[Martin Taylor 970630 16:05]
Bill Powers (970629.1649 MDT)
I doubt whether there would be any hysteresis observed if you presented the
sample sounds one day apart.
So do I. And the GFF would not predict it either, unless there were
something to keep alive the earlier category perception.
How do you know that the perceptual lags are on the order of
milliseconds? The person might issue a judgement while the >>perceptualsignal is still changing.
So you _did_ mean what I proposed in jest in my first paragraph above.
Obviously I can't _know_ it, even from intra-personal observation. >But it
seems _highly_ implausible.
Only because it contradicts what you believe to be the case -- and NEED to
believe to rule out the dynamic-lag hypothesis. The correct answer to my
question is, "I don't know -- I guess those experiments will have to be
done again if we are to rule out the dynamic-lag hypothesis."
Any hysteresis at all, in any kind of situation, electronic, biological,
or other, requires some kind of dynamic lag or memory. I thought you were
suggesting a lag on the order of the lag time of control of the relevant
perception. That's what I was (and am) sceptical about.
I don't know how you see me as _ruling out_ the dynamic-lag hypothesis. In
an experiment that involves continuous tracking, it's quite plausible.
In an experiment in which subjects render judgments that specify the
categories of individually presented patterns, it seems less plausible.
I merely pointed out its implausibility on the grounds that a perception
that one has described has at least _been_ perceived, and if the memory
of it changes later, that may affect the perception of a following sensory
input (probably will), but it's not a dynamic lag of the kind you
proposed unless the two sensory inputs somehow get mixed up.
-----------------------
HPCT does not rule out level-hopping perceptual signals; only level-hopping
reference signals.
I know that, and it's always seemed to me to be a smudge on a very elegant
picture that you can have these long level-skips one way when, for good
reason, they are clearly prohibited in the other direction. Sure it may
be the way things are, but, like Einstein, I have a predeliction for
elegance. The GFF proposal eliminates this inelegance at the cost of
eliminating a different constraint--that perceptual signals cannot return
to be inputs to other perceptual functions at the same level. Beauty is
in the eye of the beholder, of course, and maybe you see level-skipping
perceptual signals coupled with special-purpose category perceptual
functions as more elegant than having the category perceptions fall out
from permitting same-level cross-connections.
It's clear, despite what you say, that you have forgotten what the
"Grand Flip-Flop" proposal was (and is). You say things like:
Yes, this is all true, but if the situation you describe holds true, the
positive feedback is large enough to exclude any middle values: the output
is either maximum or minimum. You would not get graded outputs if it takes
a large input to produce a switch.
and
Yes. You're assuming that you already have category signals at the inputs
to your flip-flops. That is, one unit senses the category "fruit" and
another the category "vegetable." THEN a flip-flip cross-connection sees to
it that only one of the signals can be output at a time.
and
However, this
leaves out the process by which perceiving an apple, orange, banana, plum,
or pear can give rise to the perceived category "fruit", and other
perceptions give rise to "vegetable." This question is quite aside from the
question of mutual exclusivity -- that is, whether seeing a plum tomato
leads you to perceive only "fruit", only "vegetable," or both.
and
You
haven't said how the category signal itself is generated from multiple
inputs.
and
All you've considered is the _external_ connections among input
functions, not what the input functions themselves do, internally, that
creates categories. That's what I meant by saying ...It seems to me that
you're ignoring the main design problem and focusing on an >>ancillarydetail. It's like worrying about the design of the >>hubcaps before you
know how to build a wheel.
None of these comments is appropriate. So I guess I'd better recap the
design, which I had not intended to do.
···
----------------------------------
We start with any of the ordinary perceptual signals at any perceptual
level. These are analogue signals, and it doesn't matter what they
represent. They are the outputs of the perceptual input functions of
some elementary control units, but for the purposes of this discussion
we are going to ignore the rest of the control units, and consider
only the inputs and outputs to the perceptual functions.
