Reference Input Function

CSGnet Archive CSG2004
1

[Martin Taylor 2004.03.20.1116]

I thought it might be about time to inject some levity into this long
bout of serious navel gazing, so I've decided to address a technical
issue. Sorry about that, but there it is :slight_smile:

A lot of study has gone into issues of how the Perceptual Input
Function (PIF), and the Output function (OF) of an elementary control
unit change or learn. The actions induced by the OF influence the
inputs to the PIF. Changes in the PIF affect how its inputs generate
the perceptual signal. Together, they determine how well the ECU
serves its purpose as a controller within the environment(s) in which
it finds itself. In other words, the criterion for "learning" is
available from data within the ECU.

Not nearly as much attention has been given to the third connection
of an ECU with the world outside itself--the way the multiple inputs
from other places combine to form a reference signal. If we are
talking about an ECU that controls a scalar variable (the perceptual
signal), then the reference value must also be scalar. However, in
the standard HPCT hierarchy, or in any network version of PCT, a
vector of inputs contribute to the reference scalar. Therefore, there
must be a Reference Input Function (RIF) that converts the vector's
components into a single scalar variable.

In most simulations of which I am aware, the RIF has been taken to be
a simple (possibly weighted) summation. The rationale for this choice
is not clear to me, other than that it is computationally convenient,
and in the simple circumstances considered, it works. It can work,
however, only in situations in which intermediate outputs are useful.
It doesn't work when the "usefulness" of the output space is
non-monotonic.

Let me give an example. At some level, I have a reference to learn
something about differential equations, and my output provides
references to some system that controls a perception of seeing a
suitable book in my hand. Further down the hierarchy, I am
controlling arm and hand position. In front of me is a bookshelf, on
which the following three books sit in this order: "Differential
Calculus" "Who was Jesus" "Solving Differential Equations". I have no
particular preference between the first and third book, but a simple
additive RIF for whatever level control unit(s) set references for
arm position would lead me to pick up "Who was Jesus". From that, I
learn little about differential equations. I wouold have needed an
RIF that allowed my arm-position reference signal to have a value
associated with either the first or the third book, but not a value
intermediate between them.

So far as I can see, if the space in which a particular controlled
perception exists is non-monotonic or is discrete, additive RIFs
providing references to supporting ECUs will not work very well. The
reasons, though, are not related to the effectiveness of the ECU
receiving the reference signal in question. Nor are they related to
the values within any one ECU that contributes its output to the
creation of the reference signal.

Since the form and parametrization of no RIF can be attributed to the
performance of any single ECU, it follows that it must be attributed
to structural factors in the network of ECUs. In some way, it relates
to the performance of the set of ECUs that contribute to its inputs,
not to the performance of the ECU that uses its scalar reference
signal.

As such, developing the structure of RIFs has to be an aspect of
reorganization. But it's a very localized reorganization, concerning
only those ECUs on a single level that potentially could conflict
over the use of a "lower-level" control system. In other words, it
seems to be a question of reorganizing for conflict mediation (as is
a lot of reorganization, considered more globally, since conflict is
the prime source of error internal to the network or hierarchy of
ECUs).

Do we have, in this question, a pointer to a direction of research
into the properties of reorganization? Is there some engineering
design technology that answers how RIFs might be designed for
specific situations, which could suggest ways in which RIF designs
might develop through evolution and local reorganization?

More questions than answers. Perhaps I'm understimating the power of
simple weighted addition in the design of RIFs, and the problematic
situations don't arise. But I doubt it.

Sorry to have interrupted the serious business of CSGnet :slight_smile:

Martin

2

[From Bill Powers (2004.03.20.1613 MST)]

Martin Taylor 2004.03.20.1116 --

Excellent points. I think that as we try to model higher-level systems, we
will inevitably find that the basic PCT model is too simple to fit reality
without modification. For example, in controlling events, a simple error
signal driving a proportional output function can't possibly cause the sort
of correction that is needed to turn the wrong event into the right event.
Of course there must be some comparison, and some sort of error measure,
and some sort of conversion of error into a change in the action of the
system. The basic idea of negative feedback control is not likely to go
away. But I have always been acutely conscious of my inability to think of
a way to construct higher-order systems. That's why I have focused my
attention on the lower levels where relatively simple models seem to work
very well.

In your delicious example of choosing the two books, I think it might be
better to look for a selection process in the input function of the highest
system. That is, two of the books would lead to a perception of "a book
about differential equations," while the third would not. So there would be
only two candidates for controlled variables -- those that elicit a
perception of the right class of book. Other perceptions would then be
involved in picking one of them to reach for. And I don't think we need to
think of adding the reference signals together literally -- once a book has
been chosen as the object of reaching, there is no reason to reach anywhere
else, unless a conflict arises (there is a Black Widow spider on the
selected book).

I think the way to approach this is simply to try to build a model that
will do something reasonable. When you actually start making a model work,
you find that you have to things demanded by the problem and you can't
slavishly follow the simple PCT diagram. Even in the Little Man, which
first saw the light in the late '80s or early '90s, I had to ignore the
levels as I had defined them in order to make the model match what was
known about the spinal control systems. Obviously the model still belongs
to the PCT family, but its details were dictated mainly by nature, not by
the theory. I think that will continue to be the story.

Best,

Bill P.

