The three layers of octopi are arranged so that when the tentacles of
the octopi in the lowest level are brushed by something that octopi
squeezes all the octopi at the next higher level to which he is
attached. In turn the 9ctopi in the second row who got squeezed
themselves squeezed their tentacles that were connected to the highest
layer. What can be noted over time is that as different numbers of
swimming fish would brush up against the tentacles of the lowest level
of octopi that different patterns of third row octopi waving their
tentacles
in the air would
arise. In a very crude way the octopus network was reporting to the
circling seagulls in the area the density of fish below in the tidal
pool.
This simple
system demonstrates the concepts in a feedforward neural network. All
the elements connect in one direction only. The flow of information is
in one direction. The following figure from "Wet Mind" shows a schematic
for such a feedforward network. Note the connections and the weights
associated with each connection. The number on the pathway corresponds
to the relative amount of squeezing that the octopi would do when
activated himself.
The key to
understanding how the network learns, stores information and processes
subsequent stimulation is in understanding how the relative weights of
influence shift over time. In general, the more frequently a pathway is
activated the stronger the weight becomes.
The less
frequently the pathway is activated the weaker the weight and in fact
some can become inhibitory. A negative or inhibitory weight can cause
the octopi to which it is connected to need more than the normal
excitation from other sources before he will wake up and decide to start
squeezing those above him.
How does a
network learn or how does the weighting change. For this to happen there
must be some feedback to the network. In the case of the octopi this
might have occurred in the following way. When the seagulls get an
accurate picture of the number of fish below they swoop down and catch a
snack. They might reward the octopi by dropping some of the uneaten fish
down to the octopi. If the octopi report that fish are present when
indeed none are present the seagull swoops down, catches nothing, and in
the end does not reward the octopi. The seagull learns to ignore that
response. Overtime the octopi network will alter the squeeze patterns to
feed itself.
The authors
later expanded the octopi network to show that it could perform two
related tasks. When the tide was low and not fish were around a group of
swimmers would come and play with the octopi. Different characteristics
of the different swimmers in terms of how they interacted with the
octopi would fire off different tentacle waving patterns in the upper
octopi. Since some swimmers brought snacks for the seagull and others
didn't, over time the seagulls, through feedback to the octopi in the
form of some dropped snacks, altered the weights so that the seagulls
could actually tell which swimmer was in the water based on the tentacle
waving pattern. In essence, the octopus network was identifying people!
In the end all the network has done is to pair an input condition with
an output. This is a quantitative association which is a kind of
associative memory. The interesting thing demonstrated is that once the
weights are set up that the network can be used to process different
types of data which might require similar types of input output
relationships. I quote from Wet Mind a section which helps to understand
this a bit better: "The pattern of weights established on the internal
connections of a network often serves as a representation. A
representation is something that stands for something else The pattern
of excitatory and inhibitory weights on the connections represents the
combinations of features that identify the individual people. These
weights store the information about the people that allows the network
to identify them, and in that sense represent the people in their
absence. If we think about a network that recognizes objects more
generally, the patterns of weights in the network will be
representations of different objects; without the right weights, the
network cannot map the input to the proper output."3
I have
illustrated a simple type of neural network. It is important to
understand that there are many types of networks and that the networks
in the brain are far more complex with more layers and far more
interconnections than has ever been drawn or modeled. In many network
types the. feedback loop is built right in with specific connections
from the output layer going directly back to the input layer.
The computation
performed by the network is a simple association game. The authors talk
about the difference functions and a Function. When spelled with a
capital "F" it represents an overall process or ability. When spelled
with a lower case "f" it represents sub process which when combined form
the high level Function. The work done by functions is to map sets of
input to different sets of output. They do this by following the rules
which are how they are wired including the relative weighting of the
connections. The output is utilized or interpreted by the larger system
which is the Function.
The importance
of this is that the field of Wet Mind researchers see the brain as made
of many small neural networks which are performing functions. Groupings
of these small function networks are joined in such a way to form larger
networks. In essence the output from a number of small function networks
becomes the input for the large Function networks. It is interesting to
note that many of the small function networks feed their output to
multiple large Function networks.
In some
instances it is appears that a small function network may have
originally developed as necessary to perform some large Function which
is or was necessary for survival. In a number of cases later developing
large Functions, as example the authors discuss the process of reading,
have organized themselves and opportunistically used some small function
networks which were not specifically organized or trained for the new
emerging large Function. They just happened to already be doing that
which was needed and got recruited for the job.
