# Feedforward yet again

**URL:** <http://discourse.iapct.org/t/feedforward-yet-again/4362>\
**Category:** CSG2010\
**Created:** [January 1, 2010, 11:00pm UTC](http://discourse.iapct.org/t/feedforward-yet-again/4362 "2010-01-01T23:00:33Z")\
**Posts on this page:** 20\
**Page:** 1

<div class="post-metadata">

**Author:** ![rsmarken](http://discourse.iapct.org/user_avatar/discourse.iapct.org/rsmarken/32/3553_2.png) [@rsmarken](http://discourse.iapct.org/u/rsmarken)\
**Post date:** [January 1, 2010, 11:00pm UTC](http://discourse.iapct.org/t/feedforward-yet-again/4362/1 "2010-01-01T23:00:33Z")

</div>

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

---

<div class="post-metadata">

**Author:** ![Bjorn](http://discourse.iapct.org/letter_avatar_proxy/v4/letter/b/74df32/32.png) [@Bjorn](http://discourse.iapct.org/u/Bjorn)\
**Post date:** [January 2, 2010, 8:51am UTC](http://discourse.iapct.org/t/feedforward-yet-again/4362/2 "2010-01-02T08:51:53Z")

</div>

[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

---

<div class="post-metadata">

**Author:** ![Bill\_Powers1](http://discourse.iapct.org/letter_avatar_proxy/v4/letter/b/8e7dd6/32.png) [@Bill\_Powers1](http://discourse.iapct.org/u/Bill_Powers1)\
**Post date:** [January 2, 2010, 3:33pm UTC](http://discourse.iapct.org/t/feedforward-yet-again/4362/3 "2010-01-02T15:33:49Z")

</div>

[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.

---

<div class="post-metadata">

**Author:** ![MartinT](http://discourse.iapct.org/letter_avatar_proxy/v4/letter/m/ee7513/32.png) [@MartinT](http://discourse.iapct.org/u/MartinT)\
**Post date:** [January 4, 2010, 10:31pm UTC](http://discourse.iapct.org/t/feedforward-yet-again/4362/4 "2010-01-04T22:31:29Z")

</div>

[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)  
> > &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
> > 
> > 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.  
> > &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
> 
> 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

---

<div class="post-metadata">

**Author:** ![MartinT](http://discourse.iapct.org/letter_avatar_proxy/v4/letter/m/ee7513/32.png) [@MartinT](http://discourse.iapct.org/u/MartinT)\
**Post date:** [January 4, 2010, 10:41pm UTC](http://discourse.iapct.org/t/feedforward-yet-again/4362/5 "2010-01-04T22:41:39Z")

</div>

[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

---

<div class="post-metadata">

**Author:** ![rsmarken](http://discourse.iapct.org/user_avatar/discourse.iapct.org/rsmarken/32/3553_2.png) [@rsmarken](http://discourse.iapct.org/u/rsmarken)\
**Post date:** [January 4, 2010, 11:39pm UTC](http://discourse.iapct.org/t/feedforward-yet-again/4362/6 "2010-01-04T23:39:46Z")

</div>

[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

---

<div class="post-metadata">

**Author:** ![Bill\_Powers1](http://discourse.iapct.org/letter_avatar_proxy/v4/letter/b/8e7dd6/32.png) [@Bill\_Powers1](http://discourse.iapct.org/u/Bill_Powers1)\
**Post date:** [January 5, 2010, 12:04am UTC](http://discourse.iapct.org/t/feedforward-yet-again/4362/7 "2010-01-05T00:04:27Z")

</div>

[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.

---

<div class="post-metadata">

**Author:** ![Bill\_Powers1](http://discourse.iapct.org/letter_avatar_proxy/v4/letter/b/8e7dd6/32.png) [@Bill\_Powers1](http://discourse.iapct.org/u/Bill_Powers1)\
**Post date:** [January 5, 2010, 12:14am UTC](http://discourse.iapct.org/t/feedforward-yet-again/4362/8 "2010-01-05T00:14:11Z")

</div>

[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;

---

<div class="post-metadata">

**Author:** ![MartinT](http://discourse.iapct.org/letter_avatar_proxy/v4/letter/m/ee7513/32.png) [@MartinT](http://discourse.iapct.org/u/MartinT)\
**Post date:** [January 5, 2010, 4:12am UTC](http://discourse.iapct.org/t/feedforward-yet-again/4362/9 "2010-01-05T04:12:07Z")

</div>

[Martin Taylor 2010.01.04.23.03]

> [From Rick Marken (2010.01.04.1540)]
> 
> > Martin Taylor (2010.01.04.17.27)--  
> > &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
> > 
> > > &nbsp;&nbsp;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.  
> > > &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
> > 
> > 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  
> > &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
> 
> 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

---

<div class="post-metadata">

**Author:** ![MartinT](http://discourse.iapct.org/letter_avatar_proxy/v4/letter/m/ee7513/32.png) [@MartinT](http://discourse.iapct.org/u/MartinT)\
**Post date:** [January 5, 2010, 5:20am UTC](http://discourse.iapct.org/t/feedforward-yet-again/4362/10 "2010-01-05T05:20:22Z")

</div>

[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](http://discourse.iapct.org/uploads/default/original/1X/5a89ba4c207756e53d50b5e77bcce642e2817aeb.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.

> 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.

