Download A Brain-Like Computer for Cognitive Applications: The

A Brain-Like Computer for
Cognitive Applications:
The Ersatz Brain Project
James A. Anderson
[email protected]
Department of Cognitive and Linguistic Sciences
Brown University, Providence, RI 02912
Paul Allopenna
[email protected]
Aptima, Inc.
12 Gill Street, Suite 1400, Woburn, MA
Our Goal:
We want to build a first-rate, second-rate
brain.
Participants
Faculty:
Jim Anderson, Cognitive Science.
Gerry Guralnik, Physics.
Tom Dean, Computer Science
David Sheinberg, Neuroscience.
Students:
Socrates Dimitriadis, Cognitive Science.
Brian Merritt, Cognitive Science.
Benjamin Machta, Physics.
Private Industry:
Paul Allopenna, Aptima, Inc.
John Santini, Anteon, Inc.
Comparison of Silicon Computers
and Carbon Computer
Digital computers are
• Made from silicon
• Accurate (essentially no errors)
• Fast (nanoseconds)
• Execute long chains of logical
operations (billions)
• Often irritating (because they
don’t think like us).
Comparison of Silicon Computers
and Carbon Computer
Brains are
• Made from carbon
• Inaccurate (low precision, noisy)
• Slow (milliseconds, 106 times
slower)
• Execute short chains of parallel
alogical associative operations
(perhaps 10 operations/second)
• Yet largely understandable
(because they think like us).
Comparison of Silicon Computers
and Carbon Computer
• Huge disadvantage for carbon: more
than 1012 in the product of speed and
power.
• But we still do better than them in
many perceptual skills: speech
recognition, object recognition, face
recognition, motor control.
• Implication: Cognitive “software” uses
only a few but very powerful elementary
operations.
Major Point
Brains and computers are very different in their
underlying hardware, leading to major
differences in software.
Computers, as the result of 60 years of
evolution, are great at modeling physics.
They are not great (after 50 years of and largely
failing) at modeling human cognition.
One possible reason: inappropriate hardware leads
to inappropriate software.
Maybe we need something completely different: new
software, new hardware, new basic operations,
even new ideas about computation.
So Why Build a Brain-Like Computer?
1. Engineering.
Computers are all special purpose devices.
Many of the most important practical computer applications
of the next few decades will be cognitive in nature:





Natural language processing.
Internet search.
Cognitive data mining.
Decent human-computer interfaces.
Text understanding.
We claim it will be necessary to have a cortex-like
architecture (either software or hardware) to run these
applications efficiently.
2. Science:
Such a system, even in simulation, becomes a
powerful research tool.
It leads to designing software with a particular
structure to match the brain-like computer.
If we capture any of the essence of the cortex,
writing good programs will give insight into
biology and cognitive science.
If we can write good software for a vaguely brain
like computer we may show we really understand
something important about the brain.
3. Personal:
It would be the ultimate cool gadget.
A technological vision:
In 2055 the personal computer you buy in Wal-Mart will
have two CPU’s with very different architectures:
First, a traditional von Neumann machine that runs
spreadsheets, does word processing, keeps your
calendar straight, etc. etc. What they do now.
Second, a brain-like chip

To handle the interface with the von Neumann
machine,

Give you the data that you need from the Web or
your files (but didn’t think to ask for).

Be your silicon friend, guide, and confidant.
History : Technical Issues
Many have proposed the construction of brain-like
computers.
These attempts usually start with