3

From[Bill Williams 20 March 2OO4 11:OO PM CST]

[ Martin Taylor <mmt-csg[Martin Taylor 2004.03.20.1116]

Martin seems to think we recently have been having way to

much fun on the CSGnet.

And, to distract us, he has provided an interesting

problem, a technical issue, for CSGnet people to think

about. Basically the problem is, if I understand what

is involved, how do complex environmental situations

get transformed into a single neuro-current on the

output side of a biological system. This at least is

how I understand what Martin is saying in the following:

Not nearly as much attention has been given to the

third connection of an ECU with the world outside

itself--the way the multiple inputs from other places

combine to form a reference signal.

Martin says that,

there must be a Reference Input Function (RIF) that

converts the vector's components into a single scalar

variable.

And, Martin goes on to say,

In most simulations of which I am aware, the RIF has

been taken to be a simple (possibly weighted) summation.

This notion of a "simple(possibly weighted) summation"

that Martin brings up, caught my eye. This sounds just

like the system that has been adopted by neo-classical

ecnomics. To maximize utility the consumer, it is

thought, distributes purchases between commodities so

that the last unit of purchase divided by the price

of that unit provides an equal increment to the consumer's

total utility (subject to a budget constraint). This isn't

precisely what Martin described as a simple system-- it

takes quite a while to explain this to students. Andreu

Mas-Colell's 1995 text _Microeconomic Theory_ Oxford U.P.

takes a little over a thousand pages is considered the

standard text. And, the Mas-Colell treatment comes to

a mistaken conclusion regarding the Giffen paradox. And,

all the other standard texts make the same mistake.

The utility functions that have for more than a century

characterized the mainstream neo-classical orthodoxy,

are basically the simple weighted average computation

that Martin describes as being typically used to transform

a reality with many goods and prices into a decision

about how much of each good to consume.

Significantly this conception of behavior in terms of

utility functions and prices generates the wrong answer

in the case of the Giffen paradox. Increasing the price

of a Giffen commodity increases the quantity that the

consumer will purchase of the Giffen commodity. And,

this violates the fundamental principle of the law of

demand. Yet there is experimental evidence of the

Giffen effect.

The solution to the problem presented by the Giffen

paradox is a switch from this additive type input

function to a control theory input function. Using a

control theory analysis the hierarchal structure of

choices-- pay the bills, buy enough calories, buy

good tasting calories, gets translated into a decision

about how much of each commodity to purchase (Bill

Powers' single neuro-current). This input reduction

function translates the reality of many goods and

many prices into a reference level which is

compatible with a PCT type system. The Giffen

paradox was discovered more than a century ago, and

the main stream orthodox theorists-- such as

Mas-Colell still don't see that an additive type

system can not handle the problem correctly. Or,

rather they don't see any problem-because they define

economics not in terms of economic phenomena but

rather in terms of the theory that the maximization

analysis generates.

However, using control theory it is possible not

only to explain the Giffen type behavior, but also

what is considered to be economically "normal"

behavior-- that is downward sloping demand curves.

So, it looks to me as if the Giffen paradox or more

correctly "Giffen effect" when explained in control

theory terms is a case of what Martin Taylor

describes as a RIF function.

Martin, would you agree?

Bill Williams

4

[From Bjorn
Simonsen (2004.03.21,10:05 EuST)]

Martin Taylor
2004.03.20.1116

Interesting

In most
simulations of which I am aware, the RIF has been taken to be

a simple
(possibly weighted) summation. The rationale for this choice

is not clear
to me, other than that it is computationally convenient,

and in the
simple circumstances considered, it works. It can work,

however,
only in situations in which intermediate outputs are useful.

It doesn’t
work when the “usefulness” of the output space is

non-monotonic.

I perceive your concept “a non-monotonic function” as a
non-linear function”

I haven’t worked with non-linear reference values before.
Therefore I tried in Rick’s hier.exl to make a Reference non-linear. It was interesting to see what happened
when I reversed a reference from a linear value (=G5-F5) to a non-linear
function (=sin(G5-F5)). Rick’s hier.exl is a nice tutorial.

But I can’t understand how a reference value at the
time t can be non-linear. At the time t the reference value is the value it is.

I can understand how the reference value changes from
time t to time (t+1), (t+2), … . And it may gladly change in a non-linear way. This
happens because the perception signal also affects the higher levels and they
change their outputs.

Can you explain the meaning of a neuron where the “usefulness”
of the output space is non-linear? I don’t comprehend such a situation. And that is my fault.

Let me give
an example. At some level, I have a reference to learn

something
about differential equations, and my output provides

references
to some system that controls a perception of seeing a

suitable
book in my hand. Further down the hierarchy, I am

controlling
arm and hand position. In front of me is a bookshelf, on

which the
following three books sit in this order: "Differential

Calculus"
“Who was Jesus” “Solving Differential Equations”. I have no

particular
preference between the first and third book, but a simple

additive RIF
for whatever level control unit(s) set references for

arm position
would lead me to pick up “Who was Jesus”. From that, I

Zlearn little
about differential equations. I wouold have needed an

RIF that
allowed my arm-position reference signal to have a value

associated
with either the first or the third book, but not a value

intermediate
between them.

I will not explain your example, but generally we have
many references. Some of them cause conscious actions and some of them cause
unconscious actions. I experience this at present when I try to reduce. I know
I have a reference saying “Don’t eat off the meals”. But I can imagine there
are other reference values managing my level of glucose. At the end of a day I
can remember that I have eaten off the meals.

