Cite as in
K.Pribram, ed, Origins: Brain and
Self-Organization,
Additional comments since publication appended to the end. (See the book for the actual figures.)
The Brain as a Neurocontroller:
New Hypotheses and New
Experimental Possibilities
Paul
J. Werbos
Room
675, National Science Foundation*
This paper will describe how
a new body of mathematics -- initially motivated by neuroscience but developed
in recent years through engineering applications -- can begin to yield a predictive,
empirical understanding of the phenomenon of intelligence in the brain.
The paper is mainly written for neuroscientists, or for engineers working with
neuroscientists; it tries to describe crucial new experiments which need to be
performed in order to test and refine this new understanding.
The biggest single obstacle to the full use of
mathematics in real neuroscience is the sheer difficulty of the relevant
mathematics. The brain is far more complex than today's computers; therefore to
understand it, one must use even more sophisticated mathematics than the
average research engineer is familiar with. Because of this difficulty, a few
"middle men" have presented oversimplified description of biology to
the engineers, and oversimplified descriptions of the engineering to the
biologists. These oversimplifications have often led to considerable
misunderstanding and justified mistrust.
Because of these communications problems, this paper
will be written in an extremely informal style. It will consist mainly of the
transcript of a one-hour talk, edited for readability, with a few critical
updates inserted. The first section will explain the fundamental approach, and
move directly to the "bottom line" -- to some specific areas where
new experiments are badly needed. The next two sections will discuss the
underlying theory and mathematics in more detail. The second section will
discuss the issue of supervised learning, which can shed light on local
circuits within the brain. The final section will discuss the major
concepts of neurocontrol, which can shed light on the global organization
which unifies these local circuits into a truly intelligent system.
INTRODUCTION
AND OVERVIEW
Goals of This Talk
I really am grateful to
speak for once to an audience that is said to have a lot of physiologists in
it. I wish I had more chances to do this, because I think that some of the
things that we've learned on the engineering side lead to some very interesting
experimental possibilities on the physiological side; if we had more chances to
talk to each other, we could learn a lot more about experiments which nobody is
doing which could lead to some very exciting results in the future. That is
what I would really like to talk about today.
_______________________________________________________________________________
*The views herein are those
of the author, not those of NSF; however, as government work, it is in the
public domain conditional upon proper citation. This is an updated version of a
paper in Computational Neuroscience
Symposium 1992, edited by M.Penna, S.Chittajalu and P.G. Madhavan,
available from Madhavan at the Electrical Engineering Department at IUPUI in
Now, because it is late in the day, I figured it
might be useful for me to summarize everything I am going to say in one list,
so that you can see that it is finite, anyway. I'm basically going to try to
make four major points today:
(1) First, I'm going to
argue that we can understand intelligence or the brain in the same kind of
mathematical way that we understand
physics, as a real science. I'm not saying we're there yet, but I think it can
be done.
(2) Second, I'm going to
argue that neurocontrol gives us new mathematics, which is the mathematics we
need in order to understand the brain
mathematically.
(3) I'm going to argue that
neurocontrol has made enormous progress in the last few years, in terms of
new engineering applications, new
mathematical designs and ideas, and new links to the brain. Jim Bower has described this process as a
kind of convergent evolution. If you
look at the simple‑minded neural nets you see in a lot of the neural net
conferences, they don't have much connection to biology. But when you look at
people who have to solve really difficult, hard engineering control problems,
they're driven to some of the same complexities
we observe in the brain. So I would
argue concretely there are signs of convergent evolution.
(4) Finally, most important,
is that what we now have learned about what the brain might be doing suggests
new opportunities for experiment. It suggests some surprising predictions. If
the predictions are right, then you can use
experiments to surprise a lot of people and have fun changing the culture, and
if they're wrong, you can surprise a lot of mathematicians and come up with
some new computational principles that people think are impossible. So either
way, it's really important.
A caveat here is that as an
NSF program director I'm not telling you that I've got a lot of money for this.
In fact, I'm not allowed to spend money on things other than neuroengineering;
my present budget is too small to allow anything more. I think that this is a
very unfortunate situation, because if we're going to try to understand the
human mind and human learning -- subjects of truly enormous importance -- then
we have got to bring these things together; but right at the moment, there's
essentially zero dollars available for the specific kind of two-way cooperation
I'll be talking about today. I really wish somebody could fix that. (As this book goes to press, The Biology
Directorate at NSF is preparing a Collaborative Research Initiative which could
help fill this vacuum; however, the exact role of Engineering in that
initiative is not yet clear.)
If this were an audience of policy people, or people
who talk to their congressman, I would spend ninety percent of my time up here
on items number one and two on my list.
I could spend a good hour on this
-- on the theory and the philosophy and all of that. If this were an
engineering audience, I would talk about the applications and the designs; I have
done that for about eight hours at a stretch.
But here I am going to try to jump ahead to the brain stuff, but this is
a little risky. You have to bear in mind
that the kind of mathematics that's relevant to the brain is not the easy
stuff. The kind of math you can totally
understand in twenty minutes‑‑that isn't what relates to the brain.
The brain is a little more complicated, so I'm going to have to jump over some
stuff and give some citations.