To make things simple, we will make an unnecessary assumption, which is
that at least some of the perceptual outputs go two ways: (1) up to the
next analogue perceptual level, and (2) to a set of perceptual functions
that will turn out to be the category perceivers. We will call these
"category perceptual input functions" CIFs. (Each CIF is, of course,
notionally the input function of an elementary control unit).
(The reason this is an unnecessary assumption is that the analogue
perceptual functions can perform the category process themselves, provided
that there are more of them than are necessary to form on orthogonal
basis for the perceptual space--i.e., they are redundant. But it's
much easier to describe if we split off a subset that performs the
category process.)
Each CIF takes input from one or more of the analogue functions, combines
them, and provides an output perception (as before, we will ignore the
rest of the control unit for which the CIF provides the perceptual input).
How it combines them is unimportant (see your comment above about my
not having specified what the category input functions do). What is
important about the operation of the CIF is that there is the possibility
that some of the inputs may be inhibitory, and that the output is not
linearly dependent on the input. It has a low threshold at or near zero,
and saturates smoothly as the excitatory input increases (a logarithmic
function that cuts off at zero, or an arc-tan transformation, or a logistic,
might do).
A simple version of a CIF might be one that produces a weighted sum of the
inputs and then outputs the logarithm of that sum, or zero if the sum is
negative. A more complex one might do the non-linear transform at the
inputs, or allow some inputs to multiply together rather than to add...
it doesn't matter, so long as there are both excitatory and inhibitory
possibilities for the input weights.
As you see, the CIFs are quite ordinary analogue perceptual functions, and
there's nothing special about the chosen function. You could even omit
the smooth saturation, but then you would get a category system that
provided only "yes-no" answers. Any of the functions in the different
analogue levels of the hierarchy would be appropriate, provided they
eventually saturate, smoothly or otherwise (if they didn't, you'd get
a very physical explosion:-).
Now we come to the cross-connections, and why they _produce_ the category
perceptions.
The output of each CIF is connected to several of the others (conceptually,
to all, but most of the weights will be near zero, so we ignore them).
Some of these connections have postive weights, some have negative weights.
Some weights are large, some small. For this discussion we will ignore the
learning procedure that affects the weights (it's an aspect of reorganization
that we have discussed, but the feedback of the cross-linkiing generates
some special effects). Let's just say that if, in the absence of the
cross-linking, two of the CIFs would often have high outputs at the same
time, their mutual weights are more likely to to be positive than negative,
and if one (A) is usually very low when another (B) has high output, then
the weight from B to A is likely to go negative.
If you trace all the loops from a specific CIF back to itself through one
other CIF, there are four possibilities for the pattern of weights. The
weight _to_ the other node may be positive or negative, and the weight
_from_ the other node may be positive or negative. Two positives or
two negatives complete a positive feedback loop, whereas one positive
and one negative complete a negative feedback loop.
Do this with _all_ the feedback loops from a CIF back to itself, and you
get a feedback loop with considerable dynamic interest. If the weights are
high enough, the whole system of CIFs is likely to go into oscillation or
even into chaotic operation. In fact, in our simulations, we could get
multiple different behaviours of these kinds out of a single small network
with a fixed set of weights, just by putting a momentary pulse in at one
node at critical moments. But that kind of operation isn't very useful
for category judgments:-) So we have to assume that effective reorganization
has ensured that the weights are not high enough to make the CIF system
take off on its own. It must respond to its sensory inputs (the perceptual
signals from the analogue hierarchy).
Ignoring the time dimension for the moment, the input to CIF i consists
of the sensory inputs from the analogue hierarchy plus the combined effects
of the outputs of CIFs 1...n, which are, of course, affected by the output
of CIF i. The overall gain of a loop through CIF j is given by the product
of the weights ij and ji and the slope of the outputs Oi and Oj as a function
of their inputs (as the output saturates, the effect of changes in the
input gets less, and so does the loop gain).
The overall gain of the feedback loop through the whole system of CIFs,
back to CIF i, is given by the sum of all these weight and saturation
products. This self-loop gain of CIF i can be greater than unity.