massively parallel arrays of neural computing
elements

elements based on biological neurons, and

the layered 2-D anatomy of mammalian cerebral cortex.
Such attempts have failed commercially.
The early connection machines from Thinking
Machines,Inc.,(W.D. Hillis, The Connection Machine,
1987) was most nearly successful commercially and is
most like the architecture we are proposing here.
Consider the extremes of computational brain models.
First Extreme: Biological Realism
The human brain is composed of the order of 1010
neurons, connected together with at least 1014 neural
connections. (Probably underestimates.)
Biological neurons and their connections are extremely
complex electrochemical structures.
The more realistic the neuron approximation the smaller
the network that can be modeled.
There is good evidence that for cerebral cortex a
bigger brain is a better brain.
Projects that model neurons in detail are of scientific
importance.
But they are not large enough to simulate interesting
cognition.
Neural Networks.
The most successful brain
inspired models are
neural networks.
They are built from simple
approximations of
biological neurons:
nonlinear integration of
many weighted inputs.
Throw out all the other
biological detail.
Neural Network Systems
Units with these
approximations can build
systems that
  can be made large,
  can be analyzed,
  can be simulated,
  can display complex
cognitive behavior.
Neural networks have been
used to model (rather
well) important aspects of
human cognition.
Second Extreme: Associatively
Linked Networks.
The second class of brain-like
computing models is a basic
part of computer science:
Associatively linked
structures.
One example of such a
structure is a semantic
network.
Such structures underlie most
of the practically
successful applications of
artificial intelligence.
Associatively Linked Networks (2)
The connection between the biological nervous system
and such a structure is unclear.
Few believe that nodes in a semantic network
correspond in any sense to single neurons.
Physiology (fMRI) suggests that a complex cognitive
structure – a word, for instance – gives rise to
widely distributed cortical activation.
Major virtue of Linked Networks: They have sparsely
connected “interesting” nodes. (words, concepts)
In practical systems, the number of links converging
on a node range from one or two up to a dozen or so.
The Ersatz Brain Approximation:
The Network of Networks.
Conventional wisdom says neurons are the basic
computational units of the brain.
The Ersatz Brain Project is based on a different
assumption.
The Network of Networks model was developed in
collaboration with Jeff Sutton (Harvard Medical
School, now at NSBRI).
Cerebral cortex contains intermediate level
structure, between neurons and an entire
cortical region.
Intermediate level brain structures are hard to
study experimentally because they require
recording from many cells simultaneously.
Cortical Columns: Minicolumns
“The basic unit of cortical operation is the
minicolumn … It contains of the order
of 80-100 neurons except in the
primate striate cortex, where the
number is more than doubled. The
minicolumn measures of the order of
40-50 m in transverse diameter,
separated from adjacent minicolumns
by vertical, cell-sparse zones … The
minicolumn is produced by the
iterative division of a small number of
progenitor cells in the
neuroepithelium.” (Mountcastle, p. 2)
VB Mountcastle (2003). Introduction [to a special
issue of Cerebral Cortex on columns]. Cerebral
Cortex, 13, 2-4.
Figure: Nissl stain of cortex in planum
temporale.
Columns: Functional
Groupings of minicolumns seem to form the
physiologically observed functional columns.
Best known example is orientation columns in
V1.
They are significantly bigger than minicolumns,
typically around 0.3-0.5 mm.
Mountcastle’s summation:
“Cortical columns are formed by the binding together of many
minicolumns by common input and short range horizontal connections.
… The number of minicolumns per column varies … between 50 and
80. Long range intracortical projections link columns with similar
functional properties.” (p. 3)
Cells in a column ~ (80)(100) = 8000
Sparse Connectivity
The brain is sparsely connected. (Unlike most neural
nets.)
A neuron in cortex may have on the order of 100,000
synapses. There are more than 1010 neurons in the
brain. Fractional connectivity is very low: 0.001%.
Implications:
• Connections are expensive biologically since they
take up space, use energy, and are hard to wire up
correctly.
• Therefore, connections are valuable.
• The pattern of connection is under tight control.
• Short local connections are cheaper than long ones.
Our approximation makes extensive use of local
connections for computation.
Network of Networks Approximation
We use the Network of
Networks [NofN]
approximation to structure
the hardware and to reduce
the number of connections.
We assume the basic
computing units are not
neurons, but small (104
neurons) attractor
networks.
Basic Network of Networks
Architecture:
• 2 Dimensional array of
modules
• Locally connected to
neighbors
The activity of the nonlinear attractor
networks (modules) is
dominated by their
attractor states.
Attractor states may be
built in or acquired
through learning.
We approximate the
activity of a module
as a weighted sum of
attractor states.That
is: an adequate set of
basis functions.
Activity of Module:
x = Σ ciai
where the ai are the
attractor states.
Elementary Modules
The Single Module: BSB
The attractor
network we
use for the
individual
modules is
the BSB
network
(Anderson,
1993).
It can be
analyzed
using the
eigenvectors
and
eigenvalues
of its local
connections.
Interactions between Modules
Interactions between modules are described by state
interaction matrices, M.
The state interaction matrix elements give the
contribution of an attractor state in one module to the
amplitude of an attractor state in a connected module.
In the BSB linear region
x(t+1) = Σ Msi
+
f
weighted sum
input
from other modules
+
x(t)
ongoing
activity
The Linear-Nonlinear Transition
The first BSB processing stage is linear and sums
influences from other modules.
The second processing stage is nonlinear.
This linear to nonlinear transition is a powerful
computational tool for cognitive applications.
It describes the processing path taken by many
cognitive processes.
A generalization from cognitive science:
Sensory inputs  (categories, concepts, words)
Cognitive processing moves from continuous values
to discrete entities.
Binding Module Patterns Together.
An associative Hebbian
learning event will tend
to link f with g through
the local connections.
There is a speculative
connection to the
important binding
problem of cognitive
science and
neuroscience.
The larger groupings will
act like a unit.
Responses will be stronger
to the pair f,g than to
either f or g by itself.
Two adjacent modules interacting.
Hebbian learning will tend to bind
responses of modules together if f
and g frequently co-occur.
We can extend this
associative model to larger
scale groupings.
It may become possible to
suggest a natural way to
bridge the gap in scale
between single neurons and
entire brain regions.
Networks >
Networks of Networks >
Networks of
(Networks of Networks) >
Networks of
(Networks of (Networks
of Networks))
and so on …
Scaling
Interference Patterns
We are using local transmission of (vector)
patterns, not scalar activity level.
We have the potential for traveling pattern waves
using the local connections.
Lateral information flow allows the potential for
the formation of feature combinations in the
interference patterns where two different
patterns collide.
Learning the Interference Pattern
The individual modules are nonlinear learning networks.
We can form new attractor states when an interference
pattern forms when two patterns meet at a module.
Module Evolution
Module evolution with learning:

From an initial repertoire of basic attractor
states

to the development of specialized pattern
combination states unique to the history of
each module.
Biological Evidence:
Columnar Organization in Inferotemporal
Cortex
Tanaka (2003)
suggests a columnar
organization of
different response
classes in primate
inferotemporal
cortex.
There seems to be
some internal
structure in these
regions: for
example, spatial
representation of
orientation of the
image in the
column.
IT Response Clusters: Imaging
Tanaka (2003) used
intrinsic visual
imaging of cortex.
Train video camera
on exposed cortex,
cell activity can
be picked up.
At least a factor of
ten higher
resolution than
fMRI.
Size of response is
around the size of
functional columns
seen elsewhere:
300-400 microns.
Columns: Inferotemporal Cortex
Responses of a region
of IT to complex
images involve
discrete columns.
The response to a
picture of a fire
extinguisher shows
how regions of
activity are
determined.
Boundaries are where
the activity falls
by a half.
Note: some spots are
roughly equally
spaced.
Active IT Regions for a Complex Stimulus
Note the large number of roughly equally distant
spots (2 mm) for a familiar complex image.
Network of Networks Functional Summary.
• The NofN approximation assumes a two dimensional array of
attractor networks.
• The attractor states dominate the output of the system at
all levels.
• Interactions between different modules are approximated by
interactions between their attractor states.
• Lateral information propagation plus nonlinear learning
allows formation of new attractors at the location of
interference patterns.
• There is a linear and a nonlinear region of operation in
both single and multiple modules.
• The qualitative behavior of the attractor networks can be
controlled by analog gain control parameters.
Engineering Hardware Considerations
We feel that there is a size, connectivity, and computational
power “sweet spot” at the level of the parameters of the
network of network model.
If an elementary attractor network has 104 actual neurons,
that network display 50 attractor states. Each elementary
network might connect to 50 others through state
connection matrices.
A brain-sized system might consist of 106 elementary units
with about 1011 (0.1 terabyte) numbers specifying the
connections.
If 100 to 1000 elementary units can be placed on a chip there
would be a total of 1,000 to 10,000 chips in a cortex
sized system.
These numbers are large but within the upper bounds of
current technology.
A Software Example:
Sensor Fusion
A potential application is to sensor fusion. Sensor fusion
means merging information from different sensors into a
unified interpretation.
Involved in such a project in collaboration with Texas
Instruments and Distributed Data Systems, Inc.
The project was a way to do the de-interleaving problem in
radar signal processing using a neural net.
In a radar environment the problem is to determine how many
radar emitters are present and whom they belong to.
Biologically, this corresponds to the behaviorally important
question, “Who is looking at me?” (To be followed, of
course, by “And what am I going to do about it?”)
Radar
A receiver for radar pulses provide several kinds of
quantitative data:
•
•
•
•
•
frequency,
intensity,
pulse width,
angle of arrival, and
time of arrival.
The user of the radar system wants to know qualitative
information:
•
•
•
•
How many emitters?
What type are they?
Who owns them?
Has a new emitter appeared?
Concepts
The way we solved the problem was by using a
concept forming model from cognitive science.
Concepts are labels for a large class of members
that may differ substantially from each other.
(For example, birds, tables, furniture.)
We built a system where a nonlinear network
developed an attractor structure where each
attractor corresponded to an emitter.
That is, emitters became discrete, valid
concepts.
Human Concepts
One of the most useful computational properties
of human concepts is that they often show a
hierarchical structure.
Examples might be:
animal > bird > canary > Tweetie
or
artifact > motor vehicle > car > Porsche > 911.
A weakness of the radar concept model is that it
did not allow development of these important
hierarchical structures.
Sensor Fusion with the Ersatz Brain.
We can do simple sensor fusion in the Ersatz
Brain.
The data representation we develop is directly
based on the topographic data representations
used in the brain: topographic computation.
Spatializing the data, that is letting it find a
natural topographic organization that reflects
the relationships between data values, is a
technique potential power.