Can we Understand the Brain Mathematically?:
Prospects for a Newtonian Revolution
Before I get going, though,
I really do want to say a little bit about the generalities here.
I suspect that a lot of the people in neuroscience
started out by wanting to understand the human mind. They really wanted to understand something
fundamental and important. But then they ran into a problem. Do you remember
the old saying:"When you're up to your knees in alligators, it's hard to
remember that your goal was to drain the swamp."? All of us have that problem, from time to
time. I suspect that a lot of neuroscientists discover, as time goes on, that
the brain is so complex that they lose hope of figuring it out in their own
lifetimes. Some
people have made a formal
philosophy of that; they say, "look, the information content in any one
brain is more complex than what I have spare neurons to understand, so by
definition I cannot understand another brain, let alone everybody's brain."
But let us think about that idea a little more
carefully.
If you try to know all of the synapse strengths, the
connections, the state of all the networks in somebody's brain, and the
reverberatory dynamics -- then of course, that is too complicated to ever
understand in your life. There is no way that all of those details can be fully
known scientifically. There will always be lots and lots of islands of
understanding, and those islands are useful.
We've seen good examples of studying connections even here today. But
they don't tell you how intelligence works as a whole system. They're just
little islands. And that is very
discouraging.
But think back, how did physicists solve this
problem, how did physics become a science? Basically there was this guy Isaac
Newton, and what did he do? Instead of trying to describe every physical object
in the universe, physics gave up on that, and they said "let us try to
understand instead the simple underlying dynamics which change all of
that complicated stuff over time."
Maybe all of these complicated things are governed by something simple
enough you can understand it. In
physics, "simple enough" meant a page of equations and a thousand
pages of explanation -- not trivial, but understandable.
My argument is that the same kind of approach could
work on the brain if you think of learning as the dynamics. There is every reason to believe that
underneath the complexity in the cerebral cortex and so on, there is a
generalized, modular plasticity. Lashley has shown this, and I've heard of
recent experiments where they've trained linguistic cortex to develop edge
detectors just by wiring it up differently. It's very clear that there is a
uniform, generalized modularity there in the interesting parts of the brain,
which ought to be understandable if we focus on the learning, the plasticity[1].
Knowing the laws of learning would not immediately tell us a lot of specialized
things about how we process specific sensory inputs in specific ways, but
physicists have found that if you understand the underlying dynamic laws that
control everything else, that's incredibly important later on when you try to
do engineering.
So let us try to see if we can create ‑‑
I think we can create, in principle -- a Newtonian revolution, by focusing on
the basic laws of learning in the high‑level, modular organs like
the cerebral cortex, the limbic lobes,
the cerebellum, the olive, and so on. We won't ever understand the motor pools
that way; they're like ad hoc preprocessors and postprocessors. But the really
important stuff we can understand, in principle.
But of course you can't do that unless you have the
right math.
I'll talk more about these issues later on, when I
discuss recent progress in neurocontrol.
Neuroengineering and Neuroscience:
What is the Basis for Collaboration?
Let me move ahead now to the
first slide (Figure 1 on the next page).
This is again a generality slide.
Like everybody else here I'm arguing that we need interdisciplinary
cooperation, but I'd like to say a little bit about where the problem is,
because we need to do more than just say
interdisciplinary cooperation is needed; we need to have a concrete
image in our heads of what it's about, or else we'll never be able to implement
it.
A lot of people are excited because folks in the
neuroscience side of the world studying the brain are now using neural network
models. They are building up the field
of computational neuroscience, which still belongs on the left-hand side of
Figure 1. In computational neuroscience,
we describe the brain by use of differential equations or other
mathematical models, instead of just verbal anecdotes and whatnot. That's exciting. On the right-hand side of figure 1, in
neuroengineering, we are using neural network systems to solve real‑world
engineering problems; that's also very exciting.
Figure
1. An NSF Definition of Neuroengineering
But the problem is this: what is the connection
between the left and right sides of Figure 1?
Even in today's symposium, which is very interdisciplinary, it is pretty
easy to classify most of the talks into who is doing computational neuroscience
and who is doing engineering applications.
It's like a gulf. And what's the problem? What's
happening is that we're both using neural network models, but one group is
using as its standard of validation: "Does the model fit the low‑level
circuit and the empirical data down at the low‑level circuit?" Maybe more than that. But in engineering, the test is: "Does
it work?" So we have two different
communities, based on two different standards of validation. But in reality, the brain itself meets
both tests. The real circuits not
only fit their own biological data, they also work in solving very complex
control challenges. Instead of having
two communities, using two different standards of validation to inspire and to
evaluate their work, we need to think of using both standards of validation
together. And that's how we can get
feedback back and forth here. I won't elaborate on this today; this is just a
matter of general principles. As I said before, unfortunately, my tiny bit of
money is entirely on the neuroengineering side, and that's something that needs
to be changed.
Neural Nets and Neurocontrol:
Where Is the Right Mathematics?
A lot of people are worried
that the artificial neural network (ANN) community, the engineering community,
is itself caught in a kind of local minimum. It is true that 90% of the papers
you see in a neural network conference these days talk about pattern
recognition, and what are they actually doing?