The field of Wet
Mind researchers generally start by doing computational analysis. This
is a logical analysis of the information processing that is needed to
produce a specific behavior. From this information they attempt to build
neural networks, train the networks and then see if the networks behave
the researchers expect. The process repeats over and over until the
network, or in most cases, complexes of networks strung together fairly
accurately is demonstrating the original behavior.
The Five
Principles
The early work
in Wet Mind has led to the discovery of five principles. These are:
Division of Labor, Weak Modularity, Constraint Satisfaction, Concurrent
Processing and Opportunism.
The following
are short explanations of these principles.
1. Division of
Labor: Neural networks can be used to perform similar types of mappings.
However, certain types of mappings are incompatible and cannot be
meaningfully performed by the same network. Certain situation require
that a job be divided between two or more networks or groups of networks
in order to solve the problem. In the are of vision this leads to the
understanding that there are actually separate Functions for spatial
location information, where is it networks, and for object properties or
what is it networks.
2. Weak
Modularity: "Individual neural networks are not independent, discrete
'modules' within a larger system. The principle of weak modularity has
two facets, which pertain to functional relations among processing
subsystems and the localization of networks in the brain.”4 The idea
here is that a particular site in the brain may appear at some levels,
particularly at the small function level to be well localized in the
brain and related to other small functions that subserve the same large
Function. However, the large Functions, which are the behaviors which
the organism exhibits is not sited in a specific location in the brain
but may be exist only as a total state of the brain as a whole. Large
Functions are not specifically localizable.
3. Constraint
Satisfaction: The concept here is that the brain is capable of dealing
with lots of different things at the same time. Each of the separate
things may have a small constraint associated with it. The analogy was
made to how furniture is placed in a room. An example of a constraint is
that a bed with a rickety headboard is usually placed against a wall and
a small side table might be placed next to the bed and a couch with a
missing legs supported by books might need to be placed against a wall
to be stable. The specific constraints of each piece of furniture are
small. However, in a very small apartment with limited wall space the
weak constraints of each piece of furniture may combine to allow the
furniture to be arranged in one and only one way to satisfy all
constraints. It turns out that the brain is excellent at solving these
types of problems.
Another example
of this is what they term “coarse coding" and we use it to code colors.
They point out that we could have developed separate cones for each
wavelength that specifically encoded the color of an object. Instead we
have three types of cones. "Coarse coding is a way of exploiting the
fundamental idea of constraint satisfaction; each input is only a weak
constraint, and is effective only when multiple weak constraints must be
satisfied at the same time. "5 The three cone types are red, green and
blue. Although they have these labels they each actually respond over
the entire spectrum. However, they have different response curves which
overlap considerably. Coarse coding is the method of using the degree of
overlap in responses from units (nerves) or networks that have different
sensitivities to specify precise values.
4. Concurrent
Processing: All networks are always turned on and working. Networks may
process in parallel or serially. To process in parallel means that two
different functions are processing the same input at the same time and
may correspond to different combinations of subsystems Additionally, a
single system does not process a piece of data from beginning to end and
then take in the next piece. As the first piece of data is making its
way through the network the next piece is entering.
5. Opportunism:
"We perform a task using whatever information is available, even if that
information typically is not used in that context. For example.. .the
parietal lobes of the brain may be specialized for guiding action;
nevertheless, in some contexts the information used to guide action may
also be used to distinguish one object from another. "6 Wet Mind
researchers have applied their science to the areas of visual
perception, visual cognition, reading, language, movement and memory.
They have begun with computational analysis and model building. They
have studied the underlying neurophysiology and the neuroanatomy. In
particular this branch of science has looked at the overall behaviors of
the organism. They have built up a comprehensive model of the brain and
its functions. Each function has been modeled in neural networks and
many combinations of networks have been assembled to study overall large
Functions. The behaviors of the networks assembled have been put to
various forms of behavioral testing. A considerable body of evidence has
been collected by damaging these networks and seeing how they function
in this state to the understanding of various forms of brain injury.
Since one of the fastest expanding areas of the scope of practice in
behavioral optometry is in the area of traumatic brain injury the work
by the Wet Mind researchers is particularly enlightening.
My intent was to
walk you through the results of the research done by this field. This is
obviously beyond the scope of this type of presentation. I strongly
advocate the reading of this book and for our profession to dialogue
about the implications of the work in this field. I will conclude
by showing a series of overheads and demonstrating some key aspects of
the findings on this research.