Re: Finding useful functions- part 1

From: Bill Modlin (modlin1_at_metrocast.net)
Date: 10/29/04 

Date: Fri, 29 Oct 2004 02:57:47 -0700

"Wolf Kirchmeir" <wwolfkir@sympatico.ca> wrote in message
news:nk6gd.15541$rs5.865264@news20.bellglobal.com...
> Bill Modlin wrote:
>
> [...]
> >
> > Let's start over.
>
> OK.
>
> > You describe pretty much the same situation I see, in
> > which a cell "learns"... i.e. changes its various
> > operating parameters, thus changing its functional
> > mapping between inputs and outputs, based on
> > purely local signals. These local signals include its
> > own firings, activations of its synapses by other cells
> > firing, and changes in various chemical concentrations
> > in which it is immersed. As you say, none of these
> > inputs are labelled.
>
> Cells don't learn. That's a hierarchy error - its the
> network that learns, maybe. Certainly the network of
> networks that we call, say, the visual cortex learns.

Rubbish. I put the word in quotes and immediately defined
what i meant by it... "i.e. changes its various operating
parameters, thus changing its functional mapping between
inputs and outputs". When you are not busy inventing
quibbles you use the word the same way, as for example when
you earlier said "learning at the neural level requires that
genes be switched on and off", in context with messenger
molecules and the like.

> The cell's repsonses to inputs are modified by some
> inputs, yes, but that is not the same as learning. It's
> analogous to the content of a RAM location being modified
> by some inputs. I would;nt say the memory location learned
> anything - its electrical charge changed, is all.

More pointless quibbling over a word. We both know that here
we are talking about changes to the functional parameters of
a cell.

> > It seems obvious to me that under these circumstances,
> > if there is to be any systematic rule or principle
> > guiding the way the cell changes its response function,
> > it must be formulated in terms of the signals accessible
> > to the cell, with no reference to any possible
> > remote and indirect consequences of those changes.
>
> Yes.
>
> > The "adjustment rules" can depend on the strength and
> > frequency of these local signals and on the timing
> > relationships among them, and that pretty much exhausts
> > the available possibilities.
>
> In a natural system, it also includes the chemistry of the
> surrounding medium, which wil modify the way the signals
> act on and in the cell.
> That's a crucial fact, IMO. Ie, "chemical messengers" will
> promote or inhibit the transmission of siganls across the
> synpatic gaps. Since these messenger molecules are
> emitted by other cells, including non-neural ones, the
> picture is much more complex. I haven't a conceptual
> handle oin thsi, certainly not in terms of message
> content, signal labelling, etc etc etc.

Again I ask that you read what you are responding to.

I said "These local signals include its own firings,
activations of its synapses by other cells firing, and
CHANGES IN VARIOUS CHEMICAL CONCENTRATIONS
IN WHICH IT IS IMMERSED."

How does that omit anything you mention here?

> > This also seems to be the position you are taking.
> > Which confuses me, since on other occasions you seem to
> > argue for a stance much like Glen's, where all
> > "learning" is caused by remote behavioral
> > contingencies.
>
> I've already said that cells don't learn. In any case,
> figuring out how neural nets' behaviours/functions change
> doesn't refute the position that such changes are
> initiated by "remote external contingencies".

Was your substitution of "external" for "behavioral"
significant?. "External contingencies", in the sense of
statistical regularities suggesting the presence of a
coherent object, are indeed initiators for most of the
changes of interest. But the behavior of the organism
enters only incidentally into the causal chain leading to
the signalling of those regularities to the neurons and
their adaptation to them. The same changes would ensue if
a similar series of stimulii were observed passively in a
moving scene rather than scanned behaviorally from a static
scene. Behavior itself does not enter into the relevant
contingencies.

> > Let me try to pose an unambiguous example of the
> > conflict.
> >
> > A pigeon can be trained to discriminate pictures
> > containing trucks from other pictures lacking trucks.
> >
> > This is done by selectively reinforcing some behavior
> > (pecking a button?) in the presence of the truck
> > pictures, and not in the presence of others.
> >
> > At this level of description, this is a supervised
> > learning process, driven by an experimenter-enforced
> > correlation between rewards and behaviors. The rewards
> > are contingent on the production of the right behavior
> > under the right conditions, and the pigeon contains
> > mechanisms to adjust its behavior to maximize rewards.
>
> I see no reason to talk about "supervised" learning
> processes, since that word smuggles in the experimenter's
> intentions. The pigeon will leran in exactly the same in
> naturem, the only difference being that random behaviours
> will be reinforced rather trhan pre-selected ones. So
> what?

Obviously you are not aware of the ordinary technical usage
of the word "supervised" in this context. Go read a book
or something, I'm getting tired of trying to educate you.
Hint: it is still just as "supervised" when natural forces
do the supervision.

> The mechnaisms that "adjust the pigeon's behaviour"
> include the cellular changes that you seem to think
> exem[pligy some other kind of learning.
>
> > That's fine, so far as it goes.
> >
> > But when I look at discriminating that class of pictures
> > so that it can be recognized as a condition for the
> > rewarded behavior, I see a pretty complicated process.
> > There are billions of cells computing functions of
> > whatever inputs they have access to, responding to
> > all sorts of "features" at dozens of levels, bringing
> > together information from many areas of the picture, to
> > eventually reach a level at which there is a signal of
> > some sort that indicates whether or not there is a truck
> > somewhere in the picture.
>
>
> So the process is complicated. So what? When I watcvh a
> rainstorm, I see billions of raindrops, millions of
> turbulence scells, etc. The proces seems pretty
> complicated. The net result is still that tings get
> very wet.

