop. Of course this raises severe modeling questions, like what it is that makes sure z is divided by the number that, way over in the output function, determines the gain of the integrator. And there is now a strong interaction between two parameters instead of nice clean more-or-less independent effects.

I really think it's time to lay the sleep study in its final resting place, erect a headstone, and move on.

Best,

Bill P.

[From Rick Marken (2009.01.06.1230)]

Linda points out to me that tonight is Twelfth Night, for all you
Shakespeare fans.

Bill Powers (2010.01.06.0100 MSTG)--

I think we're now stumbled onto the last fatal flaw, the fact that the
derivative you added and called "prediction" actually introduced positive
feedback into the loop. If you and Rick haven't already seen the implication
of this, allow me, belatedly, to point it out: positive feedback does not
reduce error, it increases error.

The way I did it it doesn't seem to (but given my programming
credentials I'm not saying this with a lot of confidence). But here's
what I did. I changed the controlled variable in my tracking program
to one that has been incorrectly dubbed a "predictive" variable; it's
just the usual controlled variable (Target-Cursor) but it includes the
derivative of cursor (or target) movement. In the pursuit tracking
case, the controlled variable is:

P = Target + Kd * (Target - Targetp) - Cursor

where Targetp is the target position 1/60 of a second earlier. In the
compensatory tracking case the controlled variable is:

P = Target + Kd * (Target - Cursorp) - Cursor

where Cursorp is the cursor position 1/60 of a second earlier. So what
is being added to the usual controlled variable is a derivative, of
target movement in the pursuit case and of cursor movement in the
compensatory case. If Kd is 0 then the controlled variable is the same
as it was without the derivative added.

When I run the model with Kd = 0 then I get the same results as I did
without the derivative added: the results for the random disturbance
are that the RMS tracking error when Kd = 0 is 18.4 for both pursuit
and compensatory tracking. When Kd is increased, tracking _improves_
for both pursuit and compensatory cases. I can get the pursuit RMS
error down to about 1.04 by setting Kd to 9 and I can get the
compensatory RMS error down to 2.37 by setting Kd to 7. These values
are what I get when I set with the Gain and Dampling to 6.5 and .005,
respectively. There are the values of Gain and Damping that give the
best fit of the model to human data, where the model is:

Output = Output + (Gain * P - Damping * Coutput) * dt

But I cannot get the fit to the human tracking improved by increasing
Kd. I have human compensatory tracking data for the same disturbance
I'm using in the model. The best I can do in fitting a control model
to this human data is get the RMS deviation of model from actual
handle movement data to 18 pixels. This is when Kd = 0. Increasing Kd
just makes the fit of the model to the human data worse. By the way,
the human RMS error for this tracking task is 28 pixels. So the
average deviation of model from human handle movement is less than the
average deviation of cursor from target during the tracking run.

So it looks like adding the derivative of the controlled variable to
the controlled variable can improve the performance of the model, but
doing this also makes the fit of the model to the human data worse;
humans are apparently not including the derivative of the controlled
variable in their controlling.

Of course, all this has to be taken with a grain of salt until the
inevitable errors have been removed from the programs. But that's what
things look like now.

I can now almost see what happened. The clue is the fact that you had to
divide the multiplier for the derivative, z, by the gain of the output
integrator, k. If you didn't do that, any loop gain greater than 1 would
produce instant oscillations or runaway for z greater than 1. That's
probably what happened at first (Rick, how did you handle this?).

I didn't have any problem using the derivative, at least as I describe
it above.

Best

Rick

···

--
Richard S. Marken PhD
rsmarken@gmail.com
www.mindreadings.com