So far as I
can see, if the space in which a particular controlled

perception
exists is non-monotonic or is discrete, additive RIFs

providing
references to supporting ECUs will not work very well. The

reasons,
though, are not related to the effectiveness of the ECU

receiving
the reference signal in question. Nor are they related to

the values
within any one ECU that contributes its output to the

creation of
the reference signal.

I partly
agree that “additive
RIFs providing references to supporting ECUs will not work very well”. Maybe
they will do things worse. Maybe it will cause a conflict? But getting a
conflict will help if reorganization eliminates the conflict. There is also a special
way where “additive RIFs providing references to supporting ECUs will work very well”. And that is when we go
up a level.

Let me give an
example. If I activate my System Concept level “I am a slimming guy”. I think this
ECU will help. The problem is that sometimes I will get a conflict with other
System Concepts.

Since the
form and parametrization of no RIF can be attributed to the

performance
of any single ECU, it follows that it must be attributed

to
structural factors in the network of ECUs. In some way, it relates

to the
performance of the set of ECUs that contribute to its inputs,

not to the
performance of the ECU that uses its scalar reference

signal.

I may be wrong,
but if my comments above are effective, we don’t have to find other structural
factors in the network of ECUs.

over the use
of a “lower-level” control system. In other words, it

seems to be
a question of reorganizing for conflict mediation (as is

a lot of
reorganization, considered more globally, since conflict is

the prime
source of error internal to the network or hierarchy of

ECUs).

I agree. I
don’t’ think that going up a level needs any reorganization. But if going up a
level cause a conflict, then reorganization may solve the conflict. Going back
to my example. If I really manage my System Concept level “I am a slimming guy”, then there will be
a reorganization of my reference managing my glucose level. I don’t know if I exaggerate
here.

Sorry to
have interrupted the serious business of CSGnet :slight_smile:

I appreciated
your interruption, but I still work with economics.

bjorn

5

[From Peter Small (2004.03.21)]

Bill Powers (2004.03.20.1613 MST) wrote:

···

---
I think that as we try to model higher-level systems, we
will inevitably find that the basic PCT model is too simple to fit reality
without modification. For example, in controlling events, a simple error
signal driving a proportional output function can't possibly cause the sort
of correction that is needed to turn the wrong event into the right event.
Of course there must be some comparison, and some sort of error measure,
and some sort of conversion of error into a change in the action of the
system. The basic idea of negative feedback control is not likely to go
away. But I have always been acutely conscious of my inability to think of
a way to construct higher-order systems. That's why I have focused my
attention on the lower levels where relatively simple models seem to work
very well.
---
Having only recently encountered the concept of PCT, I've spent the
last couple of weeks trying to come to grips with it. However, as
probably most people do when they come across an unfamiliar paradigm,
I didn't start with a blank sheet but tried to incorporate the ideas
into my own cognitive models.

The initial problem I had with PCT was exactly what BP is saying in
the above quoted paragraph and it wasn't until I came across the
following article that I could resolve the situation:

What is the Method of Levels?
Method of Levels: A Therapeutic Approach Based on William T. Powers'
Perceptual Control Theory
by Tim Carey
http://www.iaact.com/newsletters/summer2000/concept.htm

To describe how this resolved the problems for me, I'd better first
explain where I am coming from. I am taking into consideration the
new ideas about the brain and the central nervous system - that
evolved during the 1990's - based upon self-organization and
complexity theory. PCT pre-dated this work so it is understandable
that these ideas haven't yet been incorporated into the PCT model. If
they were, many of the problem areas of PCT would disappear.

Complex interactions occur when genes in cells are able to turn each
other on and off, or, neurons are able to make each other fire. This
can cause a series of continuous cascading events due to positive
feedback. This typically happens when the state of an element sets up
a series of reactions that comes back on itself to change its own
state, which then sets up a new series of reactions. This is similar
to what happens in Conways's "Game of Life" and is popularly known as
chaos.

The important characteristic of chaotic systems is that they quickly
settle down into steady states (known as "attractor basins").

There can be many different steady states (attractor basins) that a
chaotic system can settle into and which state it does is determined
by its initial conditions (and initial conditions can be changed by
the/off state of a single element such as neuron or gene).

The steady state of a network of genes or neurons will result in all
the genes or neurons becoming 'fixed' in a particular pattern of
on/off states. Disturbing the network by introducing a change to one
of the elements can cause the network to go chaotic and settle into a
new steady state, where the 'fixed' states of all the elements can
take on quite a different pattern (of on/offs).

The key point here is that these network steady states are not
random. The same pattern will reappear in response to a particular
set of initial conditions. In other words, a particular pattern of
on/off states of either cells or neurons can be called up by changing
one or more of the element states, i.e., though a single event. In
this way highly complex patterns of muscular movements, memory or
thought processes can be triggered.

Now, if you consider not one, but many of these dynamic complex
systems being linked together in a hierarchical way, you get the
phenomenon of the hierarchic system described in PCT.

I don't know if this gross simplification is sufficient to get the
ideas across, but it does solve many of the problems associated with
PCT. Here is another description of this phenomenon, which I put into
a post to another PCT discussion forum:

It seems to me that the main differences we have is in our
conceptualization of reorganization. A PCT view appears to see this
in terms of control theory.