Usually, they are doing pattern classification, using associative memory
or other simple systems. Usually they are "training" ANNs to match
databases which contain definite targets for what the output of the ANN should
be, for every single example in the database.
There are lots of uses for this kind of task. But that's not intelligence. That's not consciousness, that's not what the
mind does. We humans are not just simple
classification machines! This really ought to be obvious to anyone.
This situation is kind of scary; you have to ask what
is the relevance of that stuff? Now, I'm
not going to talk today about consciousness or the mind/body problem; if I'm
brave at SMC on
Monday I'll talk about
that[3,4,5], but here I'm going to focus on physiology.
If we agree that neuroengineering has been
caught in a kind of local minimum or intellectual rut, then what is the way to
get out of that local minimum? If you forgive a pun, I will argue that we can
get out of that local minimum by climbing out, by climbing up a ladder
-- and here's the ladder (Figure 2, on the next page), the ladder of designs of
neurocontrol.
Again, let me warn you that this is just a quick
overview; I'll be giving you citations to more detailed information later on.
There are many, many designs in this emerging area of neurocontrol,
which I define as the use
Figure
2. The Ladder of Designs in Neurocontrol
of well‑specified
neural nets -- either natural or artificial, just mathematically‑defined
neural nets -- to generate control outputs, which could be to motors,
muscles, glands, stock transactions or whatever, but real actions in the
real world.
In the neurocontrol field, we do have very simple
designs, and these are the most popular. They're easy to do; they're a great
start for people who want to get their students going, and start to build up
software. This is the right place to start, but these designs do have very
limited power, and they certainly are not like the brain.
In the middle level of the ladder, we have what I
call the state‑of‑the‑art group, and I'd say there are about
four groups that are really
in this category. It's curious that industry is here more than academia; I don't know why. Are university
people scared to do new things? I don't know, but these state‑of‑the‑art
groups have mostly taken a couple of years to build up; maybe that's the
problem, that you've got to keep your students around long enough, and build up
modular software packages. After a couple of years of struggling, these groups
have gotten real‑world applications just this year, of things that were
only on paper two or three years ago.
And they have proven -- with really exciting, important applications --
that these more advanced, more brain‑like methods are far more powerful
in solving real-world problems. There
are just incredibly important engineering problems that have been solved that
are in the mill; again, today I won't talk about this a lot today, but I may
make some reference to it.
After these methods on paper were used in real
applications, it was a challenge to us theorists to move ahead of the
applications people and come up with new methods to overcome the limits of the
older ones, so that now on paper this year there are new methods which did not
exist two or three years ago. And now,
on paper, it looks as if these designs and ideas really have the potential to
achieve true brain‑like intelligence. So my bottom line is that at least
on paper we now have the math we need to
understand real intelligence. I'm not
saying that these ideas are working yet on real systems, and that's what I try
to pay people to do, to climb up this ladder with real engineering systems.
By the way, I'm saying that the bottom level of the
ladder is a good place to start, but when I fund people, the higher they can go
up the ladder, the higher the probability of funding. They may have to climb one step at a time,
but they had better be moving upwards in a visible way. I'm trying to develop
the engineering math that will be necessary to understand the brain. I'm using engineering as a discipline
to get the math we need for what's really interesting, which is the mind and
the brain.
Four New Empirical Possibilities: A Summary
Now before getting into the
intricacies of neurocontrol, I would first like to give you my real bottom
line. I would like to summarize four empirical areas where I think new
experimental work could be really crucial. I will try to explain the reasoning
behind all this in more detail later, but for now I will just give a summary:
(1) First, I'm going to argue that some form of
backpropagation -- not the simple three‑layer kind that most people have
seen, but a more complicated, advanced form of backpropagation -- almost
certainly must exist in the brain in order to explain some of the capabilities
that we have observed there. That in turn suggests that we
have to look for some novel mechanisms, to carry information backwards both
within and between cells. Between cells, it is now well-known that nitric oxide
(NO) acts as a backwards transmitter. In addition, a group of researchers
including Timothy Bill -- one of the important pioneers in Long-Term
Potentiation (LTP) [6] -- has discovered a new presynaptic receptor intimately
related to LTP[7]. (The group speculates that this receptor may be involved in
adapting the nearby synapse, but there is no reason to believe that this is its
only function.) Back in 1974, after I had developed the backpropagation
algorithm, I speculated that the cytoskeleton might take care of the
backwards flows within cells [2]; this still appears to be a viable
possibility [5,8,9,10], but there is new evidence that the usual kinds of field
effects in membranes could also be involved[11]. David Gardner has shown that
such backwards mechanisms are crucial to learning even at the level of aplysia[12,13].
Nevertheless, all of this is only just a beginning.
There is a lot of engineering work needed in this
area, both in theory and in instrumentation.
It's really frightening to me, when I look at how critical the
cytoskeleton is in the nervous system (it is like half the nervous system!), to
see that the amount of work that's been done understanding how the cytoskeleton
relates computationally (or might relate) is negligible. We don't yet know that it's relevant,
but we don't yet know that it's irrelevant either. It is amazing to me
that we can just sit back and ignore it and give it maybe ten thousand a year,
when we're spending a billion dollars on the other half, when we don't know
what it does is. It's really
frightening; we really need to be studying the cytoskeleton in any case, and
backpropagation is just one of the things to look for when we do it.