We are working with relationships between values,
not with the values themselves.
Spatializing the problem provides a way of
“programming” a parallel computer.
Topographic Data Representation
Low Values
Medium Values
High Values
••++++••••••••••••••••••••••••••••••••••••••••••••
•••••••••••••••••••••••++++•••••••••••••••••••••••
••••••••••••••••••••••••••••••••••••••••••••++++••
We initially will use a simple bar code to code the
value of a single parameter.
The precision of this coding is low.
But we don’t care about quantitative precision:
want qualitative analysis.
We
Brains are good at qualitative analysis, poor at
quantitative analysis. (Traditional computers are
the opposite.)
For our demo Ersatz
Brain program, we
will assume we
have four
parameters derived
from a source.
An “object” is
characterized by
values of these
four parameters,
coded as bar codes
on the edges of
the array of CPUs.
We assume local
linear
transmission of
patterns from
module to module.
Demo
Each pair of
input patterns
gives rise to
an interference
pattern, a line
perpendicular
to the midpoint
of the line
between the
pair of input
locations.
There are places
where three or four
features meet at a
module.
The higher-level
combinations
represent relations
between the
individual data
values in the input
pattern.
Combinations have
literally fused
spatial relations
of the input data,
Formation of Hierarchical Concepts.
This approach allows the formation of what look like
hierarchical concept representations.
Suppose we have three parameter values that are fixed for
each object and one value that varies widely from
example to example.
The system develops two different types of spatial data.
In the first, some high order feature combinations are
fixed since the three fixed input (core) patterns never
change.
In the second there is a varying set of feature
combinations corresponding to the details of each
specific example of the object.
The specific examples all contain the common core pattern.
Core Representation
The group of
coincidences
in the
center of
the array is
due to the
three input
values
arranged
around the
left, top
and bottom
edges.
Left are two examples where
there is a different
value on the right side
of the array. Note the
common core pattern
(above).
Development of A “Hierarchy” Through
Spatial Localization.
The coincidences due to the core (three values)
and to the examples (all four values) are
spatially separated.
We can use the core as a representation of the
examples since it is present in all of them.
It acts as the higher level in a simple
hierarchy: all examples contain the core.
This approach is based on relationships between
parameter values and not on the values
themselves.
Relationships are Valuable
Consider:
Which pair is most similar?
Experimental Results
One pair has high physical similarity to the initial
stimulus, that is, one half of the figure is
identical.
The other pair has high relational similarity, that
is, they form a pair of identical figures.
Adults tend to choose relational similarity.
Children tend to choose physical similarity.
However, It is easy to bias adults and children
toward either relational or physical similarity.
Potentially very a very flexible and programmable
system.
Cognitive Computation:
Second Example - Arithmetic
• Brains and computers are very different
in the way they do things, largely
because the underlying hardware is so
different.
• Consider a computational task that
humans and computers do frequently, but
by different means:
– Learning simple arithmetic facts
The Problem with Arithmetic
• We often congratulate ourselves on the
powers of the human mind.
• But why does this amazing structure
have such trouble learning elementary
arithmetic?
• Even adults doing arithmetic are slow
and make many errors.
• Learning the times tables takes
children several years and they find it
hard.
The Problem with Arithmetic
At the same time children are having
trouble learning arithmetic they are
knowledge sponges learning
– Several new words a day.
– Social customs.
– Many facts in other areas.
Association
In structure, arithmetic facts are simple
associations.
Consider multiplication:
(Multiplicand)(Multiplicand)  Product
Multiplication
• These are not arbitrary associations.
• They have an ambiguous structure that
gives rise to associative interference.
4 x 3 = 12
4 x 4 = 16
4 x 5 = 20
• Initial ‘4’ has associations with many
possible products.
• Ambiguity causes difficulties for
simple associative systems.
Number Magnitude
• One way to cope with ambiguity is to
embed the fact in a larger context.
• Numbers are much more than arbitrary