I had a similar mental model before I read Kelso's book "Dynamic
Patterns". This lead to a major reorganization of the way I thought
about what happens in this mental process of reorganization. Instead
of seeing the brain in terms of areas of the brain exchanging
information, I saw the brain as a complex dynamic system consisting
of hierarchies of separate dynamic complex systems within it.

In such a conceptual view, a complex dynamic system is a chaotic
system that finds stability by settling into a steady state known as
an attractor basin. With this view the organization within the brain
consists of a main attractor basin, whose stability is determined by
the attractor basins of the dynamic complex systems it contains.
These component dynamic complex systems each contain their own
complex dynamic systems, which in turn may contain their own dynamic
complex systems.

In other words, I see the brain as a hierarchy of dynamic complex
systems, where every separate dynamic complex system is in a steady
state (in an attractor basin) - but, can be tipped into a new steady
state (attractor basin) by input from the senses (learning).

Although this is potentially a totally chaotic system, stability is
achieved because of the nature of attractor basins. These allow a
limited amount of variation without changing state.

In such a system, small local areas of the brain can become chaotic
and settle into new attractor basins without necessarily affecting
the states of the dynamic complex systems they are in (i.e., the
dynamic complex systems higher up in the hierarchy). In PCT
terminology, this means local reorganization can occur without
necessarily causing a major reorganization.

In my view, learning can cause local reorganization, and sometimes
these local reorganizations can affect the organization at a higher
level (a domino effect - where a dynamic complex system in a lower
level moves into a new attractor basin where the change is sufficient
to cause the dynamic system at a higher level to also move into a new
attractor basin).

I don't know if this is making sense to you, but the point is that
learning may or may not affect reorganization at several hierarchic
levels.

My contention is that the brain is able to recognize when new
information (learning) has the potential to disrupt its internal
organization and will put up a resistance (in the form of emotions).
The larger the disruption anticipated by the brain, the greater will
be this resistance. In this way the brain is working to maintain its
stability and preventing itself from going into chaos.

There must also be emotions that favor reorganization. These are the
emotions that motivate learning and can overcome the brains
resistance to change. The relative strength of these opposing
emotions seems to vary greatly from one person to another.

For myself, I actively seek information that can lead to major
reorganization and feel a great excitement and pleasure when it
happens. My two sons, on the other hand, find reorganization
unsettling and will resist it as much as possible.

Peter Small

Author of: Lingo Sorcery, Magical A-Life Avatars, The Entrepreneurial
Web, The Ultimate Game of Strategy and Web Presence
http://www.stigmergicsystems.com

--

6

Re: Reference Input Function
[Martin Taylor 2004.03.21.10.14]

Bill Willimas and Blorn Simonsen both seem to have failed to
understand the nature of my message about the Reference Input
Function.

From[Bill Williams 20 March
2OO4 11:OO PM CST]
Basically the problem is, if I
understand what

is involved, how do complex environmental situations

get transformed into a single neuro-current on the
output side of a biological
system.

No. The problem is how the many different outputs from higher
levels are combined to form a single scalar-valued reference signal
for an ECU.

[From Bjorn Simonsen
(2004.03.21,10:05 EuST)]

I
perceive your concept “a non-monotonic function” as a non-linear
function"

I
haven’t worked with non-linear reference values
before.

No. the question has nothing to do with non-linearity, which
itself is not related to non-monotonicity. Non-monotonicity means that
as the value of x smoothly increases, the value of y sometimes
increases and sometimes decreases.

Whether you believe in the strict hierarchy of ECUs or prefer a
looser network design, the reference value for an ECU is a single
number at any one moment. But that number is in some way created from
the outputs of several other ECUs that use the ECU in question as part
of their feedback loop. My question is very simple: “How do
these contributions to a reference value get combined or
selected”, with a secondary question “How does the system
evolve or adapt so that the combination or selection process works
effectively in producing a reference value that works well for the
performance of the system as a whole?”

Martin

7

[From Richard Kennaway (2004.03.21.1551 GMT)]

[Martin Taylor 2004.03.21.10.14]
Whether you believe in the strict hierarchy of ECUs or prefer a
looser network design, the reference value for an ECU is a single
number at any one moment. But that number is in some way created
from the outputs of several other ECUs that use the ECU in question
as part of their feedback loop. My question is very simple: "How do
these contributions to a reference value get combined or selected",
with a secondary question "How does the system evolve or adapt so
that the combination or selection process works effectively in
producing a reference value that works well for the performance of
the system as a whole?"

This won't necessarily be relevant to living systems, but in the
mechanical control systems I've been constructing, the answer to the
first question is that they are combined in a weighted sum. The
weights in some cases depend on the current state of the machine. The
answer to the second is that they don't evolve, I choose the weights
(and their dependency on the state) by physical intuition.

http://www.cmp.uea.ac.uk/~jrk/temp/rk-c2004.pdf

-- Richard Kennaway

8

Re: Reference Input Function
From[Bill Williams 21 March 2004 11:25 AM CST]

[Martin Taylor 2004.03.21.10.14]

Bill Willimas and Blorn Simonsen both seem to have failed to >understand the nature of my message about the Reference Input >Function.

From[Bill Williams 20 March 2OO4 11:OO PM CST]
Basically the problem is, if I understand whatis >involved, how do complex environmental situations
get transformed into a single neuro-current on the

output side of a biological system.