In looking for backpropagation, you don't necessarily
have to look at the cytoskeletal level. There are other kinds of experiments
you can do, where region A has a forward fiber to region B (e.g., A might be a
part of the limbic zone and you move on to something like the motor cortex),
and sometimes you can find that the plasticity in A seems to depend on what
happens in B. It would be interesting to see if you could cut the fiber from A
to B and then see if you lose the plasticity in A. There's no way that could happen in a
classical neuron model that's all feedforward and membrane‑driven, but if
it does happen then that means that you can unhinge the neuron model. I
have tried to persuade Karl Pribram to look into experiments like that, and his
(informal, not for scientific publication) response was "I've already done
it, I've already proven this."
Pribram's response was really very interesting to me.
If you ask a lot of the middlemen between the neural network field and biology,
they'll tell you that this is impossible; however, when I ask Pribram he says
it's already been proven, that there is a backpropagation there. I don't know whether to take his informal
statements at face value yet; I think we need a lot closer collaboration to
evaluate those experiments to see what they mean mathematically, but it's clear
there is a lot to be done here.
(2) True reverse engineering
of hippocampal and other slices. In the talk by Sclabassi earlier today, we heard
some very exciting things about the hippocampus. It was particularly
fascinating to hear that the kind of learning you get from LTP clearly doesn't
represent the real nonlinearity of the system.
I would speculate that appropriate slices through the brain can generate
model systems that you can play with like artificial neural nets, where you can
control the inputs and outputs. Why is it that when we do experiments in neural
systems we try to always do them under natural conditions? If we think that biological neural circuits
are general purpose learning machines, then let's play with them!
Let's see if we can use a slice of neural tissue to
learn to recognize an
arbitrary pattern that
hasn't been seen in nature. Let's find
out what are the capabilities.
Let's find out what the plasticity is in these more micro, more
mathematical ways. And I would
speculate, for example, that a slice
through hippocampus and cerebral cortex that maintains those local recurrent
links will have a better learning capability, in a sense I hope to have time to
define, than any of the Hebbian
or backpropagation, feedforward nets that are in use today.
In other words, there are two classes of nets people
are using a lot -- the classic Hebbian, the Grossbergian nets, and then maybe
the multi‑layer perceptron (MLP) nets; I'm willing to bet that there are
critical learning problems which I hope to talk about, which that kind of slice
can solve better than any of the nets people now believe in, on the biological
or the engineering side. Once you prove this, empirically, then I have some
ideas for what is going on there, but the experiments are what's crucial for
now. I think if you do the experiment, you will shake up a lot of people, and
then they'll start thinking about those more powerful designs that we're just
now starting to look at in engineering.
There is a whole lot to be done in this area. Once
you have taken the first step -- demonstrating and describing plasticity on the
slice -- you can then start looking for the learning mechanisms that underlie
that plasticity. So in a way this might
be a good place to begin before getting into some of the harder issues I
discussed earlier.
Similar kinds of experiments could also be done in
culture, if the right kinds of cells can be grown together in culture. Many
biologists worry that cell cultures (and even slices) are very artificial. It
can be dangerous to draw too many conclusions from what we see in culture,
because the presence of other cell types and inputs in the brain could lead to
very different kinds of behavior. Nevertheless, when groups of cells in culture
do succeed in demonstrating certain kinds of engineering capabilities -
such as the ability to learn to approximate mathematical functions more complex
than those which Hebbian or MLP nets can learn -- then we probably can
conclude that these cells possess these capabilities (or more) in nature, in
the brain. There may be great value in figuring out what kinds of cells
need to be present, as part of a culture, to generate what kinds of learning
capabilities.
(3) A third area has to do
with the inferior olive, which governs learning in the cerebellar system. I am told by Pellionisz that Llinas and his
group have observed plasticity in the inferior olive, which is crucially
related to the cerebellum and lower‑level motor control. I haven't looked at the experiments myself,
but based on a very careful examination of the cerebellum, working jointly with
Pellionisz (not with tensor theory,
working with Pellionisz on some new ideas), it is my conclusion that something unusual is going on[14].
There are two possibilities ‑‑ or rather, I'm predicting one
of two possibilities. Both of them are very surprising. First of all, before
doing the experiment proper, the first stage is to replicate the phenomenon of
plasticity in the olive. Then you have to cut one of two fibers, and show that
cutting those fibers eliminates the plasticity; this would narrow down the
plasticity to one of two possible mechanisms. (The two fibers are: (1) the
climbing fibers; (2) the collateral fibers from the deep cerebellar nuclei and
vestibular nucleus to the olive.)
I hope that somebody can do this experiment soon. This
may well be the most finite and do‑able thing on this whole list
here. So I really hope somebody looks at
this. I have described that in more detail at the end of a recent paper[14].
This is an important experiment nobody has done‑‑I don't think it
should be that hard. And it is really
critical to our next step in understanding what the cerebellum is doing.