abstract patterns.
• Experiment:
– Which is greater?
– Which is greater?
17 or 85
73 or 74
Response Time Data
Number Magnitude
It takes much longer to compare 74 and
73.
When a “distance” intrudes into what
should be an abstract relationship it
is called a symbolic distance effect.
A computer would be unlikely to show such
an effect. (Subtract numbers, look at
sign.)
Magnitude Coding
Key observation: We see a similar pattern
when sensory magnitudes are being
compared.
Deciding which of
– two weights is heavier,
– two lights is brighter,
– two sounds is louder
– two numbers is bigger
displays the same reaction time pattern.
Magnitude Coding
This effect and many others suggest
that we have an internal
representation of number that acts
like a sensory magnitude.
Conclusion: Instead of number
being an abstract symbol, humans
use a much richer coding of number
containing powerful sensory and
perceptual components.
Magnitude Coding
This elaboration of number is a good
thing. It
– Connects number to the physical
world.
– Provides the basis for mathematical
intuition.
– Responsible for the creative aspects
of mathematics.
Model Makes Small Mistakes,
Not Big Ones
Model used a neural network based
associative system.
Buzz words: non-linear, associative,
dynamical system, attractor network.
The magnitude representation is built
into the system by assuming there is a
topographic map of magnitude somewhere
in the brain.
First Observation about
Arithmetic Errors
Arithmetic fact errors are not random.
• Errors tend to be close in size to the
correct answer.
• In the simulations, this effect is due
to the presence of the magnitude code.
Second Observation: Error
Values
• Values of incorrect answers are not
random.
• They are product numbers, that is, the
answer to some multiplication problem.
• Only 8% of errors are not the answer to
a multiplication problem.
Human Algorithm for
Multiplication
The answer to a multiplication problem
is:
1. Familiar (a product)
2. About the right size.
Human Algorithm for
Multiplication
• Arithmetic fact learning is a
memory and estimation process.
• It is not really a computation!
Flexible and programmable
Learning facts alone doesn’t get you far.
The world never looks exactly like what
you learned.
Heraclitus (500 BC):
• It is not possible to step twice
into the same river.
A major goal of learning is to apply past
learning to new situations.
Getting Correct What you
Never Learned: Comparisons
Consider number comparisons:
Is 7 bigger than 9?
We can be sure that children do not learn
number comparisons individually.
There are too many of them.
– About 100 single digit comparisons
– About 10,000 two-digit comparisons
– And so on.
Magnitude
• We now see the usefulness of the
“sensory” magnitude representation.
• We can use magnitude to do computations
like number comparisons without having
to learn special cases.
• A generalization of the multiplication
simulation did comparisons of number
pairs it had never seen before.
(Without further learning.)
Implications
We have constructed a system that acts like
like logic or symbol processing but in a
limited domain.
It does so by using its connection to
perception to do much of the computation.
These “abstract” or “symbolic” operations
display their underlying perceptual nature
in effects like symbolic distance and error
patterns in arithmetic.
Connect perception to abstraction
and gain the power of each approach
• Humans are a hybrid computer.
• We have a recently evolved, rather
buggy ability to handle abstract
quantities and symbols.
• (only 100,000 years old. We have the
alpha release of the intelligence
software.)
Connect perception to abstraction
and gain the power of each approach
• We combine symbol processing with
highly evolved, extremely effective
sensory and perceptual systems.
• Realized in a mammalian neocortex.
• (over 500 million years old. We have a
late release, high version number of
the perceptual software.)
• The two systems cooperate and work
together effectively.
Conclusions
A hybrid strategy is biological:
– Let a new system complement an old
one. Never throw anything away.
– Even a little abstract processing
goes a long way. Perhaps that is one
reason why our species has been so
successful so fast.
Conclusions
Speculation: Perhaps digital computers
and humans (and brain-like computers??)
are evolving toward a complementary
relationship.
• Each computational style has its
virtues:
– Humans (and brain-like computers):
show flexibility, estimation,
connection to the physical world
– Digital Computers: show speed, logic,
accuracy.
• Both styles are valuable. There is a
valuable place for both.