If it is, the arrival of sensory input that would, in the absence of
cross-correlation, bring CIF i up to level xi, now induces a positive
feedback loop that runs away, increasing the output of CIF i. But it
doesn't run away without limit, because of the saturation of the
output of CIF i, which at some point brings the loop gain back down to
unity, no matter what happens elswhere in the loop. The input "worth" xi
in the absence of cross-connection now produces an output of yi > xi.
The value of yi depends slightly on the value of xi, but is more dependent
on the value of the overall loop gain through the other CIFs. If some of
those that have inhibitory connections with CIF i now get sensory input
that would make their values go high, the effective loop gain from CIF i
back to itself is reduced--it takes more input to cause the runaway,
because the inhibiting one is now operating on a part of its curve where
variation of its input matters (previously is was, we assume, at zero,
unaffected by small changes in the inhibition due to CIF i).
On the other hand, if CIF k with which CIF i has mutually positive weights
gets input that would bring its output above zero, the loop gain from
CIF i back to itself will be increased, enhancing the likelihood that
category i will be perceived, or increasing the magnitude with which
the input to CIF i is seen as being category i. And the existence of
the perception of category i enhances the likelihood that the input
at the _associated_ CIF k will be seen as its category, too. In the
extreme case, perceiving category i may be enough to cause perception
of category k, as might be the case if i were a rose and k were the
verbal label "rose" (not the sound or the letters, but the label).
You can see that it is possible for CIF i to sustain high output even when
an inhibiting CIF also has high output (perception of two normally mutually
exclusive categories together), and that the perception of "category i"
is graded in magnitude, being enhanced by the presence of appropriate
context, that there is hysteresis across two mutually exclusive categories
as the sensory input moves from favouring one to favouring the other and
back again. If you recognize the time for the effects to propagate around
the system, you can see why it takes longer to perceive poor representations
as belonging to the category than it takes to perceive good prototypes,
and why category labels are more easily seen in an appropriate context
(an everyday finding in reading research).
Notice the difference between this and your conjecture:
It also implies something else I haven't mentioned so far, which is >that
it takes more time for the category perception to develop than >it does for
the sensory data to arrive, since the category >perception develops in part
from the recursive connections from >other perceptual functions--IF the
sensory data are not clear, >prototypical instances of the category in
question.Well, that makes a testable proposition. If there are category perceptions
at every level, and if the sensory data are clear and prototypical, then we
should be able to find category perceptions at, say, the configuration
level that are formed faster than relationship perceptions, which by HPCT
are at a higher level. So you should be able to name "square" and "circle"
faster than you could identify whether the square or circle was "above" or
"below" the center of the screen.
My actual prediction is that one would perceive "square" or "circle" quicker
if the drawing were geometricaly precise than if it looked like a squashed
circle or a rounded square. And did you notice that the experiment you
propose is an experiment in the speed of _association_, not of perception?
The prediction of my version of HPCT would be that the fastest speeds of
either judgement would be exactly the same, since the category perceptions
all occur at the same level, just above the level where relationships are
perceived.
I dispute that prediction, since the signals from low levels get to the
category level by bypassing the intermediate levels. As far as that is
concerned, the GFF and the "standard" design make the same prediction.
I maintain that you are stuck at your own category level, which is why you
see categories at EVERY (lower) level. When you look at the world through
category-perceivers, everything is a category.
I'm no different from you. You've acknowledged that you perceive a category
"red", a category "square", and a category "below." You see categories
at every level, too. And as you say, when you are _concerned_ with
the perception of categories, it is category perceivers that you treat.
Anyway, I hope that this all helps provide you some memory stimulus, to
remember why your comments quoted at the start of this were inappropriate.
There's too much of the rest of your message to comment on directly, but
I hope you will see that much of it also missed the point. I hope I have
satisfied the following, at least:
Define "the main design problem". If you mean the hierarchy of >perceptual
control, that's the framework on which the wheels are >fitted.
That's not what I mean. The main design problem is how you can take a set
of input signals each standing for a different lower-level perception, and
derive a single signal that is present to the degree that any one of those
lower-level perceptual signals is a member of the category.
And I hope I have explained what association means, within the GFF at least.
Martin