After this talk was given, I found out that the first
step -- of simply replicating plasticity in the olive -- itself a serious
challenge. The original experiments by Llinas et al, reported in Science in 1975, are still highly
controversial. Furthermore, there are certain learning tasks -- like those
described by Richard Thompson -- which do not seem to elicit plasticity in the
olive. (Just as most physical tasks only require the use of a few muscles, so
too do many learning tasks exercise only a part of our learning abilities.)
Hockberger and Alford at
A more technical issue, crucial to working out the
fine points of this system, is the ability of the cerebellum to learn time
sequences and delays [14]. This ability clearly depends on certain
short-term memory capabilities of Purkinje cells, but it is very tricky to
design a circuit which reproduces such capabilities. (See chapter 13 of [15].)
Tam, at the
(4) Fourth, there is room
for more true reverse engineering of the cerebellar motor system. Suzuki, Kawato et al[17]
have done a magnificent job in getting this area started, but a lot more needs
to be done. Suzuki et al have basically shown that the lower motor system is
doing optimal control, not adaptive control in the classic sense, and not
translation between different kinds of coordinate systems, but optimal
control. I think that someone could play
with that circuit a lot more than anyone has done so far. Suzuki et al, and Houk,
think they know where the reward or utility functions are coming in from; if
they are right, we could perturb these inputs and prove what the power is of
this system in optimization, in adapting to new regimes. Again, we could
play with the lower motor system, by perturbing its inputs to see what
capabilities it has as a general‑purpose optimizer.
In brief, I have described four general areas where
new kinds of experiments could be extremely useful. I don't know if I'm
describing the tasks in exactly the right way. This is just an attempt to get
the process started. I'm just a dumb engineer, as they often say. But I think that something needs to be done to get us moving into these
new kinds of areas, and there is some theory behind the ideas above.
SUPERVISED
LEARNING: RECENT ANN RESULTS
AND
IMPLICATIONS FOR NEUROCONTROL AND BIOLOGY
Supervised Learning As A Neural Net Paradigm
A lot of people in
neuroengineering get upset when I talk about control applications and control,
because a lot of people in the artificial field really have this old idea
(illustrated in Figure 3), that supervised learning is the same as neural
network theory. They think that neural
network theory is the same as learning a map from an input vector X to a target vector Y, in hopes that in the future
you'll be able to predict the right target vector. And you go through training sets and you
learn over and over again what this mapping is.
Figure
3. What Does Supervised Learning Do?
In fact, if you look at the Granger‑Lynch model
of the hippocampus (arguably the best existing model of the hippocampus as an
associative memory) ‑‑ that's another form of supervised learning;
it's just plain old pattern classification you're studying. Supervised learning tends to be an
all-pervasive paradigm, even for biologically motivated research. Many people
tend to think that supervised learning is fundamental theory, and that anything
else is just dirty applications.
Supervised Learning versus Neurocontrol
Supervised learning is
certainly useful, and it may well exist in subsystems of the brain, but
it turns out that for really powerful control systems, you have to do stuff
that is a lot harder.
What you have to do is stuff like this (see Figure 4
on the next page). When I'm giving a tutorial on how to do real neurocontrol in
engineering, it turns out that I have to spend an hour or two on each one
of the three main boxes in Figure 4. You
do have supervised learning systems in these designs, but they're like little
modules. And then you have a big system,
a neurocontrol system, that takes these lower level modules and integrates them
and links them. I often compare this
situation to how we build computers: there's a lot of science to building the
chip, but there's a lot of science to putting chips together to making a
computer. Supervised learning is a general purpose concept, but neurocontrol is
also general-purpose and fundamental; they simply address different
general-purpose tasks.
It turns out that the work that's been done in
neurocontrol at these multiple levels of organization has parallels to the
brain, at multiple levels of organization.
So the stuff we've learned down at the supervised learning level tends
to be relevant to issues like what is the circuitry like within the cortex,
within recurrent nets, or within the cerebellum, while the
higher-level stuff is important when we try to figure out the organization that
connects those systems. So that
means I should talk about both of these levels and explain them before I
talk about the brain. So I should spend eight hours before it all becomes
crystal clear. Forgive me, it won't be
quite as crystal clear as I like, because I don't have the eight hours.
Figure
4. Four Task Areas Critical to Neurocontrol
Three Supervised Learning Modules Used Today in Neurocontrol
First of all let me talk at the low level,
at the supervised learning level. Little
nets that learn pattern recognition. What has been useful in engineering?
Basically, there are three kinds of
networks that people really use in real‑world control
applications:
(1) The most common is the
multilayer perceptron (MLP). (See Figure 5 on the next page.))
Please don't call it a "backpropagation network"! The MLP is only one special case of what you
can adapt with backpropagation. Furthermore, the MLP is a lot older than what I
did in 1974. Bernie Widrow or Rosenblatt are the guys that should take credit
for the MLP design itself.
Figure 5. An Example
of a Three-Layer Multilayer Perceptron (MLP)
The MLPs are basically the McCulloch‑Pitts
networks, the feedforward things. There have been some wonderful theorems about
what they can do.
(2) and (3) Almost as common
are the CMAC and the RBF designs. (Figure 6) These networks are examples of
"local" learning systems. We have already heard about these designs
from Nick DeClaris; for example, CMAC was first proposed by Albus, for a PhD
thesis under DeClaris. There are many other local learning systems discussed in
neural net meetings, but DeClaris' students happened to hit on what was useful
more than most students. There are also many modified versions of the CMAC and
the RBF, which give improved performance in control applications[15].