An analogous situation would be if you claimed that "things
get very wet" is relevant to the path of a raindrop. The
path is part of a big picture in which all those paths
add up to a net result of things getting wet. But you can
hardly explain the details of a particular path by saying
that a drop moved a particular way just to get things wet.

> > That truck-signal is correlated with the rewards and the
> > behavior, so it makes sense at least at a handwaving
> > level that a supervised learning process could
> > incorporate it, and produce the behavioral
> > modifications that we observe.
> >
> > But most of those intermediate signals in the long path
> > from retina to truck-signal are not correllated with
> > anything in the high level description of the
> > experiment. They aren't correlated with trucks,
> > or rewards, or pecking, and therefore could not have
> > been shaped by any of those things.
>
> Yes, that's true, but why should they be?

They should not and are not. But the behaviorist viewpoint
Glen espouses entails that contingencies among such
externally describable and observable things are all we are
allowed to invoke in explanation of the shaping of behavior.

> ASn analogous problem: how doe the hundreds or thousands
> of fish in a school of fish all "know how to cahnge
> dierction? They don't Each fish knows that the immediately
> surrounding fish are coming closer or getting
> further away, so it adjusts its direction and speed to
> mainatin ceratin distance. That's a fine example of "local
> correlations", and IMO is the way one must think about it.
> It doesn't matter where the chnage in duirection
> originates (s few fish see a shark, and chnage direction)
> the fish inside the school don't get the message "Shark
> nearby, get out of the way". They get only messages about
> chnaging distance between themselves, and that's what they
> respond to.
>
> Let the fish be signals moving through a NN, let the
> changing distances be variations in signals passin between
> neurons, and let the resspnse of the fish be the
> cellular/synaptic changes. Then the school's change of
> direction ie the result is different NN functions. The
> analogy is good enough to clarify the concept, IMO.
>

Ah! Finally a clue as to how you can believe things that
appear so silly to me. Perhaps this explains Glen's
misperception as well. Thank you, thank you, thank you!

The problem with this analogy is that the coupling functions
between neighboring fish in a school are linear and thus
correlation-preserving, while the coupling between
neighboring neurons in a network is nonlinear and
correlation-changing.

I imagine that you understand at some level the distinction
between linear and nonlinear functions. You probably know
about intermodulation of variables input to a nonlinear
function, so that the output can no longer be treated as a
sum of independent functions applied to each variable but
must be represented as a function of the combined state of
all the inputs.

But you probably have not fully assimilated this knowledge
into your reasoning. Which allows you to imagine that a
linear network might be usefully analogous to a nonlinear
one for purposes of our current discuassion, though it is
not. This lack of assimilation also prevents you from
appreciating the significance of "local correlations", as in
your linear view of a network there is no significance as
correlations persist throughout.

In the network of fish essentially the same signal is
recreated at each node, so that it retains its close
correlation with the original summary behavioral response to
the shark on the part of a few fish nearest the shark. This
ripples out from the origin in a pleasingly intuitive
manner, with easily visualized linear interactions with
other inputs such as obstacles or constrictions to to flow
of the school.

Things don't work that way in a non-linear network.

At each node multiple signals are combined in such a way
that they intermodulate to produce new signals rather than
linear transforms of the ones with which we started. These
new signals have new correlations with new things
corresponding to aggregates or combinations of their inputs,
and weaker correlations with individual inputs. Formally,
there is no necessary correlation at all with the inputs.
In practice we rely on the probable coupling of real-world
relationships across multiple statistical orders to allow us
to use the original pairwise statistics as heuristic guides
to finding useful higher order functions. But despite this
heuristically useful coupling, correlations with the inputs
are weakened at each node, and after a few steps disappear
into the background noise.

In general, there is no correlation between inputs and
outputs of a multi-stage nonlinear multivariate transform.

For a deep multilayer network, interior variables will
generally have no significant correllation with either
inputs or outputs of the network as a whole, but only with a
subset of the interior hidden variables generated at similar
levels of indirectness or abstraction.

In such networks there are no spreading ripples conveying
the same message throughout the network. At each node there
is a new message, conveying new and different information.
Some of these may be correlated, most are not. Only
correlated signals are useful for the directed modification
of the function to be performed by any particular node.

-----

That should be enough to make the original point that
externally identifiable factors such as behavior or
contingent results of that behavior are generally
uncorrelated with the proper function of interior nodes of a
complex nonlinear network, even though those interior nodes
are ultimately part of the causal chain leading to the
behavior.

Which means that behavior-based explanations are irrelevant
to the appropriate adaptation of those interior functions.

The next step is to introduce relevant explanations of how
interior cells come to perform useful functions, which is
what I intended for "part 2" of this topic. It may be
obvious by now that first we need ways to collect correlated
signals together, and then we need ways to generate useful
new outputs from those correlated signals.

Part 2, a sketch of possible approaches to finding and
exploiting correlations among interior hidden variables,
should be coming soon.

Right now it's hard to see for sure what will be in part 3.
I'd guess that the next topic should probably be about how
we bridge from unsupervised data-directed self organization
to goal directed behavior... how we actually implement
reinforement learning or operant conditioning on top of this
substructure. But I'll have to see how the conversation
goes...

Bill

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