---

<div class="post-metadata">

**Author:** ![Bill\_Powers1](http://discourse.iapct.org/letter_avatar_proxy/v4/letter/b/8e7dd6/32.png) [@Bill\_Powers1](http://discourse.iapct.org/u/Bill_Powers1)\
**Post date:** [January 5, 2010, 6:51pm UTC](http://discourse.iapct.org/t/feedforward-yet-again/4362/11 "2010-01-05T18:51:10Z")

</div>

[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](http://discourse.iapct.org/uploads/default/original/1X/94e6d0b72d9873d99d9583f28eb98a074604225c.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). 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.

---

<div class="post-metadata">

**Author:** ![rsmarken](http://discourse.iapct.org/user_avatar/discourse.iapct.org/rsmarken/32/3553_2.png) [@rsmarken](http://discourse.iapct.org/u/rsmarken)\
**Post date:** [January 5, 2010, 6:57pm UTC](http://discourse.iapct.org/t/feedforward-yet-again/4362/12 "2010-01-05T18:57:36Z")

</div>

[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?

> ![](http://mail.google.com/mail/?ui=2&ik=f4dcc9166a&view=att&th=125ffc2db116e596&attid=0.1&disp=emb&realattid=0.1.1&zw)
> 
> 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](mailto:rsmarken@gmail.com)
> 
> [www.mindreadings.com](http://www.mindreadings.com)

---

<div class="post-metadata">

**Author:** ![MartinT](http://discourse.iapct.org/letter_avatar_proxy/v4/letter/m/ee7513/32.png) [@MartinT](http://discourse.iapct.org/u/MartinT)\
**Post date:** [January 5, 2010, 7:54pm UTC](http://discourse.iapct.org/t/feedforward-yet-again/4362/13 "2010-01-05T19:54:41Z")

</div>

[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](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.

---

<div class="post-metadata">

**Author:** ![rsmarken](http://discourse.iapct.org/user_avatar/discourse.iapct.org/rsmarken/32/3553_2.png) [@rsmarken](http://discourse.iapct.org/u/rsmarken)\
**Post date:** [January 5, 2010, 9:08pm UTC](http://discourse.iapct.org/t/feedforward-yet-again/4362/14 "2010-01-05T21:08:41Z")

</div>

[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](mailto:rsmarken@gmail.com)  
> [www.mindreadings.com](http://www.mindreadings.com)

---

<div class="post-metadata">

**Author:** ![Bill\_Powers1](http://discourse.iapct.org/letter_avatar_proxy/v4/letter/b/8e7dd6/32.png) [@Bill\_Powers1](http://discourse.iapct.org/u/Bill_Powers1)\
**Post date:** [January 6, 2010, 1:19am UTC](http://discourse.iapct.org/t/feedforward-yet-again/4362/15 "2010-01-06T01:19:01Z")

</div>

[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](http://discourse.iapct.org/uploads/short-url/A1DzEfGgURCwqcA47Do4gfXq2kt.doc) (74.5 KB)

---

<div class="post-metadata">

**Author:** ![rsmarken](http://discourse.iapct.org/user_avatar/discourse.iapct.org/rsmarken/32/3553_2.png) [@rsmarken](http://discourse.iapct.org/u/rsmarken)\
**Post date:** [January 6, 2010, 1:46am UTC](http://discourse.iapct.org/t/feedforward-yet-again/4362/16 "2010-01-06T01:46:13Z")

</div>

[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

---

<div class="post-metadata">

**Author:** ![MartinT](http://discourse.iapct.org/letter_avatar_proxy/v4/letter/m/ee7513/32.png) [@MartinT](http://discourse.iapct.org/u/MartinT)\
**Post date:** [January 6, 2010, 5:15am UTC](http://discourse.iapct.org/t/feedforward-yet-again/4362/17 "2010-01-06T05:15:50Z")

</div>

[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?  
> > > &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
> > 
> > Martin attached it to a post. Here it is again.  
> > &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
> 
> 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](http://discourse.iapct.org/uploads/short-url/b45KPF8iLUEQe3Gg8nKbcdoUoXA.pdf) (259 KB)

---

<div class="post-metadata">

**Author:** ![MartinT](http://discourse.iapct.org/letter_avatar_proxy/v4/letter/m/ee7513/32.png) [@MartinT](http://discourse.iapct.org/u/MartinT)\
**Post date:** [January 6, 2010, 6:14am UTC](http://discourse.iapct.org/t/feedforward-yet-again/4362/18 "2010-01-06T06:14:34Z")

</div>

[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

---

<div class="post-metadata">

**Author:** ![Bill\_Powers1](http://discourse.iapct.org/letter_avatar_proxy/v4/letter/b/8e7dd6/32.png) [@Bill\_Powers1](http://discourse.iapct.org/u/Bill_Powers1)\
**Post date:** [January 6, 2010, 8:46am UTC](http://discourse.iapct.org/t/feedforward-yet-again/4362/19 "2010-01-06T08:46:26Z")

</div>

[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.

---

<div class="post-metadata">

**Author:** ![rsmarken](http://discourse.iapct.org/user_avatar/discourse.iapct.org/rsmarken/32/3553_2.png) [@rsmarken](http://discourse.iapct.org/u/rsmarken)\
**Post date:** [January 6, 2010, 8:30pm UTC](http://discourse.iapct.org/t/feedforward-yet-again/4362/20 "2010-01-06T20:30:32Z")

</div>

[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

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