Figure
6. Structure of CMAC or RBF Network
Basically, these local learning rules perform
forecasting by association. The MLP
gives you a global model and is good for learning global functions, causal
relations, etc. The local systems are
more like forecasting by
precedent. When you've got a new situation, you predict the result will be like
what it was before when you had a similar situation. It's an associative memory, and
this is what the Granger‑Lynch
stuff is, just another example of the same general principle.
So these are the things that most people use. These
are feedforward nets, easy to implement and I'll show in a couple of charts how
some people have used them. There are many other forms of associative memory,
based on Hebbian learning, which have appeared in the biologically oriented
literature; however, those kinds of nets are not used very often, for one reason
or another. Most likely, people feel that the Hebbian nets now available are
very similar in capability to the CMAC and RBF, because they are based on
forecasting by precedent, while being harder to implement in real time. Why
work harder to achieve the same capability? Another factor, however, is that
people do tend to implement what is easiest first, not what is most powerful.
Local learning systems can be adapted in a variety of
ways -- through least squares, through backpropagation (i.e. derivative-based
learning), etc. No matter how they are adapted, they tend to be faster to adapt
than global MLPs, because they do not have to "undo" what was learned
in a previous region of space when they explore a new region of space. They are
usually set up so that different weights are active in different
regions of space. They tend to require many more weights, but learn faster.
There may be ways to combine the best advantages of global and local networks
together in one system[18], but no one has implemented the right kind of hybrid
as yet.
What Kinds of Functions Can Such Modules Represent?
So what are the capabilities
of these different kind of networks? Well, there are a lot of theorems. There's a guy named Andy Barron who has
proven some beautiful theorems showing that those three‑layer neural nets
like MLPs are much better than
In control applications, however, to really control
an arm efficiently, sometimes you don't have a smooth function. Then you've got a problem and it often
doesn't work, and a lot of control applications three layers won't work. So, a guy named Sontag at
But there's another problem. You can approximate any
function, but you need to approximate it parsimoniously. MLPs are as good as any other feedforward
net, but in general there are some functions which you cannot approximate
parsimoniously with any feedforward net. This means that you need
enormous numbers of hidden layers to approximate them, and enormous numbers of
hidden neurons.
Marvin Minsky, years ago, gave an example of this in
his famous book Perceptrons. He described the "connectedness"
problem, which sounds at first like a very typical character‑recognition,
pixel‑type problems, but it turns out to be a little different. Imagine
that you've got a grid of 50x50 input pixels and that they're all either white
or black, and that you're trying to recognize a desired pattern. What you're trying to do is to output a one
if the blacks are all connected, and a zero if they're not.
Now it turns out that Minsky showed that the number
of hidden units required for this task is just enormous. As the number of
pixels grows, it becomes astronomical; no feedforward net of any kind is going
to do a good job. But if you allow
recurrence, recurrent feedback connections, what I call simultaneous recurrence
(a special kind of feedback connection), then you can represent
it parsimoniously.
I would argue that the kind of language-processing
problem that Jim Anderson described earlier (from Fodor) is a problem in this
family, where a feedforward net can't represent it parsimoniously, but a
simultaneous recurrent net can represent it parsimoniously. And I've seen systems of that general sort,
which so seem to work on that kind of problem, but I haven't studied Fodor's
example in great detail.
It turns out that, if you want to deal with control
problems like navigating a robot through a cluttered room where the clutter
keeps moving and it's in a new position, you need to worry about finding a
connected path. So there are good
arguments[15,18] that higher‑level intelligence has to use these kind of
networks.
So that seems easy, but is it? Well, first of all, what happens if you have
parts of the brain that have to make decisions quickly? Simultaneous-recurrent
nets take time to settle down‑‑what then? Then you've got to have a feedforward net,
and what happens then?
Fast Feedforward Nets: The Cerebellum
Well, Figure 7 (on the next page) shows an
example of a feedforward net with two hidden layers that is good for fast,
general motor control. This comes from
Nauta[1]; it is a diagram of the cerebellum. In the cerebellum, you start out
with inputs along the mossy fibers (which some people would call an input
"layer"). These inputs go to the granule cells, which operate as a
first hidden layer, and you've got zillions of them. Some people say there are
more granule cells than there are any other kind of cell in the brain, maybe
ten times that number. That reinforces
the point‑‑you
need a lot of hidden nodes if you try to do complex tasks with a (relatively
local) feedforward net.
The next hidden layer in the cerebellum is
the Purkinje cell layer. The output layer is basically the deep cerebellar
layer and the vestibular nucleus (the FTN cells of the vestibular nucleus, to
be precise); those two systems are basically together ‑‑ they're
not right next to each other but they form one output layer, for functional
purposes. In summary, the cerebellum is not based on simultaneous-recurrence,
which is slow but powerful. Strictly speaking, however, it is not just a static
MLP, either. Above all, the Purkinje layer has some working memory
capabilities[14], similar to well-known ANN designs. Such capabilities are
tricky to adapt[15, chapter 13]; this, in turn, suggests that Purkinje cells
might possibly be adapted by a combination of the well known
olive-to-cerebellum mechanism, plus a local mechanism supporting the
working memory effects. Also, because the Purkinje cells are large cells, and
because continuity in output is very desirable at this level, it is conceivable
that dendritic field effects, as described by Pribram, could occur within these
cells[4,18].