No. The problem is how the many different outputs from higher levels >are combined to form a single scalar-valued reference signal for an ECU.

Isn’t what happens something like this:

Ennvironment Organism

< < < < < < < < ^

complex features A B

Apercept >

                                              ^        ^

Bpercept >|

ECU

V

^

A > RIFa ^

^

B > RIFb Giffen Effect model >>> reference levels

single current

C > RIFc

In the simple Giffen effect model there are three environmental factors, the budget, the cheap food and the more expensive better tasting food.

The Giffen effect explained as a control theory analysis converts the complex environmental situation into a single current which serves as the reference level for two commodities the cheap nasty tasting and the expensive good tasting food. The budget is the price of the two commodities times the quantity of the two commodities.

My first RIF post must have sounded as if I was going to leave the ECU out of the story entirely. What I was attempting to say was a complex situation which an organism faces has to be somehow converted into the single current that finds expression on the output side of the loop. But, of course the loop has be completed through the ECU’s. In the Giffen effect the RIFs would convert the three factors budget , good tasting expensive good, and bad tasting cheap good into two reference levels and then there would be two ECU’s to handle the two commodities.

If your approach using RIF in a larger loop which includes ECU is adopted then when re-organization is necessary it could take place primarily or perhaps altogether in the RIF modules and thus leave the ECU’s largely or altogether undisturbed.

Now, Martin, does the giffen analysis look and sound like a proper RIF to you.

Bill Williams

···

[Martin Taylor 2004.03.21.10.14]

Bill Willimas and Blorn Simonsen both seem to have failed to understand the nature of my message about the Reference Input Function.

From[Bill Williams  20 March 2OO4   11:OO PM CST]
Basically the problem is, if I understand what

is involved, how do complex environmental situations

get transformed into a single neuro-current on the

output side of a biological system.

No. The problem is how the many different outputs from higher levels are combined to form a single scalar-valued reference signal for an ECU.

[From Bjorn Simonsen (2004.03.21,10:05 EuST)]

I perceive your concept "a non-monotonic function" as a non-linear function"
I haven't worked with non-linear reference values before.

No. the question has nothing to do with non-linearity, which itself is not related to non-monotonicity. Non-monotonicity means that as the value of x smoothly increases, the value of y sometimes increases and sometimes decreases.

Whether you believe in the strict hierarchy of ECUs or prefer a looser network design, the reference value for an ECU is a single number at any one moment. But that number is in some way created from the outputs of several other ECUs that use the ECU in question as part of their feedback loop. My question is very simple: “How do these contributions to a reference value get combined or selected”, with a secondary question “How does the system evolve or adapt so that the combination or selection process works effectively in producing a reference value that works well for the performance of the system as a whole?”

Martin

9

Re: Reference Input Function
[Martin Taylor 2004.03.21.13.50]

Bill,

Your messages come out in various sizes and fonts, never
predictable. This one was one of the smallest, and it contains what
seems to have been intended as a figure, but which comes out as a
scattering of “<” and other signs, with some one and
three-letter groups here and there.

From[Bill
Williams 21 March 2004 11:25 AM
CST]

Isn’t what
happens something like this:

Ennvironment
Organism

                       <

< <
< <
< <
< ^

complex
features A
B

Apercept >
> ^
^

Bpercept >|
ECU
V
^
A

RIFa ^

^
B

 RIFb     Giffen

Effect model

reference

levels

                                                                  single current
   C 

  RIFc

However, I do get the impression
that you are putting Reference Input Functions somewhere in the
environment. Reference input functions only connect the outputs of
ECUs to the Reference inputs of other ECUs. They have no connection to
the environment.

I hope I got that much correctly out
of the figure. If not, I apologize for the redundancy.

Martin

10

Re: Reference Input Function
From[Bill Williams 21 March 2004 2:00 PM CST]

Martin, I have no idea what is going on in my email system when I post. It seems to change frequently. Maybe the thing to do is for me to send you snail mail a diagram. If this seems the way to go, you could send me your surface address and I will mail you and who ever else might be interested a paper copy.

I think I understand the contribution you RIF notion makes to a control theory analysis. But, I found your brief remarks in response to my attempted clarification puzzling.

Sorry for the confusion, but I am probably more confused than you are.

Bill williams

11

Re: Reference Input Function
[Martin Taylor 20-04.03.21.1720]

From[Bill
Williams 21 March 2004 2:00 PM
CST]
Martin, I
have no idea what is going on in my email system when I post. It seems
to change frequently. Maybe the thing to do is for me to send
you snail mail a diagram. If this seems the way to go, you could
send me your surface address and I will mail you and who ever else
might be interested a paper copy.

I’ve no objection to giving you my s-mail address, but I don’t
think it would profit the discussion. If you are able to create a Jpeg
of your diagram, everyone could see what you are talking about.
Likewise, I could (and will) diagram what I’m getting at, and attach
it to (or embed it in) a message, the way Rick does his graphs.

I think I
understand the contribution you RIF notion makes to a control theory
analysis. But, I found your brief remarks in response to my
attempted clarification puzzling.
Sorry for
the confusion, but I am probably more confused than you
are.

I think Peter could give a good dynamic analysis of how confusion
breeds more confusion!

