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A Brain-Like Computer for Cognitive Applications: The Ersatz Brain Project. James A. Anderson James_Anderson@brown.edu Department of Cognitive and Linguistic Sciences Brown University, Providence, RI 02912 Paul Allopenna email@example.com Aptima, Inc.
James A. Anderson
Department of Cognitive and Linguistic Sciences
Brown University, Providence, RI 02912
12 Gill Street, Suite 1400, Woburn, MA
We want to build a first-rate, second-rate brain.
Jim Anderson, Cognitive Science.
Gerry Guralnik, Physics.
Tom Dean, Computer Science
David Sheinberg, Neuroscience.
Socrates Dimitriadis, Cognitive Science.
Brian Merritt, Cognitive Science.
Benjamin Machta, Physics.
Paul Allopenna, Aptima, Inc.
John Santini, Anteon, Inc.
Digital computers are
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.
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.
·Cognitive data mining.
·Decent human-computer interfaces.
We claim it will be necessary to have a cortex-like architecture (either software or hardware) to run these applications efficiently.
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.
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.
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.
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.
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.
Units with these approximations can build systems that
Neural networks have been used to model (rather well) important aspects of human cognition.
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.
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 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.
“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.
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.
“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
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 1010neurons in the brain. Fractional connectivity is very low: 0.001%.
Our approximation makes extensive use of local connections for computation.
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:
The activity of the non-linear 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 = Σciai
where the ai are the attractor states.
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 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) = ΣMsi + f + x(t)
weighted sum input ongoing
from other modules activity
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.
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.
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 of Networks >
(Networks of Networks) >
(Networks of (Networks
and so on …
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.
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 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.
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.
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.
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.
Note the large number of roughly equally distant spots (2 mm) for a familiar complex image.
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 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 problemin 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?”)
A receiver for radar pulses provide several kinds of quantitative data:
The user of the radar system wants to know qualitative information:
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.
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
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.
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.
The precision of this coding is low.
But we don’t care about quantitative precision: We want qualitative analysis.
Brains are good at qualitative analysis, poor at quantitative analysis. (Traditional computers are the opposite.)
Low Values Medium Values High Values
••••••••••••••••••••••••••••••••••••••••••••++++••Topographic Data Representation
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.
The higher-level combinations represent relations between the individual data values in the input pattern.
Combinations have literally fusedspatial relations of the input data,
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.
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.
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.
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.
At the same time children are having trouble learning arithmetic they are knowledge sponges learning
In structure, arithmetic facts are simple associations.
4 x 3 = 12
4 x 4 = 16
4 x 5 = 20
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.)
Key observation: We see a similar pattern when sensory magnitudes are being compared.
Deciding which of
displays the same reaction time pattern.
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.
This elaboration of number is a good thing. It
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.
Arithmetic fact errors are not random.
The answer to a multiplication problem is:
1. Familiar (a product)
2. About the right size.
Learning facts alone doesn’t get you far.
The world never looks exactly like what you learned.
Heraclitus (500 BC):
A major goal of learning is to apply past learning to new situations.
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.
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.
A hybrid strategy is biological:
Speculation: Perhaps digital computers and humans (and brain-like computers??) are evolving toward a complementary relationship.