Figure
7. The cerebellum, from Nauta [1]
Slower, More Powerful Nets: The Cerebrum
But again, this kind of
feedforward arrangement is not very good for the really higher‑level
kinds of functions like finding a connected path or connectedness. There are
some kinds of functions you just can't expect the cerebellum to solve, because
they require a more sophisticated processing.
That leads to a prediction that somehow or other the higher levels, like
the limbic lobes and the cerebral cortex, must form a kind of two‑level
system, where the low level is settling down...but first let me describe Figure
8, which shows what a simultaneous recurrent net (SRN) is.
Figure
8. A Simultaneous Recurrent Network
Mathematically, an engineer would say that you plug
in the inputs into any old feedforward structure (the net labelled f in Figure 8). But then you
take the outputs of f, and
feed them back in as inputs to f,
and see how that changes the outputs. You keep feeding the outputs back in as
inputs, again and again, until the values of the outputs settle down to some
kind of equilibrium, y∞.
Now, to use a system like that... you have to plug in the inputs, wait through
many cycles of the inner system f
until the outputs settle down, and then that becomes just one cycle time
of your bigger system. Now, when I first
saw the engineering of this[15], I said this can't have anything to do with the
brain, because you need really fast cycles inside of a longer cycle; how could
that be biologically plausible? I knew
that we needed all this to get intelligence in engineering, and I couldn't
think of anything else; therefore, in the 1990 Decade of the Brain Symposium
(sponsored by the National Federation for Brain Research and the INNS), I
presented this from an Engineering point of view, without any notion of how the
connection to the brain could be made.
Later that same day, Walter Freeman presented his
model of the hippocampus, which involved exactly the same kind of loops
within loops as in my model! He showed how very close inner recurrent loops
operate at a very high cycle time, embedded within a larger, slower theta
rhythm. For the inner loop, he said that the basic calculation cycle time is
like 400 hertz, versus about 4 hertz -- quite enough to implement Figure 8.
(Some people quote 80 hertz -- based on Fourier analysis rather than cycle
times -- but that still would be enough for some functionality in this design.
When I checked with Pribram, he assured me that fast, 1ms. synapses allow such
high-frequency computation.) VonderMalsburg has convinced me that such
dual-loop effects are even more certain to occur in the neocortex, but the
neocortex contains additional capabilities and complexity which may make it harder
to work with at present. I would speculate that SRN capabilities are crucial
both to binocular vision and to the image segmentation capabilities of
neocortex.
In brief, the biological data appears to fit the
model beautifully. Now, if you look
at Granger and Lynch's model
of the hippocampus, it doesn't do that.
In their model its like a feed forward, associative memory, and you only
have an outer recurrence that's used to generate the
associative memory. So what is that inner loop doing? Maybe the hippocampus is more powerful than
associative memory. Maybe we need something more powerful than an associative
memory to form emotions and make plans in our life, and maybe somebody can do
an experiment proving it. I hope
so.
Parenthetically, it should be noted that SRNs --
unlike feedforward networks -- can have problems in settling down to a stable
equilibrium. In engineering, one can use a "tension" term [15,18] to
reduce the probability of instability, but the possibility cannot be totally
eliminated. The tension parameter is a global parameter, with an interesting
analogy to the global level of adrenalin in the bloodstream. Karl Pribram has
pointed out that there is a strong analogy between this "tension"
term and the "unpleasure" principle of Freud[19], which plays a key
role in understanding the possibility of instability in human brains. In the
human limbic system, Pribram's empirical discussion [20] suggests that the
hippocampus is an SRN, acting mainly as a "hidden layer" of the
limbic network, a network in which the amygdala is the ultimate or penultimate
output layer. (This suggests a kind of crude analogy between the hippocampus
and the cerebellar cortex.)
Other Forms of Hebbian Learning
That covers most of what I
really want to say about supervised learning. Again, please excuse my glossing
over the many, many details; each one of these topics can be discussed in much
more detail, and is so discussed in the papers cited.
For the sake of completeness, however, I should say a
little about two forms of Hebbian learning which I did not mention
above.
Most people who work with Hebbian learning would
argue that there are really two different kinds of Hebbian learning system
which could be used on supervised learning problems. There are local
associative memory systems, which I discussed above. But there are also global
systems, which are generally linear, and require that inputs be decorrelated
before they enter the supervised learning system. A lot of decorrelating
networks have been designed for use with such nets. However, after discussing
this matter with Pribram, I am convinced that this latter class of network is
not relevant to systems like the human brain. Pribram and others have shown
again and again that biological representation systems have a great deal of
redundancy (e.g., like wavelets but with a 1.5 amplification factor instead of
2, etc., as in the Simmons talk today). One would expect such
redundancy, in any system which also has to have a high degree of fault
tolerance. This is inconsistent with the mathematical requirement of
orthogonality. In addition, the limitation to the linear case is not
encouraging, either.