Martin

12

[From
Bjorn Simonsen (2004.03.22,13:30)]

[Martin
Taylor 2004.03.21.10.14]

Thank
you for your indication that you didn’t mean non-linear saying non-monotonic. I
will come into line with your last part of [Martin Taylor 2004.03.21.10.14] in a later mail. Here
I will concentrate about your first part.

One step at a time.

from other places combine to form a reference signal. If we are

talking about an ECU that controls a
scalar variable (the perceptual

signal), then the reference value must also be scalar. However, in

the standard HPCT hierarchy, or in any network version of PCT, a

vector of inputs contribute to the reference scalar. Therefore,
there

must be a Reference Input Function (RIF) that converts the vector’s

components into a single scalar variable.

PCT uses the concept “vector”, but I have never seen the arithmetical
rules for vectors used in PCT. Viewed against chapter 3 in BCP where BP
consider addision/subtrqction (and more) of neural currents I evaluated his vector-presentation
in chapter 8 (Second-order Control Systems: Sensation Control or Vector
control) as if the sensation vector is a sum of many scalar variables. I conceive this vector (the perception signal) as
scalar.

I also imagine that PIFs at higher levels receives perceptual signals from
lower levels in the same way and that the resulting perceptual signal at a
higher level may be read as a vector. I nevertheless
conceive all perceptual signals as a scalar. This is also the way I
understand your first part of the first sentence over. Am I wrong so far?

At level 1 physical variables from the extern world are reversed to
perceptual signals. Therefore there is a PIF for conversion. At higher levels there are also PIFs,
but they receive perceptual signals. Her we don’t need to convert physical
signals to a perceptual signal, we just add perceptual signals.

In an ECU there are an OF and the output signal coming from the OF is a
scalar. The output signals from many RIFs are summed to a Reference signal. I
haven’t seen a box where these output signals are summed to a Reference signal,
but it is no problem for me to imagine the reference signal as a sum of many
output signals being influenced of a perceptual signal in the Comparator. I conceive the error signal leaving the
Comparator as a Scalar.

Maybe I have a wrong argumentation, so please point it out. If my
argumentation is not wrong, I can’t understand your last sentence over.

I will come back to your central theme in
your last part of [Martin Taylor
2004.03.21.10.14] in an other mail. There are things I am taken up with.

I control the perception that you didn’t
read the part of my mail [From Bjorn Simonsen
(2004.03.21,10:05 EuST)] after my statement ” I perceive your concept “a
non-monotonic function” as a non-linear function”. Am I wrong?

bjorn

13

[From Bjorn Simonsen(2004.03.22,15:15 EuST)]

[Martin Taylor 2004.03.20.1116]

In most simulations of which I am aware, the RIF has been taken to
be

a simple (possibly weighted) summation. The rationale for this
choice

is not clear to me, other than that it is computationally
convenient,

and in the simple circumstances considered, it works. It can work,

however, only in situations in which intermediate outputs are
useful.

It doesn’t work when the “usefulness” of the output space
is

non-monotonic.

I am not used to the concept non-monotonic. But I know
it is both a mathematical and a logical concept. Because of your comment [Martin Taylor 2004.03.21.10.14];
“….Non-monotonic means that as the value of x smoothly increases, the value of
y sometimes increases and sometimes decreases.” And I conceive monotonic means
that as the value of x smoothly increases, the value of y also increases.

For me the rational for a weighted
summation is the following axioms:

A single neuron may have thousands of neurons
synapsing on it. Some of them release activating neurotransmitters and other
release inhibitory neurotransmitters.

The receiving cell integrates these signals.

The action potential (nerve impulse) tells us about
depolarisation in a neuron and the frequency of the action potentials that are
generated tells us about the strength of the signal.

When a dispatching neuron with the Action
Potential 0.5mV and frequency 700 impulses per second and an other dispatching
cell with Action Potential 0.5mV
and frequency 800 send their signals to a receiving cell. The receiving Cell
will thus get an energy =(0.5700+0.5800) Joule.

Why can you be so sure that “It
doesn’t work when the “usefulness” of the output space is
non-monotonic”?

We know that there are Excitatory and
Inhibitory synapses and on a link y will necessary not increase with increasing
x if a receiving cell receives signals from many inhibitory synapses.

bjorn

14

From[Bill Williams 22 March 2004 1:00 PM CST]

[From Bjorn Simonsen(2004.03.22,15:15 EuST)]

[Martin Taylor 2004.03.20.1116]

Among a great many other things Bjorn raises the question,

Why can you be so sure that “It doesn’t work when the “usefulness” of the output space is non-monotonic”?

My experience in economics isn’t in any way a “proof” that what Martin is claiming is correct, but it seems rather clear that additive preference functions are not capable of generating the correct behavior in at least some situations. If someone knows of a proof out there I could make good use of it. Having a proof would be lots better than saying, I am entirely convinced that … "

Bill Williams

···

[From Bjorn Simonsen(2004.03.22,15:15 EuST)]

[Martin Taylor 2004.03.20.1116]

In most simulations of which I am aware, the RIF has been taken to be

a simple (possibly weighted) summation. The rationale for this choice

is not clear to me, other than that it is computationally convenient,

and in the simple circumstances considered, it works. It can work,

however, only in situations in which intermediate outputs are useful.

It doesn’t work when the “usefulness” of the output space is

non-monotonic.

I am not used to the concept non-monotonic. But I know it is both a mathematical and a logical concept. Because of your comment [Martin Taylor 2004.03.21.10.14]; “….Non-monotonic means that as the value of x smoothly increases, the value of y sometimes increases and sometimes decreases.” And I conceive monotonic means that as the value of x smoothly increases, the value of y also increases.

For me the rational for a weighted summation is the following axioms:

  1.     A single neuron may have thousands of neurons synapsing on it. Some of them release activating neurotransmitters and other release inhibitory neurotransmitters.

  1.     The receiving cell integrates these signals.

  1.     The action potential (nerve impulse) tells us about depolarisation in a neuron and the frequency of the action potentials that are generated tells us about the strength of the signal.

When a dispatching neuron with the Action Potential 0.5mV and frequency 700 impulses per second and an other dispatching cell with Action Potential 0.5mV and frequency 800 send their signals to a receiving cell. The receiving Cell will thus get an energy =(0.5700+0.5800) Joule.

Why can you be so sure that “ It doesn’t work when the “usefulness” of the output space is non-monotonic”?

We know that there are Excitatory and Inhibitory synapses and on a link y will necessary not increase with increasing x if a receiving cell receives signals from many inhibitory synapses.

bjorn

15

Re: Reference Input Function
[Martin Taylor 2004.03.22.1710]

[From Bjorn Simonsen (2004.03.22,13:30)]
commenting on
[Martin Taylor 2004.03.21.10.14]

Thank you for your indication that you didn’t mean
non-linear saying non-monotonic. I will come into line with your last
part of [Martin Taylor 2004.03.21.10.14] in a later mail. Here I will
concentrate about your first part.

OK

…I
also imagine that PIFs at higher levels receives perceptual signals
from lower levels in the same way and that the resulting perceptual
signal at a higher level may be read as a vector. I nevertheless
conceive all perceptual signals as a scalar. This is also the way
I understand your first part of the first sentence over. Am I wrong so
far?
At
level 1 physical variables from the extern world are reversed to
perceptual signals. Therefore there is a PIF for conversion. At
higher levels there are also PIFs, but they receive perceptual
signals. Her we don’t need to convert physical signals to a
perceptual signal, we just add perceptual signals.

Fine so far, except that the PIF is ordinarily much more
complicated than something that just adds, or even creates a weighted
sum. At low levels, that may be essentially all it does (although its
output must be a nonlinear function of the sum).

In
an ECU there are an OF and the output signal coming from the OF is a
scalar. The output signals from many RIFs are summed to a Reference
signal. I haven’t seen a box where these output signals are summed
to a Reference signal, but it is no problem for me to imagine the
reference signal as a sum of many output signals being influenced of a
perceptual signal in the Comparator. I conceive the error signal
leaving the Comparator as a Scalar.

I’m not sure of your precise intent here. I think you have it correct,
but in case not, I’ll try to reword it.

Each ECU has one scalar output signal from its OF. This output
signal may be distributed to the reference inputs of many other ECUs,
and each of those ECUs may receive inputs toward its reference signal
from the output signals of many ECUs. The Reference Input Function
takes these many inputs and converts than into a scala rreference
signal which is compared with the perceptual signal in the Comparator
of the ECU.

Maybe I have a wrong argumentation, so please point it
out.

I don’t think you are wrong. I hope that my rewording corresponds
to what you intended to say.

I
control the perception that you didn’t read the part of my mail
[From Bjorn Simonsen (2004.03.21,10:05 EuST)] after my
statement " I perceive your concept “a non-monotonic function”
as a non-linear function". Am I wrong?

Yes, you are wrong. I read it all. But the point I wanted to
address was just the distinction between non-linear and
non-monotonic.

Martin

16

Re: Reference Input Function
[Martin Taylor 2004.03.22 1730]

[From Bjorn Simonsen(2004.03.22,15:15
EuST)]
[Martin Taylor 2004.03.20.1116]

In most simulations of which I am aware, the RIF
has been taken to be
a simple (possibly weighted) summation. The
rationale for this choice
is not clear to me, other than that it is
computationally convenient,
and in the simple circumstances considered, it
works. It can work,
however, only in situations in which intermediate
outputs are useful.
It doesn’t work when the “usefulness” of
the output space is
non-monotonic.

I am
not used to the concept non-monotonic. But I know it is both a
mathematical and a logical concept. Because of your comment [Martin
Taylor 2004.03.21.10.14]; “Š.Non-monotonic means that as the value
of x smoothly increases, the value of y sometimes increases and
sometimes decreases.” And I conceive monotonic means that as the
value of x smoothly increases, the value of y also
increases.

That is correct. In the context of the example I gave, with three
books on a shelf, the outer two of which would serve to bring a
particular perception closer to its reference value and the middle one
would not, the controller for arm position will have inputs to its
Reference signal from (at least) two ECUs, one controlling for arm
position at the left-hand book, one controlling for arm position at
the right-hand book. The resulting reference signal should not be any
kind of a weighted average of the outputs from the two “perceive
this book in the hand” controllers, because the utility of an
intermediate arm position is essentially zero, measuring
“utility” as the effectiveness of the position in satifying
the higher level control system(s). The utility of an arm position
near either of the two books is high. The utility is a non-monotonic
function of arm position along the bookshelft. It hgas two positive
peaks with a distinctly lower value in between.