In 1992, I developed an alternative
learning design which appears Hebbian in character, but has radically different
properties[4,18]. It provides a mathematical representation of certain ideas by
Pribram about dendritic field processing, which the talk today by Simmons
provides strong empirical support for. It is closely linked to Chris Atkeson's
experiments with locally-weighted regression, which has performed very well in
robotics experiments at MIT. In retrospect, as I reconsider the issue of
information flows around dendrites, I suspect that the design still needs to be
revised, to account explicitly for the three-dimensional nature of local
information flows, at least for biological modeling. In any case, the
alternative design is still feedforward in terms of what it accomplishes;
therefore, it might possibly be worth considering as a model of the innermost loop
of the neocortex, but it does not obviate the need for simultaneous recurrence,
and for the unusual kinds of nonHebbian feedback (as in Figure 8) required to
adapt key parts of the neocortex and hippocampus -- if those systems are as
powerful as I suspect.
Summary
In summary, I predict that
the human brain contains some very complex circuitry, as required to solve some
very complex adaptation problems. At present, most people would find it hard to
believe that something that complicated is there, even though it does fit these
new results of Freeman and so on. I think we need new experiments, based on
living slices, to help get home to people that it's this kind of complexity
that's in that system, and that the old models are simply not good enough. So that's the end of supervised
learning.
THE
HIGHER LEVEL OF ORGANIZATION: NEUROCONTROL
Now let me talk about
neurocontrol. This is a subject I've
talked about for eight hours at a stretch, so I will have to cut out a lot of
important material here today. First, I want to talk about why this is crucial
to understanding intelligence. I'll skip over my slides on engineering
application areas. I will talk a little bit about the kind of designs
that engineers are using today, but only a little. Mainly I will focus on the design concepts
which relate directly to understanding the brain.
Why is Neurocontrol the Right Mathematics For Understanding the Brain?
This is a chart (Figure 9)
that people look at and say, "I already know this." But if people could understand the
implications of what they already know, this world would be a different place.
There are some implications in what we already know that people haven't thought
through. Now what I am going to talk about
here is the reason why the human brain is a neurocontroller; let me give you
the argument in a few stages.
Figure
9. The Brain As a Neurocontroller
Step one: we know that the brain is an information
processing system. I would call it a
computer, except that people will think of sequential machines. But it's really a computer; it's an
information processing system; its sole biological function is to be a
computer. And what does it compute? It computes actions that control
glands and muscles. So the point is that
the function of the brain as a whole system is to perform control.
Some people think of control as something that's only
in the cerebellum, just to control finger movements. That's not true. Nauta, in his classic text on
neuroanatomy[1], stresses how you cannot separate what is the control system
from the rest of the brain. Now that
doesn't mean that the whole brain does tracking or pursuit movements; no, it
doesn't do that; it does a higher order kind of control, of course. And you might use the term "sensorimotor
control," if you will. But the
point is that the brain as a whole system has the function of
calculating these things. Everything in
the brain is there to help it compute these outputs. So the function of the brain is to do that;
if you want to understand the brain as a whole system, you have to understand
the mathematics of what it takes to build a controller that has these kind of
control capabilities, which again go far beyond mere trajectory tracking.
(Those who think of control as trajectory planning may still have
troubles with this; I urge them to reconsider the definition of control,
and recognize that the overall mathematical literature on control has always
been far wider than this in scope.)
Furthermore, you can't even understand a subsystem
until you know how it fits into the whole system. Therefore, you can't even
understand subsystems of the brain until you put them into this greater
context, which is neurocontrol: the brain is a neurocontroller.
Capabilities of the Brain As a Controller
So, next slide (Figure
10). This slide shows what I regard as
the most exciting and crucial capabilities of the brain as an intelligent
controller. I should have added an extra
line here about learning in real time; it's just so obvious, but it's something
we've got to keep in mind.
Figure 10.
Capabilities of the Brain As a Neurocontroller
The brain can control millions of actuators in
parallel -- well, maybe only 900,000 ‑‑ it's the same principle,
huge numbers. What about conventional controllers? Most control engineers
regard one actuator as a normal problem and ten as a large problem. Thus the brain has an incredible capability,
very exciting to engineers. It can
handle nonlinearity and noise routinely, without being destabilized. And above all, most critical, it includes
what you might call a long‑term planning horizon. The AI people would say the long-term
planning capability is the real intelligence.
And the brain also has a high‑speed coordination capability
through the cerebellum, basically.
Brain Capabilities Versus ANN Capabilities
Now, how do these
capabilities compare with anything we can conceive of in mathematics? Is there any hope of understanding them? Well, we presume there's a hope of understanding
them, but is there a way that we can conceive of to understand them?
The next slide (Figure 11) provides a list of what's
been done in Artificial Neural Networks in control. These are the basic kinds
of capabilities that exist today. I've
read hundreds of papers on this topic, but they all boil down to this. I've seen a lot of people try to wriggle out
of my basic taxonomies, but these are basically the capabilities you've
got. You've got people using neural nets
in subsystems in control; that's not really neurocontrol. You've got people who have learned to clone
experts, learned to copy a human movement.
You've got people who
N