Technically, the situation is a conflict, which ought to create
ever increasing output from the two “perceive this book”
control systems. Usually, no such conflict is experienced (though it
may be in more complex examples). I don’t think that the conflict can
be resolved at the level of the “perceive this book in hand”
ECUs that are actually in conflict. It has to be resolved either by
“going up a level” so that the “Read about differential
equations” ECU discards the possibility of using one of the two
useful books, or, by “going down a level”, in the Reference
Input Function for the Arm-position ECU.

Why
can you be so sure that “It doesn’t work when the “usefulness”
of the output space is non-monotonic”?

Does the above help?

Actually, although I did say “it doesn’t work”, I
should not have said that. I should have said that I could not see how
it could work.

We
know that there are Excitatory and Inhibitory synapses and on a link y
will necessary not increase with increasing x if a receiving cell
receives signals from many inhibitory synapses.

Yep, and it’s exactly that
that permits non-linear RIFs with catastrophic functions to exist. I
actually think it likely that at least some RIFs embody a cusp
catastrophe, or, in electronic terms, a variably coupled
flip-flop.

Martin

17

Re: Reference Input Function
[Martin Taylor 2004.03.23.0912]

From[Bill Williams 23 March
2004 5:40 AM CST]

Bill seems to be using the phrase “Reference Input Tunction”
to mean something quite different from what I mean when I use the term
(as witness the following):

… at least sufficiently
like
what was expected that the perception
does match the reference level
after passing through the Reference
Input Function.

I thought it might help if I tried to provide a picture to show
what I mean by the RIF in an ECU. I hope it comes through OK.

The Reference Input Function is the rectangular box at the top,
into which come many signals from the outputs of other ECUs. The
perceptual signal goes nowhere near it. The perceptual signal is
generated from many variables in the environment of the ECU (including
variables not shown in the picture because they are not affected by
the output of the ECU).

The RIF processes the many signals that come into it, and
generates a scalar reference signal. The Perceptual input function
processes the many signals that come into it and produces a scalar
perceptual signal. The Comparator processes the two scalars and
produces a scalar error signal.

My original question, which several writers have addressed, was
how the RIF could evolve and adapt, recognizing that its form and its
parameters do not affect the effectiveness of control by the ECU to
which it belongs. The form and parameters of the RIF only affect
control by the ECUs that provide its inputs. To me, this implies that
the form and parameters of the RIF must be developed through
reorganization, or through unguided Hebbian learning. This is
different from the cases of the PIF, the Comparator, and the OF, all
of which affect the ability to control of the individual ECU of which
they form part.

Martin

ECUWithRIF.jpg

18

Re: Reference Input Function
From[Bill Williams 23 March 2004 1:00 PM CST]

[Martin Taylor 2004.03.23.0912]

Since the term and concept RIF is Martin’s “baby” I won’t try to insist that I understand what he is talking better than he does. Whatever either of us is talking about, I find the ideas that popped into my thinking as a result of Martin’s discussion of reference input functions explained some relationships that I hadn’t played much attention to in the past. Whether what I am thinking about as result of what Martin has said about RIF’s has anything to do with what Martin meant-- maybe best to let Martin decide.

I would hope Martin would go to elaborate his diagram. As the diagram stands there are upward signals that are not terminated and there are downward signals who’s origins are not specified. The phrase “To and from other ECUs” leaves a lot to be defined.

What ever it is that Martin is actually talking I like my perception, however misguided it may be. In the future to avoid embarrassing Martin, I will refer to my mis-informed understanding of RIFs with the symbol “BWRIF” (Bill Williams’ Reference Input Function).

Bill Williams

19

Re: Reference Input Function
[Martin Taylor 2004.03.23.1511]

From[Bill
Williams 23 March 2004 1:00 PM CST]
[Martin Taylor
2004.03.23.0912]
I would hope
Martin would go to elaborate his diagram. As the diagram stands
there are upward signals that are not terminated and there are
downward signals who’s origins are not specified. The
phrase “To and from other ECUs” leaves a lot to be
defined.

Deliberately. I didn’t want to presuppose that the ECU was
embedded in a classic hierarchy. But if you do, then the terminations
of the arrows at the top of the figure are at various ECUs in the
levels above. Perceptual signals go to perceptual Input Functions on
the level above, and signals coming down into the Reference Input
Function come from the output functions of the ECUs in the level
above. And of course, the feedback paths shown as complete curves
actually go through the ECUs of the level below, The direct
connections being to the RIFs of the ECUs of the levels below, but
it’s not necessary to show that in the diagram.

What ever it
is that Martin is actually talking I like my perception, however
misguided it may be. In the future to avoid embarrassing Martin,
I will refer to my mis-informed understanding of RIFs with the
symbol “BWRIF” (Bill Williams’ Reference Input
Function).

How about showing a diagram, so we know what you mean? I haven’t
figured it out from your text, wxcept that somehow it affects the
perceptual signal.

Martin

20

From[Bill Williams 23 March 2003 4:50 PM CST]

I will plead an absence of time to generate and transmit a graphic
just right now. What your discussion has helped me to see, I least
this is the way I view it, is that some at least of the economics models
I have worked on could be explicitly connected to a HPCT model. And,
your identification of RIF and PIF functions has suggested to me ways
of thinking, or at least attempting to think, about where re-organization
might take place, and what it might do.

I will look forward to someone, maybe it will even be me, posting a "working
model" that emphasizes a RIF or PIF module.

Bill Williams